carbon epoxy

Research Article Impact Factor: 4.226 ISSN: 2319-507X Arunkumar SM, IJPRET, 2014; Volume 3 (2): 131-156 IJPRET

Available Online at www.ijpret.com

131

INTERNATIONAL JOURNAL OF PURE AND APPLIED RESEARCH IN ENGINEERING AND

TECHNOLOGY A PATH FOR HORIZING YOUR INNOVATIVE WORK

FINITE ELEMENT ANALYSIS OF CFRP COMPOSITE PRESSURE STORAGE VESSEL

FOR VARIOUS FIBER ORIENTATION ANGLES

ARUNKUMAR SM1, THIPPESWAMY EKBOTE 2

1. Postgraduate Student, Machine Design, Bapuji Institute of Engineering and Technology, Davangere, India. 2. Associate Professor and Head, PG Program in Machine Design, Bapuji Institute of Engineering and Technology, Davangere, India.

Accepted Date: 12/08/2014; Published Date: 01/10/2014

\

Abstract: The composite materials are used for fabrication of pressure vessels by placing the fibers in different orientations for each layer. These layers are stacked in such a way to achieve high stiffness and strength. The design of the composite vessel as a fundamental research work relates the physical and mechanical properties of materials to the geometric specifications. The project demonstrates a study on High-Pressure Hydrogen Storage Vessel of carbon fiber reinforced polymer (CFRP) composite having four layers. The pressure vessel is designed and modeled using the finite element software ANSYS 14.0. Laminate plies were oriented symmetrically with [+15 / -15]s, [+30 /- 30]s, [+45 /- 45]s, [+60 / -60]s, [+75 / -75]s, and [+90 / -90]s, orientations separately. For each combination of fiber orientation, the effect of pressure vessel deflection and stress were obtained and discussed. Finally the best fiber orientation was selected.

Keywords: Modeling- ANSYS Design Modeler, Meshing-ANSYS Meshing, Analysis- ANSYS 14.0.

Corresponding Author: MR. ARUNKUMAR S. M.

Access Online On:

www.ijpret.com

How to Cite This Article:

Arunkumar SM, Thippeswamy Ekbote; IJPRET, 2014; Volume 3 (2): 131-

156

PAPER-QR CODE



132

INTRODUCTION

A composite material is made by combining two or more materials to give a unique

combination of properties. The above definition is more general and can include metals alloys,

plastic co-polymers, minerals, and wood. Fiber-reinforced composite materials differ from the

above materials in that the constituent materials are different at the molecular level and are

mechanically separable. In bulk form, the constituent materials work together but remain in

their original forms. The final properties of composite materials are better than constituent

material properties.

The main concept of a composite is that it contains matrix materials. Typically, composite

material is formed by reinforcing fibers in a matrix resin as shown in Fig. 1. The reinforcements

can be fibers, particulates, or whiskers, and the matrix materials can be metals, plastics, or

ceramics.

Carbon/Epoxy Composite Material

The material utilized for this design project is carbon fibers in an epoxy matrix. It will be

implemented using lamina sheets of the material. Carbon fiber and epoxy are quite different

materials when their individual properties are viewed. The carbon fiber is made out of long,

thin sheets of carbon. It is a chemically inert rigid material that is difficult to stretch and

compress. On the other hand, epoxy is a thermosetting plastic, or resin that is liquid when

prepared but hardens and becomes rigid when is heated.

Carbon-epoxy materials are finding increased structural uses in areas such as aerospace,

structural engineering, automotive, and sporting goods applications.

The primary goal of this design project is to use the knowledge gained about composites and

their advantages to create a carbon fiber / epoxy pressure vessel. The materials utilized in this

project will consist of carbon / graphite fibers acting as reinforcement in an epoxy matrix

formed in several layers or lamina. These materials are usually flexible, and can be molded into

almost any desired shape in this case they will be molded into a cylinder and then baked in a

kiln or high pressure oven until both materials mesh together and become a single hard

structure.

Pressure Vessel

It is a closed container designed to hold gases or liquids at a pressure substantially

different from the ambient pressure. The pressure vessels may be thin or thick. When the ratio



133

of the plate thickness to mean radius of the pressure is less than 1/15 then the pressure vessel

is termed as a thin pressure vessel, otherwise, a thick pressure vessel.

