fem model and mechanical behavior of flexible risers

9th International Conference on Fracture & Strength of Solids June 9-13, 2013, Jeju, Korea

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FEM Model and Mechanical Behavior of Flexible Risers Jingyuan Li1, Hua Wang1, Kai Zhang1,

Xiaochuan You2, Jinsan Ju1,* 1Dept. of Civil Engineering, China Agricultural University, Beijing, China

2Dept. of Engineering Mechnics, Tsinghua University, Beijing, China

Abstract: This paper presents a detailed finite-element model for a 10 layers unbonded flexible riser. The model is created by using about half million nodes of shell and solid elements. It takes full account of the main features of the riser such as geometric nonlinearity, contact interaction, and friction with very little simplified assumptions. ABAQUS/Explicit analysis module was employed to simulate the riser’s mechanical behavior under three load cases—tension, outer pressure and inner pressure. The model was solved by a fully explicit time-integration scheme implemented in a parallel environment on an eight-processor cluster and 32-G memory computer. The calculated stress and deformation of each layer among the ten layers can be achieved and analyzed. Simulation results for key layers can be obtained and show a good agreement with those from analytical formula and recommended practical method. It can be seen that the method in this paper is feasible way to get precise solution for multi-layer composite material riser. The detailed finite-element virtual model can be used to predict the mechanical behavior of the unbounded flexible riser in different load cases instead of mechanical tests. Keywords: flexible riser, tension, pressure, numerical simulation, mechanical behavior 1. Introduction The unbonded flexible riser is a pipe composed of several layers without adhesive agents between the layers. It is widely used in the subsea oil industry for its capacity dealing with large deformation and displacement due to its lower bending stiffness comparing with rigid steel risers. To achieve the advantage of flexible risers requires complicated inner structure. Different layers are designed for specific tasks. One of the problems associated is the difficulty in the analysis particularly under the very deep water. Current methods are generally divided into two categories: analytical models and finite-element models. In the past decades, researchers have conducted several analytical works on this subject. Among the first pioneers, Kapp [1] derived the stiffness matrix for a helically armored cable subjected to tension and torsion. He took into account the compressibility of the core and the variation in lay angles. The research on the response of helically armored cables subjected to tension, torsion, and bending was conducted by Lanteigne [2]. In his study, the influences of internal radial forces and curvature on the effective flexural rigidity were investigated. Feret and Bournazel [3] presented a formulation for the slip of tendons undergoing bending on assumption that armor tendons followed a geodesic path once slip took place. Kraincanic and Kebadze [4, 5] presented a non-linear formulation in consideration of the variation of the bending stiffness due to frictional sliding between layers. And an analytical model of an unbonded flexible pipe was proposed. However all the analytical models share many simplified assumptions inevitably [6-9], which significantly limit the application range of the results. On the other hand, the analytical models are quite complicated due to the large nonlinear of the complex structure [10]. What mentioned above motivates many researchers into the study of refined finite-element models which takes into account many details of the real risers that the analytical model can hardly contain. And the detailed FEM model can be achieved conveniently benefiting from the widely use of computers. In this paper, a further research on the refined finite-element model of unbonded flexible riser is conducted. And the mechanical behaviors of the riser in different load cases are obtained. 2. Finite element model A detailed finite element model is shown in Fig. 1. Ten layers are simulated separately considering the contact interfaces. All the radial displacement of layers is assumed to be the same and layer separation is neglected. 0.1 is assumed to be the friction coefficient between layers. Hourglass control is considered.

* Corresponding author: E-mail: [email protected]; Tel: +86-010-6273-7130 Hua Wang and Jingyuan Li contribute equally to this work.


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Fig.1 Ten layers riser

The sequence of layers is presented from inside out in Table 1.

Table 1 Layers of the riser Layer Type

1 Carcass layer 2 Inner pressure protection armor 3 Interlocking pressure protection armor 4 Preparatory pressure protection armor 5 Anti-wear layer 6 Tension armor 1 7 Anti-wear layer 8 Tension armor 2 9 Anti-wear layer

10 Outer sheath The FEM model was created in a global cylindrical coordinate system with its origin located at the center of the riser’s bottom. The model consisted of ten separate cylindrical layers. Carcass layer was modeled by 3D, 4 nodes reduced-integration shell elements S4R. There were 55440 elements and 61610 nodes adopted. The interlocking structure of it shows in Fig.2.

Carcass layer

Inner pressure

protection armor

Interlocking pressure

protection armor

Preparatory pressure protection armor Anti-wear layer

Tension armor 1

Anti-wear layer Tension armor 2

Anti-wear layer

Outer sheath


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Fig 2.Model of carcass layer

As shown in Fig.3, inner pressure protection armor was modeled by 3D, 8 nodes linear brick, reduced-integration elements C3D8R. 25200 elements and 38052 nodes were adopted here.

