collapse of reinforced thermoplastic pipe (rtp) under external pressure

COLLAPSE OF REINFORCED THERMOPLASTIC PIPE (RTP) UNDER EXTERNAL PRESSURE

Yong BaiZheJiang UniversityHangZhou, China

[email protected]

Nuosi WangZheJiang UniversityHangZhou, China

[email protected]

Peng ChengZheJiang UniversityHangZhou, China

[email protected]

Binbin YuZheJiang UniversityHangZhou, China

[email protected]

Mohd Fauzi BadaruddinPetronas Caligali Sdn Bhd

(PCSB), Kuala Lumpur, Malaysia

Mohd AshriPetronas Caligali Sdn Bhd

(PCSB)Kuala Lumpur, Malaysia

ABSTRACT Reinforced Thermoplastic Pipe (RTP) is a multi-layered

thermoplastic pipe. It is increasingly used for transporting gas, oil and water etc. RTP pipe has many advantages compared with steel pipe, e.g. it is cheaper to produce, easier to install, more corrosion resistant and so on.

Collapse under external pressure is often the governing design parameter for offshore pipelines. This paper presents the recent study result of RTP’s capacity under external pressure. Firstly, the calculation is carried out by mathematical analysis. In the mathematical analysis, RTP is assumed to be a 3-layered cylinder. The major factor that affects the collapse pressure is the flexural stiffness in hoop direction, so the reinforced layer (anisotropic) is simplified to be an isotropic layer with the same flexural stiffness as in hoop direction. The stiffness of this isotropic layer is the same with the RTP pipe. Secondly, Finite Element Analysis (FEA) method is employed to predict collapse pressure using ABAQUS. In the model the pipe is established as a 3-layered pipe with continuum shell element. The model is extended to take into account the initial imperfection and the plastic property of materials. Thirdly, to demonstrate the accuracy of the mathematical analysis and the FE model some test is carried out.

This paper focuses on the calculation of RTP’s collapsepressure, using three approaches. The results from the three agree very well. The reasons for the deviations and the factors which influence the collapse pressure are discussed. The capacity

equations and FEA models can be useful tools for design of RTP pipe. 1 INTRODUCTION

RTP pipe is a multi-layered flexible pipe developed to meet the requirements of transporting corrosive fluid at pressures up to 100 bar. The typical structure of RTP pipe usually consists of three layers (Fig. 1). The first layer is a thermoplastic liner (usually High Density Polyethylene, HDPE), whose major function is serving as a leak free and corrosion resistant containment for liquid. The second layer is a reinforced layer outside the liner pipe, and there are some (even number) helical windings of continuous reinforcement. The reinforcement usually consists of carbon, glass or aramid fibers that are embedded in thermoplastic matrix. This layer is mainly used to hold the internal pressure, outside pressure or longitudinal stress. The third layer provides mechanical protection of the reinforced layer from external damage.

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Fig. 1 Typical structure of RTP pipe

RTP pipe can be manufactured using various types of helical winding processes. The pipe in this study is manufactured using helical tape wrapping method. The liner pipe, helical tape, and the cover layer are of the same generic type of plastic material. These layers are heat bonded together, thus providing a rather strong connection between two adjacent layers.

The collapse pressure of a pipe is usually the most important factors to be considered for an offshore pipeline. When a pipe is installed without internal pressure or it experiences a drop of internal pressure during service the pipe may collapse due to the high external pressure. In general, a structure like pipe under external pressure loses its structural stiffness and shows a large amount of deflection at the collapse point. The collapse will cause great trouble for a project and lead to great economic losses. Therefore it is of great usefulness to find a way to predict the buckling/collapse pressure of RTP.

Many previous researches focusing on cylinder-type buckling had been carried out, while the study on the buckling of RTP pipe was insufficient. The buckling of infinite long pipe under external pressure has been provided by theory of stability (Timoshenko[1],1961), and the critical pressure of thin pipe was calculated using the suggested equation. Hur and his colleagues[2] employed FEA approach and experimental approach to study the buckling and post buckling behavior of composite cylinders under external hydrostatic pressure. Yang, Pang and Zhao[3] studied the buckling of thick-walled composite pipe under external pressure, and they mainly used mathematical approach and experimental approach with the transverse shear deformation included in consideration. Papadakis[4] suggested a new analytical expression for critical load of thick cylinder buckling. A new variable � was introduced in the expression to consider the influence of large wall thickness. To calculate the collapse pressure of RTP, the section stiffness of the reinforced layer in should be paid more attention because of the irregular shape of its section.