Pressure Vessel Theory

Pressure vessel is a container designed to operate at pressures. The design of a pressure vessel

is entirely reliant upon mechanics of materials. Prediction of the ultimate strength of a

designed vessel is done using various failure theories. When building a pressure vessel out of

composite materials, some the theories employed to optimize strength and predict failure are

the Tsia Hill energy based interaction theory, and maximum stress and strain theory. The

forces applied in the different directions of the pressure vessel are directly related to the

magnitude of the pressure and are given below.

1. Hoop stress

Hoop stress is a circumferential loading of a cylindrical mechanical body. It is the

circumferential stress in a cylindrically shaped part caused by internal or external pressure. [12]

(i)

2. Longitudinal stress or axial stress.

When the vessel has closed ends the internal pressure acts on them to develop a force along

the axis of the cylinder. [12]

= (ii)

3. Radial stress

Radial stress in thin cylinder can be neglected as the radial pressure is not generally high and

that radial pressure acts on a larger area.

Assumptions for Thin Cylindrical Pressure Vessel

The key assumptions used here are: wall thinness and geometric symmetries.

1. Wall Thinness. The wall is assumed to be very thin compared to the other dimensions of the

vessel. Usually R/t >10, As a result, we may assume that the stresses are uniform across the

wall.

2. Symmetries. In cylindrical vessels, the geometry and the loading are cylindrically symmetric.



134

3. Uniform Internal Pressure. The internal pressure, denoted by P is uniform and everywhere

positive.

4. Ignoring End Effects. Features that may affect the symmetry assumptions are ignored. This

includes supports and cylinder end caps.

Pressure Vessel Model Data

Internal pressure is P = 1.6 MPa,

Inner diameter of pressure vessel is d = 5170 mm,

Cylinder length of pressure vessel is L = 8000 mm and

Pressure vessel thickness is t = 30 to 100 mm.

5 MPa, tensile yield -6 Kg/mm3

Analytical calculation of the stress

Inner Radius of pressure vessel r = 2585 mm.

Thickness of pressure vessel t=30 mm

Hoop stress =137.8667 MPa.

Longitudinal stress = = 68.933 MPa.

Equivalent stress [12]

=119.40 MPa.

Analysis of CFRP Composite Pressure Vessel for Various Fiber Orientation Angles

The layered configuration is the most important characteristic of a composite material. The

layered configurations are determined by specifying individual layer properties and therefore

the properties of the composite as a whole depends greatly on its layered configuration. The

material properties, the fiber orientation angle, the layer thickness and the number of



135

integration points per layer must be specified for individual the definition of the layered

configuration to be complete.

The CFRP layers in the composite pressure vessels are assumed to be orthotropic. Therefore

nine material properties are required for the purpose of the analysis. The material properties

for carbon/epoxy are listed in Table.3.

The cylindrical composite pressure vessel is designed for various fiber orientations. The

modeling is performed for the CFRP cylindrical pressure vessel for both, the hoop and the

helical windings of the carbon fiber. For the hoop windings of the carbon fibers, the fibers are

oriented at an angle of 0 with the axis of the cylindrical pressure vessel. The fibers are oriented

for various fiber orientations such as 15, 30, 45, 60, 75 and 90, in symmetrical

stacking sequence.

Thickness of composite pressure vessel =50 mm,

Each layer Thickness =12.5 mm. Material- Carbon/Epoxy

Results

Fiber Angle [+15/-15/-15/+15]

Fig. 6 shows the enlarged view of angle of orientation of 4 layers of the composite pressure

vessel.

Fig. 7 shows the maximum and minimum total deformation of composite pressure vessel. The

maximum deformation is 27.44 mm and minimum deformation is 4.94 mm.

Fig. 8 shows the maximum and minimum equivalent stress of composite pressure vessel. The

maximum equivalent stress is 314.41 MPa and minimum equivalent stress is 13.10 MPa.

Fig. 9 shows the maximum and minimum principal stress of composite pressure vessel. The

maximum stress is 130.69 MPa and minimum stress is -0.0166 MPa.

Fiber Angle [+30/-30/-30/+30]







136


maximum stress is 103.66 MPa and minimum stress is 3.50 MPa.

