Scholarly article on topic 'The Effects of Fiber Winding Angle At Carbon - Epoxy FW Pipes in Natural Gas Transmission Pipelines and Calculating the Optimum Winding Angle with Genetic Algorithm'

The Effects of Fiber Winding Angle At Carbon - Epoxy FW Pipes in Natural Gas Transmission Pipelines and Calculating the Optimum Winding Angle with Genetic Algorithm Academic research paper on "Materials engineering"

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{Composite / "Natural Gas" / "Transmission Pipeline" / Carbon-Epoxy / "FW Pipes" / "Genetic Algorithm" / Optimization.}

Abstract of research paper on Materials engineering, author of scientific article — A.A.E. Satellou, T. Hamzehpour

Abstract Advance knowledge in the field of oil and gas industry, will guide us towards the use of new materials, especially composite materials. Natural gas transmission pipelines as the longest energy materials transportation lines, can be one of the best capacities for the study and design of composite materials to be used. Also, Genetic algorithms provide a simple and almost generic method to solve complex optimization problems. Despite simplicity of it, genetic algorithm needs careful selection of settings like parent selection methods, mutation methods, population size to be able to find good solutions. Choosing unsuitable parameters and methods might result into longer program runs or even bad optimization results. In this paper, we will review the effect of fiber angle change in the mechanical properties of tubes made of four layered FW carbon - epoxy material studied under uniform internal pressure in natural gas transmission pipelines. Then will be calculated optimal fiber winding angle using Genetic Algorithms suitable for situations where in longitudinal strain, twist and longitudinal strain - twist simultaneously are Optimization factor. Finally, the optimal winding angle will be introduced. It is explained that this layering is as the symmetrical.

Academic research paper on topic "The Effects of Fiber Winding Angle At Carbon - Epoxy FW Pipes in Natural Gas Transmission Pipelines and Calculating the Optimum Winding Angle with Genetic Algorithm"

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Procedía Engineering 130 (2015) 48 - 56

Procedía Engineering

www.elsevier.com/locate/procedia

14th International Conference on Pressure Vessel Technology

The Effects of Fiber Winding Angle At Carbon - Epoxy FW Pipes in Natural Gas Transmission Pipelines and Calculating the Optimum Winding Angle with Genetic Algorithm

A.A.E. Satelloua'*, T. Hamzehpourb

aIranian Gas Transmission Company, 8th District of Gas Transmission Operation (IGTC-DIST8), Tabriz, Iran, bIranian Gas Transmission Company, 8th District of Gas Transmission Operation (IGTC-DIST8), Tabriz, Iran,

Abstract

Advance knowledge in the field of oil and gas industry, will guide us towards the use of new materials, especially composite materials. Natural gas transmission pipelines as the longest energy materials transportation lines, can be one of the best capacities for the study and design of composite materials to be used. Also, Genetic algorithms provide a simple and almost generic method to solve complex optimization problems. Despite simplicity of it, genetic algorithm needs careful selection of settings like parent selection methods, mutation methods, population size to be able to find good solutions. Choosing unsuitable parameters and methods might result into longer program runs or even bad optimization results. In this paper, we will review the effect of fiber angle change in the mechanical properties of tubes made of four layered FW carbon - epoxy material studied under uniform internal pressure in natural gas transmission pipelines. Then will be calculated optimal fiber winding angle using Genetic Algorithms suitable for situations where in longitudinal strain, twist and longitudinal strain - twist simultaneously are Optimization factor. Finally, the optimal winding angle will be introduced. It is explained that this layering is as the symmetrical. © 2015PublishedbyElsevierLtd. Thisisanopenaccess article under the CC BY-NC-ND license (http://creativecommons.Org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ICPVT-14

Keywords: Composite, Natural Gas, Transmission Pipeline, Carbon-Epoxy, FW Pipes, Genetic Algorithm, Optimization.

* Corresponding author. Tel.: +98-413-328-2104; fax: +98-413-328-2104. E-mail address: aa_emami@nige-dist8.ir

1877-7058 © 2015 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of the organizing committee of ICPVT-14

doi:10.1016/j.proeng.2015.12.174

1. Introduction

At present, tend to use ofFW composite pipes is increasing in different industries and structures. Filament-wound (FW) composite pipes made of fiber-reinforced plastics have many potential advantages over pipes made from conventional materials, such as high specific stiffness and strength, good corrosion resistance and thermal insulation [1]. With the development of manufacturing technology to produce FW pipes, there has been a growing interest in application of the FW fiber-reinforced cylindrical composite structures [2].