The motivation of this paper is to inspect the properties of RTP pipe under external hydrostatic pressure. Both the FE model and the mathematical equation suggested in this paper can give good results to predict RTP pipe’s collapse pressure. 2 LABORATORY TEST2.1 Introduction of laboratory test

Collapse test of RTP had been conducted to observe the behavior of RTP when it collapses under external hydrostatic pressure, and to verify results from mathematical method and FEA method. The test was following the standard of API RP 17B “Recommended Practice for Flexible Pipe”.

The main test facility was a pressure chamber with a 70MPa pressure capacity. (shown in Fig. 2 . The external pressure was applied to the pressure chamber using a pump.Then the pressure was loaded on RTP’s external surface through water. A pressure gauge on the end of the chamber was employed to indicate the water pressure and the pressure was recorded by a digital camera.

Fig.2 Pressure chamber

Fig. 3 The pressure loaded on the specimen

During the test, the chamber was filled with water and pressurized at a certain rate about 0.5 MPa/min until the collapse occur in about 5 minutes. During the test, the specimen



was free from axial support so it was under the loads of lateral and axial pressure simultaneously. 2.2 Specimen preparation

The typical configuration of the specimen along with the load condition of the test is shown in Fig. 3. Each end of the RTP pipe was sealed up with a two-layered steel end fitting which provided protection against leakage by clamping the wall of RTP.

Table 1 Geometric parameters of RTP

Layer No. External diameter (mm)

Thickness (mm)

Material

#1 110 6.3 PE100#2 119 4.5 Aramid

embedded in PE80 matrix

#3 125 3 PE80

Eight points were marked on the external surface of the pipe along the axial to measure the initial geometric imperfections. The initial external diameters of the pipe were measured at these points and the initial ovalities are listed below.

0max min

max min

D DD D

��

� (1)

Table 2 Initial ovality of RTP specimen

Point Dmax Dmin Maximum initial ovality1 125.00 124.70 0.0012014422 125.02 124.80 0.0008806343 125.10 124.52 0.0023235324 125.10 124.50 0.0024038465 125.00 124.10 0.0036130076 124.92 124.32 0.0024073187 125.10 124.60 0.0020024038 124.80 124.50 0.001203369

It should be pointed out that significant variations of thickness may be added to the pipe geometry due to the manufacture process. The variation of thickness in a certain layer also brings about asymmetry of the pipe. This asymmetry will also lead to buckling and can be considered as initial geometric imperfection. The volume of water pressed in the chamber, value of pressure and time were recorded on a computer-operated data acquisition system. In a typical test the collapse will occur with a sudden pressure drop as well as a low sound.

Table 3 Initial wall thickness of RTP specimen

Layer No. Nominal value (mm)

Measured value (mm)Mean value Max/min

#1 6.30 5.65 1.29#2 4.50 4.30 1.30#3 3.00 2.95 1.86

2.3 Test results

Table 4 Test result

Collapse pressure (MPa) 2.19Collapse mode shape m=1,n=2

m: the number of half-wave along the cylinder. n: the number of full wave around the circumference.

Fig. 4 Time-pressure curve

Fig. 4 shows the relationship between time and pressure of the laboratory test. At the beginning part of the time-pressure (the first 50 seconds) the pressure appeared to grow slowly. This was because some voids existed in the equipment and they were compressed. After the beginning period, the pressure increased almost linearly. It indicated that the pipe had sufficient stiffness to maintain its original configuration. The decrease of the volume of RTP was small and the materials work in their elastic region. The speed of pressure increasing appeared to be slightly lower around the peak value of the pressure. And it was believed that the changes in the pipe shape began to accelerate. Shortly after that the collapse occurred and the pressure dropped sharply.

Fig. 5 Failure mode shape



Fig. 5 shows the collapse mode shape after the collapse test. It can be easily observed that the pipe collapse with a mode shape of m=1, n=2 (one half-wave along the cylinder and two full waves around the circumference). But it is worth noting that the two full waves around the circumference seem to have a bad symmetry in the test. The full wave in one side is obvious but the one in the other side is far less obvious. 3 MATHEMATICAL SOLUTIONS3.1 Introduction of mathematical solutions

The buckling pressure of infinite long pipe (m=1, n=2) under external pressure can be calculated by the following equation:

cr 2 3

3EIP =1- r�

(2)

crP : critical buckling pressure EI: flexural stiffness of the of the pipe section (E: modulus

of elasticity, I: moment of inertia of the section) � : Poisson’s ratio r: mean radius of section The equation (2) is related to the plane strain state. If no

confining in axial direction is considered the buckling pressure of a structure in plane stress state can be calculated using a similar equation below:

cr 3

3EIP =r

(3)

