Finite Element Analysis of Aluminum-Kevlar/Epoxy Pressure Vessel

S. Sulaiman1, a*, S. Borazjani1, b and A. Roshan1, c

1Department of Mechanical and Manufacturing Engineering

Faculty of Engineering, Universiti Putra Malaysia

43400 UPM , Serdang , Selangor, Malaysia

Email: asuddin@eng.upm.edu.my , bsoroush_borazjani@yahoo.com , camirroshan25@yahoo.com

Keywords: Failure pressure, Composite pressure vessel, Finite element analysis, Winding angle.

Abstract. In this present work, the composite pressure vessel type three has been investigated by

finite element method (FEM). The aluminum pressure vessel reinforced with Kevlar/Epoxy

(Aramid 149) was analyzed under internal pressure to predict the ultimate failure pressure of the

vessel. Also the optimum winding angle which provides the highest strength for the vessel was

determined by applying Tsai-Wu and Tsai-Hill failure theories. The asymmetric fiber orientation

for six different winding angles was utilized to reinforce the aluminum vessel. The commercial

code ABAQUS/CAE was employed to analyze the composite vessel. Results obtained from the

simulation were in good consistency with the analytical and the experimental outcomes.

Introduction

The significant pressure vessel role in industrial zones leads the researchers to improve the design

of these vessels. Beside the high manufacturing costs for previous vessels, they deal with the human

lives. Using composites due to their high strength, lower weight [1] and more durability becomes an

alternative method to develop pressure vessel design and safety. Today new generations of

composite vessels called type three and type four are presented in the market. These vessels are

usually intended for portable applications and mostly are made of aluminum linear overwrapping

with Carbon, Glass and Kevlar fibers [2] produced by filament winding process.

Martines et al. [3] compared the experimental work with simulation analysis (UMAT subroutine)

to predict the failure pressure of composite tube subjected under internal pressure. Different

researches have been done on structure of composite vessels and tubes to analyse the failure modes

and ultimate failure pressure of them. First-ply failure and progressive failure analyses are the two

main methods (along with utilizing simulation codes) to predict the strength of composite structures

[4-6]. A number of studies have been carried out on determining the optimum laminates lay-up and

the optimum winding angle in composite pressure vessel. Most of the results confirmed that

composites show the highest strength in asymmetric fiber orientation [7,8]. Liu et. al [9] applied a

multiscale damage model to predict the failure properties and ultimate burst pressure of composite

vessel. First a damage model was utilized to predict the progressive failure properties of the

representation volume element (RVE) which related to damage evolution and stiffness properties of

the composite vessel. Second the multiscale method was utilized to link stiffness degradation of

RVE in the fiber direction; both analyses were implemented by using simulation softwares.

In this paper efforts have been made to evaluate the effects of winding angle on the composite

pressure vessel failure. Also the ultimate failure pressure (burst pressure) and the optimum winding

angle of composite pressure vessel are determined. The validation of results is proved by comparing

to the experimental ones.

Advanced Materials Research Vol. 903 (2014) pp 27-32Online available since 2014/Feb/27 at www.scientific.net© (2014) Trans Tech Publications, Switzerlanddoi:10.4028/www.scientific.net/AMR.903.27

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Winding Angle in Composite Vessel

Winding angle for a geodesic winding path (non-slip winding) is determined by Eq. 1 at any radius

R of the vessel head [9]:

= arcsin(r/R). (1)

In this equation, r is the radius of the polar axis.

In order to determine the optimum winding angle, the netting analysis is defined for a thin-wall

filament-wound composite vessel subjected under internal pressure with a hoop-to-axial-stress ratio

of 2:1 [10]. The optimum fiber angle for a vessel with the shell thickness of “t” is determined

during Eqs. 2-5 [11]. The schematic of forces and internal pressure are shown at Fig. 1.

NØ = , Nθ = PR . (2)

σ = Ø = , σ = = . (3)

Nθ = σ t sin2α , NØ =σ t cos

2α . (4)

Ø = tan

2 α = 2 α = arc tan (√2 ) = 54.7

0. (5)

In the mentioned equations NØ , Nθ , σ , σ and α are axial force, hoop force, axial stress,

hoop stress and winding angle respectively.

Fig. 1: Schematic of axial and hoop forces and internal pressure [11].

Finite Element Analysis of Composite Pressure Vessel

Finite Element Modeling

The following analysis of structure concentrates on the cylindrical composite pressure vessel. The

vessel is made of aluminum linear overwrapping with Kevlar/Epoxy composite fibers. Material

properties of composite vessel are presented at Table 1. The vessel is designed with 1200 mm

length and diameter of 300 mm at the center point. The thickness of the vessel considering the shell

thickness (0.3 mm) and six Kevlar/Epoxy laminates (4.572 mm) becomes 4.872 mm.