Fig.3 model of inner pressure protection armor Interlocking pressure protection armor and preparatory pressure protection armor were composed of groove steels, together they made up the pressure protection armor (refer to Fig. 4). Both of the layers were modeled by 3D, 8 nodes linear brick, reduced-integration elements C3D8R.113280 elements and 264348 nodes were adopted in all.

Fig. 4 Model of the pressure protection armor

There were 3 anti-wear layers modeled between preparatory pressure protection armor, tension armor 1, tension armor 2 and outer sheath. The model of anti-wear layer shows in Fig.5. There were totally 89000 elements and 178712 nodes adopted. 3D, 8 nodes linear brick, reduced-integration elements C3D8R was selected for the modeling.


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Fig.5 Model of anti-wear layer

As shown in Fig. 6, the lay angles of two helical armor layers were in opposite directions. The inner tension armor consisted of 58 steel strips while the outer one consisted of 60. Both of them were modeled by 3D, 8 nodes linear brick, reduced-integration elements C3D8R. There were 7772 elements, 23664 nodes for the inner tension armor and 8040 elements, 24480 nodes for the outer tension armor.

Fig.6 model of tension armor

Fig. 7 shows the detailed dimensions of the riser’s cross section.

Fig. 7 Detailed dimensions of the riser’s cross section Due to the complication and scale of the structure, modeling in ABAQUS/CAE is difficult and time-

Outer Radius=256mm

Inner Radius=178mm

Lay angle for helical armors 30o

Layer angle for protection armors 88o


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consuming. A parametric modeling procedure of ANSYS was adopted in this paper. After modeling in ANSYS, the model would be solved in ABAQUS/Explicit analysis module [11]. With the help of the parametric modeling procedures, only the geometry parameters of the layers and the components of each layer were needed, such as number of wound steel strips in tension layer etc. The advantage of this method is obvious for it is convenient to achieve, easy to modify and with high veracity at the same time. 3. Material properties The material properties for layers of the flexible riser are shown in Table 2.

Table 2 Material properties

Carcass layer

Inner pressure protection armor

Pressure protection

armor

Anti- wear layer

Tension armor Outer Sheath

Steel strip Q345

Low-density polyethylene

Steel strip Q235

Nylon braid

Steel strip Q235

Low-density polyethylene

Density (kg/m3) 7800 920 7800 920 7800 920

Young's modulus

(GPa) 207 0.18 207 0.18 207 0.18

Poisson's ratio 0.3 0.38 0.3 0.38 0.3 0.38

4. Load case, calculation results and analyses Load case study conducted on the finite-element model described above. There were two reference nodes rigidly connected to the nodes set belong to the each end sections, loads and boundary conditions were then applied to these two reference nodes. The reference node connected to the bottom end was constrained in all directions and rotations during the analysis while the other one was totally free. Three typical loads (tension, outer pressure and inner pressure) were applied on a 3.0m long riser to demonstrate the accuracy and computational suitability of the method. 4.1 Case 1: Tension load In this case, a 200 kN concentrated load was applied on the free end of the riser. Numerical calculation results for the first load case are shown in Fig. 8 and Fig. 9. Fig. 8 shows the axial-deformation of the riser. The maximum stretching of the riser in axial direction is 2.092mm, and the elongation is about 0.1046%. The Mises-stress contour plot for the middle part of the riser under tension load is shown in Fig. 9. The Mises-stress results of each layer are listed in Table 3.

Fig. 8 Axial-deformation of the riser under tension load


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Fig. 9 Mises-stress contour for the middle part of the riser under tension load

Table 3 Mises-stress of each layer

Carcass layer

Inner pressure

protection armor


protection armor

Preparatory pressure

protection armor

Tension armor 1

Tension armor 2

Outer Sheath

Mises stress (MPa)

40.18 0.63 72.56 52.15 119.6 100.2 0.19

As shown in Fig.9, stress mostly concentrated at the tension armor layers. It means that the tension armor layers work well when subjected to tension because of their specific structure. The Mises-stress for the inner tension amour is about 119.6 MPa. It is significantly larger than the results from other layers. It is in good agreement with result obtained from Recommended practice for flexible pipe [12]. It also can be seen that Mises-stress in inner tension armor is slightly greater than that in outer tension armor due to the difference in their radii. To have a better view of the maximum stress distribution in the inner tension armor, the other layers are hidden in Fig. 10.

Fig. 10 Mises-stress contour for the middle part of tension amour 1 under tension load 4.2 Case 2: Outer pressure A 2 MPa outer pressure load was applied on the riser with the free end clamped. The Mises-stress contour plot for the middle part of the riser under outer pressure is shown in Fig. 11. The Mises-stress


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results of each layer are listed in Table 4.