From the previous study we can conclude that the flexural stiffness EI in the hoop direction of a pipe is the major factor that influences the pipe’s buckling pressure. So in the following analysis the reinforced layer (anisotropic) is simplified to be an isotropic layer which has the same EI with the reinforced layer. Considering the compressive strength of aramid is much lower than that of HDPE, the compressive strength of aramid is taken as zero when calculating the flexural stiffness of the pipe section. Fig. 6 shows details of the simplification of the reinforced layer (The angle between the pipe axial and the aramid is 55 so the section of aramid appears to be oval).

Fig.6 The simplification of the reinforced layer

It is also assumed that there is no relative slip between layers because the matrix heat bonded together had sufficient strength to make the connecting layers move together under external pressure. The flexural stiffness can be considered as the sum of the flexural stiffness of all the three isotropic layers, given by equation (4).

eq 1 1 2 2 3 3(EI) = E I +E I +E I (4) 3.2 Results

Table 5 Mechanical parameters and results of mathematical solutions

Flexural stiffness ValueEI1 (N*m) 105.20EI2 (N*m) 3.27EI3 (N*m) 71.62Pcr (MPa) 3.07

4 FINITE ELEMENT ANALYSIS4.1 Introduction of the model

The finite element model was developed to predict the collapse pressure of RTP pipe. The analysis was performed using finite element analysis software ABAQUS. 8-node continuum shell element with reduced integration (SC8R) was used to discretize the structure. The geometric parameters were defined using the measured value (mean value) as in Table 3.

In the model the pipe consists of three layers. The mesh ofthe model is shown in Fig. 7. The structure was a three-layeredpipe. The length of the model was 690 mm, equaling to the length of the specimens in the test. Along the direction of thickness the pipe section was defined as 3 layers with different properties. All the three layers were defined as isotropic. The reinforced layer was simplified using the same method (use equivalent stiffness in reinforced layer) as mentioned in part 3.1. In the circumferential direction, each layer of the pipe was discretized to 60 elements and the elements from two adjacent layers share their nodes.

Fig. 7 Mesh of the model



Fig. 8 Boundary condition

One of the pipe’s end surface was fixed in X,Y and Z direction, representing the end totally fixed by the end fitting. The second end surface was fixed in X and Y direction, providing an axially free boundary condition. To make the two end surfaces remain plane surfaces instead of curved after collapse the constraint of coupling was applied on the second end surface. Then the boundary condition of the model was the same as in the collapse test. The connection between layers wasdefined as constraint of tie because each two layers that were heat bonded together move together without relative slip. Fig. 8 shows the first end surface where boundary condition is applied.

To calculate the collapse pressure and compare it with the mathematical equations the collapse pressure of two cases were carried out. The first case was the buckling of RTP pipe, and the second case was the collapse analysis with imperfections (4.2) and the plastic properties of material included (4.3). 4.2 Buckling of RTP pipe

Different from what was shown in Fig. 3, the pressure was only applied on the external surface of the pipe (without end surfaces) in this case. The mechanical parameters in Table 5 were employed. The pipe collapsed with the mode shape shown in Fig. 9, two waves in hoof direction and one wave in axial direction.

Fig. 9 Buckling mode shape in FE analysis

4.3 Collapse with imperfections and material plasticity The pressure obtained from the buckling analysis was the

collapse pressure for an ideally perfect pipe which did not exist in application, but the value could be used to estimate the collapse pressure of the pipe with imperfections and material plasticity.

The pressure was applied on the external surface and the two end surfaces simultaneously in this case, which was the same load condition as in the collapse test.

Prior to the analysis in this case the nodal displacement after the buckling in 4.1 had been extracted. It was used as the initial geometric imperfection of the structure. The maximum initial ovality of the pipe was 0.0036, which was the maximum measured ovality of the pipe. The data of plastic properties of the three layers were obtained from the stress-stain curves below.