28 Manufacturing Engineering

Table 1: Mechanical properties of Kevlar/Epoxy composite and Al 6061 [8,9]

Density[kg/m

3] E1 [GPa] E2 [GPa] υ12 G12 [GPa] τ [MPa]

AL 6061 2750*

70 70 0.3 27 600

Kevlar/Epoxy 1380*

87 5.5 0.34 2.2 - *. [12]

The commercial code “ABAQUS/CAE” is utilized to obtain the mesh modeling of composite

vessel as shown in Fig. 2. The mesh consists of 4290 nodes and 7822 elements with the global size

of 0.01.

Fig. 2: Meshing model of composite vessel

Failure Criteria of Composite Materials

Failure analysis of composite laminates is implemented by using failure theories. Failure theories

are able to predict the failure modes and failure strength of composite materials properly.

a. Tsai-wu failure criterion

Tsai-Wu theory predicts failure in an orthotropic lamina under plane stress condition [13] by

applying Eq. 6:

F σ + F σ + F τ + F σ + F σ + 2F σ σ ≥ 1. (6)

F ,F ,F ,F , F , F are the strength parameters and given by at Eq. 7 :

F = − . , F = − . , F = . ,

F = . , F = . , F = − F F . (7)

b. Tsai-hill failure criterion

Tsai-Hill failure criterion satisfies the Eq. 8 at following [14]:

F σ + F σ + F τ + 2F σ σ ≥ 1. (8)

The strength parameters ofF ,F ,F ,F , F , F are given by at Eq. 9:

F = . , F = . , F = . , F = − ( + ). (9)

Advanced Materials Research Vol. 903 29

The strength parameters of Kevlar/Epoxy are listed at Table 2:

Table 2: Strength parameters for Kevlar/Epoxy composite [8]

Xt [MPa] 1280

Xc [MPa] 335

Yt [MPa] 30

Yc [MPa] 158

S [MPa] 49

Simulation Analysis

The simulation analysis is accomplished by defining the model and assigning the material

properties of vessel into it. The aluminum pressure vessel is reinforced with six layers of

Kevlar/Epoxy which are set on the inside aluminum layer. The laminates are wrapped around the

aluminum layer at asymmetric fiber orientation for the six winding angle of 300, 45

0, 55

0, 60

0,

750 and 90

0 as shown in Fig. 3.

Fig. 3: The stacking sequences for 550 winding angle

In order to determine the optimum winding angle and the burst pressure for each fiber

orientation, the vessel is subjected under the internal pressure. Modification of the internal pressure

is done by applying Tsai-Wu and Tsai-Hill failure criteria to reach the failure coefficients around

one. As failure coefficients become slightly higher than one, the vessel is talented to place in critical

condition. In this way, internal pressure is the burst pressure of composite vessel which can lead the

vessel to failure.

Results and Discussion

The distribution of ultimate failure pressure (burst pressure) under increasing winding angle is

presented at Fig. 4. The graph exposes that the failure pressure increases with increasing winding

angle in the range of 300-55

0. As soon as the angle equals to 55

0, the burst pressure decreases

sharply up to reach the 900. The maximum failure pressures of 11.5 MPa and 9.5 MPa belong to 55

0

winding angle based on Tsai-Wu and Tsai-Hill criteria respectively.

The optimum winding angle is the condition in which the composite fibers show more resistance

to hoop stress than axial stress under the internal pressure [15]. These maximum burst pressures

prove that the optimum angle for asymmetric fiber orientation in filament wound composite

pressure vessel is 550 winding angle which has a good consistency with the netting analysis

estimation [10] and the experimental works [16,17]. Fig. 5 shows the values of Tsai-Wu and Tsai-

Hill failure coefficients related to the maximum burst pressures of 11.5 and 9.5 MPa respectively. It

30 Manufacturing Engineering

is obvious that the critical part more prone to failure is allocated to the dome of the vessel which has

higher failure coefficients. The values of failure coefficients are around 1 based on the failure

criteria principle.

Fig. 4: Variation of failure pressure with increasing winding angle

Fig. 5: Failure coefficients of 550 winding angle under internal pressure

Conclusion

In this paper, the failure analysis of aluminium pressure vessel reinforced with Kevlar/Epoxy layers

was investigated. Finite element method along with Tsai-Wu and Tsai-Hill failure criteria was

utilized to study the ultimate strength of composite pressure vessel. Results proved that the

maximum burst pressure occurs at 550 winding angle in which the fibers show more strength

against the internal pressure. They also confirmed that the optimum winding angle for reinforcing

aluminium pressure vessel is obtained by overwrapping composite fibers in 550 winding angle

which is in a good consistency with analytical and experimental analyses.

Acknowledgements

The authors would like to thank the Faculty of Mechanical and Manufacturing Engineering in

University Putra Malaysia (UPM) for its supporting and encouraging.

0

5

10

15

30 50 70 90Ult

imate

Fail

ure

Pre

ssu

re

(MP

a)

Winding Angle (Degree)

Tsai-Wu Failure Theory

Tsai-Hill Failure Theory

Advanced Materials Research Vol. 903 31

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32 Manufacturing Engineering

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