Fig. 11 Mises-stress contour for the middle part of the riser under outer pressure

Table 4. Mises-stress of each layer

Carcass layer

Inner pressure

protection armor


protection armor


protection armor

Tension armor 1

Tension armor 2

Outer Sheath

Mises stress (MPa)

54.79 0.4826 76.98 82.49 31.97 41.01 0.9855

Under the outer pressure, the stresses mostly concentrated at the pressure protection armor layers instead. The stress in preparatory pressure protection armor is 82.49 MPa, while the stress in interlocking pressure protection armor is 76.98 MPa. The reason for the change in distribution of stresses of the cross section is that the helical geometry of the tension armor determines it can hardly work well in hoop direction, while the pressure protection armors obtains a high hoop direction stiffness due to the interlocking structure. In Fig. 12, the other layers are hidden for a better view of distribution of stress in preparatory pressure protection armor.

Fig. 12 Mises-stress contour for the middle part of preparatory pressure protection armor under outer

pressure


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4.3 Case 3: Inner pressure In this case, a 6.4 MPa inner pressure load was applied on the riser with the free end clamped. Numerical calculation result for the Mises-stress contour plot of middle part of the riser under the second load case is shown in Fig. 13. The results for the Mises-stress of each layer are listed in Table 5.

Fig. 13 Mises-stress contour for the middle part of the riser under inner pressure

Table 5 Mises-stress of each layer of the riser

Carcass layer

Inner pressure

protection armor


protection armor


protection armor

Tension armor 1

Tension armor 2

Outer Sheath

Mises stress (MPa)

1.35 3.46 101.0 114.7 10.35 19.98 0.071

Under the inner pressure, the stresses mostly concentrated at the pressure protection armor. The stress in the preparatory pressure protection armor layer is 114.7 MPa as shown in Fig.14. The results from the simulation agree well with the analytical results from Xu [13].

Fig. 14 Mises-stress contour for the middle part of preparatory pressure protection armor under inner

pressure


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5. Conclusions From the above investigation, the following conclusions can be drawn: (1) A detailed finite element model for a ten-layer unbonded flexible riser has been built for the analysis of the riser’s responses in three load cases. It took geometric nonlinearity, contact interaction, and friction into account, which makes it more convincing than the analytical model. (2) From the FEM model detailed stress and deformation information about each layer of the riser under different loads can be obtained. The calculation results show a good agreement with those from analytical formula and recommended practical method. (3) It suggests that the detailed finite element model can be used to predict mechanical behavior of the riser in different load cases. Using the numerical method, physical experimental tests will only be required as one-off checks to validate the virtual model. A defined numerical model enables cost-effective parametric investigations, which can in turn lead to improved riser design.

Acknowledgement Support for this research by National Science Foundation of China (51279206), and Chinese Doctoral Fund (20100008110010).

References [1] Knapp R. H. Derivation of a new stiffness matrix for helically armored cables considering tension

and torsion. Int. J. Numer. Methods Eng. 1979;14(4):515-529. [2] Lanteigne J. Theoretical estimation of the response of helically armored cables to tension, torsion,

and bending. ASME J. Appl. Mech. 1985;52(2):423-432. [3] Feret JJ, and Bournaze CL. Calculation of stresses and slip in structural layers of unbonded

flexible pipes. ASME J. Offshore Mech. Arct. Eng. 1987;109:263-269. [4] Kraincanic I, and Kebadze E. Slip initiation and progression in helical armoring layers of

unbonded flexible pipes and its effect on pipe bending behavior. J. Strain Anal. Eng. Des. 2001;36(3):265-275.

[5] Kebadze E. Theoretical modeling of unbonded flexible pipe cross-sections. Ph.D. thesis, South Bank University, London, UK 2000.

[6] Bahtui A, Bahai H, and Alfano G. Numerical and analytical modeling of unbonded flexible risers. ASME J. Offshore Mech. Arct. Eng. 2009;131(5):021401.

[7] Feret JJ, Bournazel CL. Calculation of stresses and slip in structural layers of unbonded flexible pipes. Journal of Offshore Mechanics and Arctic Engineering1987;109:263-9.

[8] Harte AM, McNamara JF. Modeling procedures for the stress analysis of flexible pipe cross sections. Transactions of the ASME1993;115:46-51.

[9] Claydon P, Cook G, Brown PA, Chandwani R. A theoretical approach to prediction of service life of unbonded flexible pipes under dynamic loading conditions. Marine Structures1992;5(5):399-429.

[10] Bahtui A, Bahai H, and Alfano G. A finite element analysis for unbonded flexible risers under torsion. ASME J. Offshore Mech. Arct. Eng. 2008;130(4): 041301.

[11] ABAQUS theory manual, ABAQUS, Version 6.10 Documentation. 2010. [12] Recommended practice for flexible pipe. ISO 13628-11:2007 [13] Xu Z.L, Elastic mechanics, Version 2. 1982.

fem model and mechanical behavior of flexible risers

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