Fiber Angle [+45/-45/-45/+45]






maximum stress is 63.42 MPa and minimum stress is 0.1399 MPa.

Fig. 30 to 32 we can observe that the middle principal stresses, equivalent stresses, strains and

deformations are minimum for the fiber angle orientation of 45 for all pressure values. Hence

fiber angle orientation 45 is the optimizing angle for the composite pressure vessel

Fiber Angle [+60/-60/-60/+60]







Fiber Angle [+75/-75/-75/+75]







Fiber Angle [+90/-90/-90/+90]



137






maximum stress is 89.84MPa and minimum stress is -0.094075MPa.

Weight Reduction

The Table. 4. shows the properties of structural steel and composite pressure vessel. The mass

of the composite pressure vessel is reduced when compared to steel for same volume and

surface area.

Design of Experiments Study

In general, the DOE techniques can be classified as classical and modern DOE methods. The

classical DOE methods were developed for laboratory and field tests which have random error

sources while the modern DOE methods relate to deterministic computer simulations.

Design Explorer

Design Explorer is based on a method called Design of Experiments (DOE). This together with

various optimization methods helps the program to develop an optimized structure based on

selected input and output parameters. Input parameters can either come from Design Modeler

or from various CAD systems. These parameters can be in terms of thickness, length, etc. They

can also come from Mechanical in terms of forces, material properties, etc. The output

parameters are calculated in Mechanical and can for example be in terms of total mass, stress

or frequency response. After setting up an analysis with a number of input parameters and out

parameters there are the steps that can be run within DesignXplorer:

Design of Experiments

Response surface

Optimization

Six Sigma Analysis



138

Optimization of Pressure Vessel Ply Angle

Fig. 29 shows the complete workflow for optimization study. In this project from the CAD

creation to ANSYS simulation steps performed within the Workbench framework.

Once the complete ANSYS process was set, Goal Driven Optimization (GDO) was started. The

1ststep towards GDO was to make a Design of experiments. The range in which the two design

parameters should change to get the most optimized design was chosen. Table 5 to 7 shows

these ranges. A Central Composite Design (CCD) based DOE was setup, which created nine

Design Points for the identified five input design parameters. These 27 Design Points were then

run automatically to make output at these points. No manual involvement was needed to run

calculations at these points and right from geometry modification to determining the value of

the output parameter, the complete process was carried out automatically.

As mentioned above, the goal of the study was to optimize the angle in the permissible range of

input design parameters to minimum Equivalent Stress. A DOE with 27 design points was

started and the results were investigated. Response surfaces in 2D and 3D were generated from

the results of the 27 design points. On the full second order polynomial method which uses

different regression analysis to obtain a polynomial Standard Response Surface 2nd-Order

Polynomial, is default meta-model which creates a Standard Response Surface. This is effective

when the variation of the output is smooth with regard to the input parameters. Fig. 26 to 28

shows 3D response surfaces variation of the output parameter maximum von-Misses stress as a

result of variation of five input parameters. It can be seen Equivalent stress decreases at ply

1and 4 angle between 85 to 90 degree angles.

CONCLUSION

Finite element method was an advantage to design a pressure vessel more effectively. In this

study, a finite element analysis approach is employed using ANSYS. Initially Metal Pressure

vessel is done using Analytical and FEA method. Then the cylindrical composite pressure vessel

is designed for various fiber orientations. The modeling is performed for the CFRP cylindrical

pressure vessel for the fibers oriented for various fiber orientations such as 15, 30, 45,

60, 75 and 90, in symmetrical stacking sequence. The cylindrical composite pressure

vessel is modeled for four uniform thickness layers. Then the ANSYS results show that the fiber

angle 45 is optimizing angle for the composite pressure vessel. Then Design of Experiments

optimization study was carried out.



139

A Central Composite Design (CCD) based on DOE was setup, which created nine Design Points

for the identified five input design parameters. These 27 Design Points were then run

automatically to make output at these points. As mentioned above, the goal of the study was to

optimize the angle in the permissible range of input design parameters to minimum Equivalent

Stress. It shows the 45 fibre angle gives less stress, which is similar to range of manual

optimization. From the finite element analysis report of 45 the maximum stress obtained in

each lamina is less than the allowable working strength of the CFRP lamina. So shell design is

safe.