Numerous studies, including bending [3], transverse loading [4], axial compression [5], and internal pressure loading conditions [6], has been conducted on themechanical properties and Failure ofFWpipes. The elasticity solution of isotropic cylindrical shells subjected to uniform radial linear loads has been studied by klosner et al. [7]. Based on the solution of Lekhnitskii [8], Wild and Vickers [9] have developed an analytical procedure for the orthotopic cylindrical sheets. Xia et al. [6] have developed an analytical procedure to assess the multi-layered FW composite pipes under internal pressure. Also, other people such as Wahab [10], Bakaiyan [11] and Ansari [12] have done extensive research in various load conditions on composite pipes.

Laney [2] has described the use of composite pipe materials in transportation of natural gas. Note that natural gas is dangerousand incendiarymaterial,soyoucan usea substance for preventingthe spread of fire. Mouritz [13] has introduced the Carbon-Epoxy as the most often used composite in load-bearing aircraft structures, which is flammable and readily decomposes when exposed to heat and fire. Funucci [14] has reported that the thermal conductivity of a solid char at room temperature is 0.17 Wm"1K"1, whereas the in-plane conductivity for a virgin carbon-epoxy laminate is so higher at about 8-12 Wm"1K"1, depending on fiber content. Low density and highly porous chars tend to provide the best thermal insulation [15]. Emami Satellou et al. shows 53.829° the optimum winding angle of Carbon-Epoxy FW Pipes in Natural Gas Transmission pipelines by using Approximation Methods [16].

Nomenclature

Cj Stiffness matrix element (/, j = 1,2,..., 6 ).

Ex The Young's modulus of the lamina in the longitudinal direction of fiber.

Ey The Young's modulus of the lamina in the transverse direction.

Ef The Young's modulus of the fiber in the longitudinal direction.

Ef The Young's modulus of the fiber in the transverse direction.

Em The Young's modulus of the matrix.

G Shear modulus.

ui Displacement along i direction (i = r,0, z ).

Vf Fiber volume fraction.

Vm Matrix volume fraction.

r,.j Shear strain in i, j plane (i, j = r,0,z ).

Zi Normal strain in i direction (i = r ,0, z ).

V The Poison's Ratio.

^ Normal stress in i direction (i = r,0, z ).

Ttj Shear stress (the first index i indicates that the stress acts on a plane normal to the xt axis, and the second

index j denotes the direction in which the stress acts. (i, j = r,0,z ).

2. Analysis procedure

2.1. Characterization of a Unidirectional Lamina

Consider a 4-layered FW laminated composite cylindrical pipe subjected to an internal pressure loading as shown in Fig. 1. We denote by r the radial, 6? the hoop, and z the axial direction in cylindrical coordinates.

Fig. 1. 4-Layerd FW composite pipe in cylindrical coordinates.

Cracks in composite materials are divided into internal cracks and interlaminar cracks. Eshraghi [15] has shown when increase the value of ExjEy , decreases the likelihood of internal cracks (see Fig. 2). Due to this we can write:

Ex = EfVf + EmVm Ey ~ E_ + Em

Vf + Vm = 1 If we obtain:

H = ^ = [e_V_ + Em (l - Vf)]

V_ (i - V_ y

( x, y, z ): Material principal coordinate system ( r,d, z ): Cylindrical coordinate system Fig. 2. Relation of coordinate system between principal material axis and cylindrical axes.

Since the Eq. (3) Vf is variable; therefore, the ratio of ExjEy or, in other words, the value ofH, be maximum, it must be established with following:

dH - o (4)

Thus by solving Eq. (3):

"EE" ~ ~EJ

2\ EL _ EL _ El+1

1 Ef Em Ef

The optimum value of Vf will be calculated.

2.2. Stress and deformation analyses

See Fig. 1 again. When pipes are subjected to axisymmetric loading ( d / SO = 0 ), the stresses and strain are independent of 0. In addition, the radial and axial displacement does not depend on the axial ( z ) and radial (r) directions, respectively.

