A modified strain-controlled reference stress approach for submarine pipelines under large-scale plastic strain
Introduction
With an over-exploitation of land resources, large reserves of marine resources have received attention in recent years. Submarine exploitation is being gradually applied to industry. However, for complex submarine surroundings, high-quality long-distance pipelines are required [1], [2], [3], and some common exploitation methods such as J-lay [4], [5], S-lay [6], [7], and reel-lay [8] have been applied. With traditional J-lay and S-lay methods, it is difficult to guarantee the quality control during the process of offshore welding and nondestructive testing (NDT). The latest reel-lay method does not require offshore welding, and the pipelines are instead welded on land, reeled onto a huge roller, and then unreeled at the laying sites. During the reeling and unreeling process, the pipelines are subjected to 1–4% plastic strain [9], [10], [11]. Some micro-defects might not be found through NDT, or the repair process may be expensive. Therefore, an engineering critical assessment (ECA) is crucial in this type of case.
Some common ECA methods such as EPRI estimation [12], a reference stress approach [13], and a reference strain approach [14] have been applied. EPRI estimation was derived from the electric power research institute's J integral manual. The reference stress approach comes from the EPRI approach under the assumption of h(n) ≈ h(1) [13], and therefore the accuracy is sacrificed. However, the reference stress approach can be applied to materials not corresponding to Ramberg–Osgood's constitutive model. One of the most frequently input parameters of the reference stress approach are the limit load solution, PL. The selection of PL largely influences the accuracy of the evaluation. Another input parameter is the applied load, P. However, submarine pipelines are subjected to large-scale plastic strain during the reel-lay process. Therefore, reference stress approach is inaccurately applied directly to submarine pipelines under strain-controlled conditions. To apply the reference stress approach, the nominal strain should be transformed into the nominal stress. Chen et al. [15] conducted a numerical analysis of defective pipelines under complex loading systems through a reference stress approach. Kim et al. [16] conducted a comparison between an analytical solution and an experimental solution for circumferential through-wall cracked pipes. Østby et al. [17] applied a 3D finite element analysis of pipelines with surface cracks under large deformations. The relationship between the bending moment and strain was used to determine the bending moment of a specified strain, and relationship between CTOD and the bending moment was studied. Kamaya and Machida [18] conducted a numerical analysis of pipe containing inner circumferential cracking under a bending load. A comparison between the finite element analysis (FEA) and R6 Option 2 was applied, the results of which proved their good agreement. Based on numerical analyses [15], [16], [17], [18], the boundary conditions are all load-controlled rather than strain-controlled. It is over conservative for a strain-controlled condition to be replaced with a load-controlled condition [19]. The reference strain approach is based on a strain-controlled or displacement-controlled condition, which was first proposed by Linkens et al. [14]. However, there is a limitation to a reference strain approach in that it can only be applied to shallow cracks that do not affect the compliance of the entire component [20]. To date, a theoretical derivation of the reference stress approach based on the strain-controlled boundary condition has yet to be found. A simple nominal strain equivalent to the true strain is inaccurate for large-scale plastic deformation of submarine pipelines.
A series of numerical calculations were conducted in the present study under strain-controlled boundary conditions closer to the process of reel-lay submarine pipelines. The nominal stress σn was acquired using the derived implicit equation, f(σn, εn) = 0, according to the relationships among the true stress σtrue, true strain εtrue, nominal stress σn, nominal strain εn, and Ramberg–Osgood's constitutive model. Therefore, an applied load P can be acquired using σn. A modified γ factor was applied to the reference stress approach to guarantee the accuracy of the limit load. A regression analysis was conducted to acquire an empirical formula of the γ factor. The proposed modified strain-controlled reference stress approach was shown to be in contrast to other ECA methods.
Section snippets
Reference stress approach
In 1984, Ainsworth [13] proposed a new ECA method, which integrates the concept of the reference stress and EPRI J evaluation [21], which is widely known as a reference stress approach. The reference stress σref as an input parameter is defined as Eq. (1):where σ0 is the yield stress.
A failure assessment diagram (FAD) is a typical application of the reference stress approach, and is widely used in a fitness-for-purpose criterion such as R6 [22], BS 7910 [23], and API 579 [24]. There
Geometry and material
The pipeline parameters, crack geometries, and material properties are listed in Table 1. The material selected in the FEA is X65. According to Kim and Budden [29] and Tkaczyk et al.[31], n does not have a significant influence on γ, while γ slightly increases with an increase in n. Therefore, n = 10 was selected in this work to obtain a lower bound of γ and assure the conservation of a higher n. The values of yield strength σ0 and tensile strength σu correspond to [32]. The true material
Determination of γ
All FEA results before the yield stage are safe when applying parameters shown in Table 1. Therefore, only the results after the yield stage are selected in the regression analysis of γ. In R6 Option 3 [22], the FAC in the reference stress approach applies an alternative method, which is defined as Eq. (15):where Je is the elastic component of the J integral, and J is the total J integral. Here, Je can be determined corresponding to Eq. (16), and J can be calculated corresponding
Contrast among various ECA methods
Various reference strain approaches were applied to evaluate the pipelines along with the geometry and crack parameter a/t of 0.1 through 0.4, as shown in Fig. 13. The result of the FAC using an FEA deviates slightly from that using R6 Option 2 [22]. R6 Option 2 is nearly the lower bound for cracks with a/t within the range of 0.1 through 0.4. All evaluation points are safe under the condition that a/t is 0.1. When a/t is 0.2, εn of the critical evaluation points are 5.7% and 5.1% corresponding
Summary of experimental validation method
Bastola et al. [37] and Østby et al [38] performed a series of full-scale pipe experiments which can be used as the experimental validation method. In their research, full-scale pipes with surface cracks were subjected to four-point bending test and reeling test. The four-point bending rig and the test pipes were placed in the horizontal plane. The midpoint of the crack front was in the bending neutral axis. A schematic of the experimental process is shown in Fig. 15.
A quasi-static condition
Application procedure of strain-controlled reference stress approach
The procedure used in the strain-based reference stress approach for pipelines with circumferential surface cracks under axial strain is summarized as follows:
- (1)
Determine whether the component is under strain or displacement control.
- (2)
Nominal stress σn should be determined using Eq. (25).
- (3)
Determine γ through Eq. (30) or other regression value.
- (4)
Determine PLM through Eqs. (7) and (20). Therefore, Lr is also determined.
- (5)
Select a stress intensity factor KI of the geometry of interest and determine Kr
- (6)
Plot
Conclusion
An ECA for pipelines with circumferential surface cracks under large-scale axial strain was applied using a modified strain-controlled reference stress approach. The limit load solution of Kastner was modified through the γ factor. The empirical equation of γ was determined. An evaluation of the modified strain-controlled reference stress approach was closer to that of the reference stress approach according to an FEA, and more accurate than the reference stress approach according to R6 Option
Acknowledgements
The authors wish to acknowledge the financial support provided by the Project of the National Natural Science Foundation of China (Grant number 51575382) and Marine Strategic Emerging Industry Special Funded Projects of China (Grant number BHSF2017-22).
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