Fig. 10 Stress-strain curve of materials

5 COMPARISON OF RESULTS

Table 6 Comparison of results (Mathematical solution & FEA)

Mathematical solution 3.07

Finite element analysis Case 1: 2.85 7.7%

Table 7 Comparison of results (Test & FEA)

Collapse pressure Collapse pressure (MPa) Deviation (%)

Test 2.19Finite element

analysis Case 2: 2.48 12.3%



Fig. 11 Load proportionalfactor-Maximum nodal displacement curve

Table 6 shows the collapse pressure obtained from mathematical solution and finite analysis (Case 1). Both the mathematical solution and case 1 of the finite analysis give the result of the buckling pressure of a perfect RTP pipe under external pressure. It is noteworthy that the deviation of thebuckling pressure given by finite analysis (case 1) and the mathematical solution is about 7.7%. It indicates that the model used in the finite analysis is established properly. From Fig. 11 we can find the trend given by finite analysis showed good agreement with the pressure-time curve in the test. So the model can be used to simulate the collapse of RTP pipe with a high reliability. Table 7 shows the collapse pressure obtained from test and finite analysis (Case 2). The result obtained from case 2 of finite analysis has a deviation of about 12.3%, compared with the result get from the collapse test. The deviation may be produced by the underestimating of initial geometric imperfections (like nonuniformity of wall thickness) in mathematical calculation and FEA.

No obvious relative slip has been found after collapse and the assumption of no slip between layers can be considered reasonable. The mathematical solutions for the buckling pressure of a structure only takes into account the elastic properties of the material. To consider the influence of imperfection and the plastic properties of material the reduction coefficient is often used. The reduction coefficients used for calculating the bucking pressure of thin-walled cylinder under different loads vary from 0.68 to 0.75[5]. Considering the test value, a coefficient of 0.72 seems proper here. 6 CONCLUSIONS

In this study, test, FE analysis and mathematical analysis was used to predict the collapse pressure of reinforced thermoplastic pipe under external pressure. The FE model and mathematical solution show good agreement with experiment

result. The predicting method provided in this paper can be applied to RTP with similar structures. Engineer will gain greater confidence to use pipes made of composite materials, although the application of them are relatively uncommon.

REFERENCES [1] Timoshenko, S.P., Gere, J.M., 1961. Theory of Elastic Stability. McGraw-Hill Book Company. [2] Seong-Hwa Hur, Hee-Jin Son, Jin-Hwe Kweon, Jin-Ho Choi, 2008. “Postbuckling of composite cylinders under external hydrostatic pressure”. Composite Structures, 86(2008), pp. 114-124. [3] Chihdar Yang, Su-Seng Pang and Yi Zhao, 1997, “Buckling analysis of thick-walled composite pipe under External Pressure”. Journal of Composite Materials, Vol. 31, No. 4/1997, pp. 409-426. [4] George Papadakis, 2008. “Buckling of thick cylindrical shells under external pressure: A new analytical expression for the critical load and comparison with elasticity solutions”. International Journal of Solids and Structures, 45(2008),pp.5308-5321. [5] Vinson J R and Sieraknowski R L. “The Behaviour of Structures Composed of Composite Materials.” Martinns Nijhoff Publishers, 1986. [6] Xiang Li, Jinyang Zheng, Jianfeng Shi, Yaxian Li and Ping Xu, 2010. “Experimental Investigation on Buckling of Plastic Pipe Reinforced by Winding Steel Wires Under External Pressure”. Journal of thermoplastic composite materials, Vol. 00. pp. 1-17. [7] N.G. Tsouvalis, A.A. Zafeiratou, V.J. Papazoglou, 2003. “The effect of geometric imperfections on the buckling behaviour of composite laminated cylinders under external hydrostatic pressure”. Composites: Part B 34 (2003), pp. 217-226.[8] Chul-Jin Moon, In-Hoon Kim, Bae-Hyeon Choi, Jin-Hwe Kweon, Jin-Ho Choi, 2010. “Buckling of filament-wound composite cylinders subjected to hydrostatic pressure for underwater vehicle applications”. Composite Structures, 92 (2010) pp. 2241-2251. [9] M.P. Kruijer, L.L. Warnet, R. Akkerman, 2005. “Analysis of the mechanical properties of a reinforced thermoplastic pipe (RTP)”. Composites: Part A 36 (2005), pp. 291–300.[10] J.Y. Han, H.Y. Jung, J.R. Cho, J.H. Choi, W.B. Bae, 2008. “Buckling analysis and test of composite shells underhydrostatic pressure”. Journal of materials processing technology 201 (2008), pp.742-745.[11] Bert Dalmolen, John Newbert, 2006. “Corrosion protection and cost reduction by using Reinforced Thermoplastic Pipe (RTP)”. INDOPIPE 2006 Conference & Exhibition. Jakarta, Indonesia, 5,2006



collapse of reinforced thermoplastic pipe (rtp) under external pressure

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