According to Xia et al. [6] studies:

^z (k ) ~Cn C12 Ci3 0 0 Ci6 (k)

Cl2 C 22 C 23 0 0 C 26

ar Cl3 C 23 C 33 0 0 C 36 £r

0 0 0 C 44 C 45 0 Yer

0 0 0 C 45 C 55 0 7zr

Tz0. Ci6 C 26 C 36 0 0 C 66 7,6

. (k _

du (k >

du^ dz

du (k ) rJk> - ^ = n r

(k) _,

du (k} u (k) _ uue "e

For the anisotropic materials used in this study, there exist C22k' I C33k' > 0 and C22k' I C33k' ^ 1 If 0-k) =yjC22(kV Cjk} we have:

K <k) = d<k > r ^ k' + E(k > r ^' + ai(k >£0 r + a2k >„ r2

Where:

- <k) - <k) (k) ^ C12 - Cl3

^ — m — m

C 33 — C 22

— (k) - (k)

(k) C 26 — 2C 36

1"1 ~ — (k) — (k) 4C 33 — C 22

And E(k) and D(t-1 are integration constants.

2.3. 3D Laminated plate properties

To define the 3D alternate-ply material properties, the material modulus matrix elements Cij (i, j = x, y, z) and Gu(i = x,y, z) are needed. These values are calculated by following equations.

G = G ,

yy zz'

G„ =-

2(1 + ^ )

(10) (11)

xx xy :

Sym C,

1 ~Vzy

The off-axis stiffness constants in Eq.(6), |Cj<kk |, can be calculated from the on-axis stiffness constants, |Cj<k} |, by using a stiffness transformation matrix [ Au ], written as:

C<k > } = [ A, № k >}

C (k ) >12 C k) C ( k) C < k) >^16 ^ 22 C ( k) > 23 C ( k) ^ 26 C (k ) >^33 C (k ) >^36 C (k ) C (k ) C < k) C <k HT ^ 44 ^ 45 ^ 55 >^66 j

- {Cjk , C (k) ' yy , C " Z2 ( k) C (k ) C ( k'1 ' xy ' xz , C (k) yz , G (k xx , G (k) ' VV , G (k) zz }T

4 m n4 0 2m2 n2 0 0 0 0 4m2 n2

2 2 m n 2 2 m n 0 4 . 4 m + n 0 0 0 0 -4m2 n2

0 0 0 0 2 m 2 n 0 0 0

m3 n -mn3 0 -m3 n + mn3 0 0 0 0 -2m3 n + 2mn3

4 n 4 m 0 2m2 n2 0 0 0 0 4m2 n2

0 0 0 0 2 n 2 m 0 0 0

mn3 -m3 n 0 m3n - mn3 0 0 0 0 2m3n - 2mn3

0 0 1 0 0 0 0 0 0

0 0 0 0 mn —mn 0 0 0

0 0 0 0 0 0 m2 n2 0

0 0 0 0 0 0 —mn mn 0

0 0 0 0 0 0 2 n 2 m 0

2 2 m n 2 2 m n 0 -2m2 n2 0 0 0 0 ¡2 2\2 1 m - n 1

where m = cos^ and n = sin ^ , and ^ is the cylindrical angle of the filament from the

pipe axis.

2.4. Boundary condition

All the unknown integration constants in Eq. (8) may be determined by substituting these equations into boundary conditions and solving the algebraic equations. These boundary conditions are:

\ar (1)(r0) = -P0

k (n>(r* ) - o

^(1Vo) = w(r0) = 0 ^(n>(ra) = V«) = 0

\ur <k\rk ) = ur <k) [«,<k\rk ) = u*+\rk )

^(k\rh ) = ^(k+ Vk )

k^ "r Vk

^(k Vk ) = (k+1)(rk ) - (k\rk ) = (k+Vk )

where P0 istheinternalpressure, r0 and ra are theinnerandouterradius,respectively. In addition, the two integral conditions can be expressed as:

r *'}(r)rdr =xr02P0 k=i rM

tJ k >(r )r2 dr = 0

The first integral condition satisfies the axial equilibrium for a cylinder with closed ends, and the second equation is the zero torsion condition.

The integration constants' E(, D(t-1, and e0, ya for 4-layered pipe can be obtained from the solution of the simultaneous equation as follows:

dn 0 0 0 eil 0 0 0 «11 «12 -1 -Po

D(2) d21 d 22 0 0 e21 e22 0 0 «21 «22 0

D<3) 0 d32 d33 0 0 e32 e33 0 «31 «32 0

D<4) 0 0 d 43 d44 0 0 e43 e44 «41 «42 0

E(1) d51 d52 0 0 e51 ®52 0 0 «51 «52 0

E(2) 0 d62 d63 0 0 e(,2 e63 0 «61 «62 0

E(3) 0 0 d73 d74 0 0 e73 e74 «71 «72 0

E(4) 0 0 0 d84 0 0 0 e84 «81 «82 0

d91 d92 d93 d94 e91 e92 e92 e93 «91 «92 r„2 P„/2

_d01 d02 d03 d04 ®01 e02 e03 e04 «01 «02 _ 0

where parameters of d, e, a are given in Appendix A. 3. Numerical results

In this analysis, all pipes are made with four plies of pipes with carbon fiber-epoxy with inner radius 498 mm and outer radius 508 mm (40 inches outer diameter). Internal pressure is 9 MPa. Table 1 shows carbon (fiber) and epoxy 105/206 (matrix) engineering constants.

Table 1. Carbon (fiber) and epoxy 105/206 (matrix) engineering constants

Ef Ef 2 Gf Em vf M2 vf Vm

233 (GPa) 23.1 (GPa) 8.96 (GPa) 4.62 (GPa) 0.200 0.400 0.360

According to Eq. (5), Vf is equal to 0.615. Therefore, engineering constants for lamia has shown in Table 2.

Table 2. Engineering constants for lamia made ofcarbon/epoxy

Vf = 0.6149

Ex Ey Ez Gyy Gz Vxy ^xz

145.0475 9.0928 9.0928 3.25 3.25 3.3857 0.2616 0.400 0.2616

(GPa) (GPa) (GPa) (GPa) (GPa) (GPa)

4. Optimization procedure

With solving Eqs. (13) and (20) for different combinations of angles, we find the different results for values of s0, /0[16]. Therefore, we have three variables for optimization procedure that include s0 , y0and ^ . This procedure has shown in Table 3.

Table 3. Optimization procedure

Function Eq. (20)

Optimization factor Winding angle

Fitness To

First population 0, 90

Operators Encoding, Evaluation, Crossover, Mutation, Decoding

Based on optimization by GA, if the value of s0 is the optimization Fitness criteria, the optimal winding angle occurs when applied to the 53.829 This result is entirely consistent with the results obtained from the analysis of different scenarios based on the of Emami results (53.829 °) [16].

Ifbased on GA, the value of /0 is the optimization Fitness criteria, optimization occurs when the winding angle is applied to the 42.2

Finally, if based GA, the values of s0, /0 are the optimization Fitness criteria, optimization occurs when the winding angle is the 7.93 Although it is theoretically optimal angle of both the amount of twist and longitudinal displacement of the pipe, however, cannot be an appropriate response for composite pipes used in Natural Gas pipelines. Because the longitudinal displacement occurs the bending moment at the end of the tube and can cause acute conditions, leads to the bending of the pipe [17].

5. Conclusions

(a) Carbon-epoxy composite material with good heat conductivity and good resistance to ignition and fire growth is suitable material for use in natural gas composite transmission pipelines.

(b) According GA results, the minimum twist occurs at 42.2

(c) According GA results, the minimum longitudinal displacement occurs at 7.93

(d) Although the desire in the 53.829° the values of s0 towards zero, due to manufacturing considerations and prevent of the disjointing, composite pipe always should be under small tensions, so it seems more logical to use 55°for the pipe.

Acknowledgment

Corresponding Author is grateful to the Iranian Gas Transmission Company 8th District of Gas Transmission Operation (IGTC-DIST8) for the support.

Appendix A. Eq (20) Elements [6]

dtl =(C23<1' ^33® ) r0^(1>- e„ =(CC ),

alt = CI,® (C23® + C33® ) a12 = ^C36(1) +«2(1) |c23'

d = r d = -r "22 '1

e21 = ri ' -fjm e22 _ 1

a2i "(«I'1'-a,<2))r. a22 =(«/>-a2<2>

_flC2)

d d33 _ r2 e — r p 32 '2

e — —r' 32 '2 a31 =(a1i'2'> -a^ j r2

a32 =(«2<2> -a2<3))r/ d - r ^

d44 = -r3-^(4> e43 — r3

e — —r' 44 '3 a41 =(a,<3) -a,<4)) r3

a42 = (a® -a2<4) d52 =-(c23<2>+^>C33<2>).

'33 Kl

- (1) _ C (2)\ , „(1)/ C (!)

"16 ^36 )

e = -iC (2)

52 ^ 23

4,3 H^+^C®),-/''

+ 2C33® )-a2<2) (C23<2) + 2C33<2))] r

e = -(c <3)

aH = [(0®- C3/3>) + a2<2>(C23<2> + 2C33<2>;

C33<2))-a2<3)(C23<3) + 2C33<3))] r2

d74 ^-(c^+rcr'yr-

elt = -(c23<4>-^4>C33<4> a72 = [a2<3)(C23<3) + 2Cr<3)

733<4>) r^'

-a2<4)(C23<4) + 2C33<4)

e84 =(C23<4) -^<4)C3 <4) V

'33^ ' ) a2(' ' (

"33(4,

'11 J | ri

a82 = [C36<4) + a2<4> (C23<4) + 2C33<4) )| ra d _ C12'2> +^(2)C13(2) r ]

"92 . „(2) 1/2 'l |

z) + i(2)C13(2) r i+^<2) L'

C12(4) +1(4)C13(4)

w +^(4)C,3(4) r ^ r ^ 1 + ^(4) La 3

C <2) _ R(2)C <2)

e _ ° 12 r °13 '2 , „(2)

' -rci' \r _ ri

i_^<2> L2 1 J

C <4> _ «<4>C <4)

e _ °12 r °13 94 . .0(4)

0 (4) r-

~P Ci3 rr-f^"+1 - r

i _^<4> Lr- r

a52 = £ p/k > + > (C12'k > + 2C,/k > )]£

r3 - 31

c II r„

d - r V1' U12~ '2

d5I = (£*<» +^<«C33<" ),

e5, =(C23<" -^<«C33<")fl

a51 =(C13<1) -C13'2>) + < (C23(1) + C33(1)(C2

d62 =(C23<2>+^2>C33<2>) rf'-1

e62 =(C23<2)-^<2)C33<2') r/^

a61 _(C13 _ C13 ) + (C23 + C33 (C2

d73 =(C23<3'+^<3'C33<3') rf'-1

e73 _ (C23^ ^ _^ ^ ^ ) r3 A

a,, = (C13(3) -C13(3)) + o,<3> (C23<3) + C33(3))-o,<4>(C2

d84 =(C23<4>+^4>C33<4>) r/^

a81 = C13(4) + a,<4) (C23<4> + C33(4))

d _ C12(" C13(" rrr ,(„+1 t Si 1+^(1) ro J

d _ C12<3) +^<3)Ci3<3) rr _ r 1

d'3 " l + Lr3 r2 J

e _ C12"' -l'"^"» rr_r +1 n

e"" i-^m l1 " \

e _ C12'3) -fPc,3<3) rr _ r 1 e93 " 1_„<3) Lr3 72 J

^ (2) , C (2)\

'2Z 33 I

'23 + C33 )

(4) , C <4)) '23 S-33 I

'n2 - 2)

a,, [C„(t > (<C12lt > + C,f

k =1 ^

d _ C26(1> +^(1)C36(1) rr,(.)+2 r ,(1)+2 n

m 2 + Lr> r° J

2 + ^(2) I 2 1

. C26<4) +^<4)C36<4) r r ^

d 26 'A7 36 I +2 _

d»4 - 2 +.(4)

d _ C/> +^(3>C36(3> r. ^ r ^ "

03 2+^(3) L3 2 -

¿M .+2 - .+21

C (4) _ fl<4)C <4) _

. ^26 P 36 I . -^4>+2 _ . -/4>+2

a.2 [C66(t> +«2(t> (C2f + 2CJ6

a01 = ±[C16«k' +a<k' (C26<k> + C36<k')]

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