However comparing similar thickness of the pressure vessel the weight of the composite is

reduced by approximately 80%

Fig. 1 Formation of a composite material using fibers and resin.

Fig. 2 Geometric dimensions for one half pressure vessel.

Axis of pressure vessel

Pressure vessel end

30mm

5170mm

2585mm

4000mm



140

Fig. 3 Pressure vessel created by ANSYS design modeler and meshed by ANSYS design

meshing.

Fig. 4 Pressure Vessel model for analysis and Boundary conditions.



141

Fig. 5 Equivalent (Von-Mises) Stress from ANSYS.



142

1st Layer +15 Enlarged view

2nd Layer -15 Enlarged view

3rd Layer -15 Enlarged view

4th Layer +15 Enlarged view

Fig. 6 Four layers fiber angle [+15/-15/-15/+15] of pressure vessel.



143

Fig. 7 Total Deformation [+15 / -15]s. Fig. 8 Equivalent Stress [+15 / -15]s.

Fig. 9 Principal Stress [+15 / -15]s.




144






145






146






147

Fig. 25 Workflow for optimization.

Fig. 26 Response surfaces ply angle 1 & 3 Fig. 27 Response surfaces ply angle

variation V/s Maximum Stress. 1 & 4 variation V/s Maximum Stress.

ANSYS Workbench

Geometry

Design Modeler

Initial CAD

Optimized

Design

Mesh

ANSYS Meshing

WB solver

ANSYS

Mechanical

Optimization

DesignXplorer

upda

te

update

update



148

Fig. 28 Response surfaces ply angle 2& 3 variation V/s Maximum Stress.

Fig. 29 Comparison of FEA and analytical Results for different thickness of Structural steel

pressure vessel.

Pressure vessel thickness mm

Analytical Equivalent stress MPa FEA Equivalent stress MPa

Equ

ival

ent

stre

ss

MP

a



149

Fig. 30 Middle Principal Stress v/s angle of fiber orientation for different pressure.

Fig. 31 Equivalent Stress v/s angle of fiber orientation for different pressure.

0

20

40

60

80

100

120

140

0 15 30 45 60 75 90

Mid

dle

Pri

nci

pal

Str

ess

MP

a

Angle of fiber orientation (Degree)

1.6 MPa

0

50

100

150

200

250

300

350

0 15 30 45 60 75 90

Eq

uiv

ale

nt

Str

ess

MP

a


1.6 MPa

Pressure

Pressure



150

Fig. 32 Deformation v/s angle of fiber orientation for different pressure.

Table.1. Comparison of Thickness v/s Equivalent Stress of structural steel.

0

5

10

15

20

25

30

35

40

45

50

0 15 30 45 60 75 90

Def

orm

ati

on

mm


1.6 MPa

t Thickness

mm

Inner radius mm Longitudinal Stress MPa Hoop Stress MPa Equivalent

Stress MPa

30 2585 68.933 137.866 119.40

40 2585 51.70 103.40 89.54

50 2585 41.36 82.722 71.64

60 2585 34.466 68.935 59.70

70 2585 29.54 59.087 51.17

80 2585 25.775 51.70 44.77

90 2585 22.98 45.96 39.80

100 2585 20.68 41.361 35.80

Pressure



151

Table.2. Comparison of analytical and FEA Results of structural steel.

Thickness

t mm

Analytical Equivalent Stress MPa FEA Equivalent

Stress MPa

Error %

30 119.40 122.94 -2.96

40 89.54 92.71 -3.54

50 71.64 74.58 -4.1

60 59.70 62.50 -4.6

70 51.17 53.87 -5.2

80 44.77 47.40 -5.86

90 39.80 42.37 -6.4

100 35.82 38.34 -7.0

Table.3. Material properties for Carbon/Epoxy from ANSYS engineering data.

1.21E+05 MPa

8600 MPa

Modulus in Z direction 8600 MPa

0.27

0.4

0.27

Shear Modulus XY 4700 MPa

Shear Modulus YZ 3100 MPa

Shear Modulus XZ 4700 MPa



152

Table.4. Results of carbon/epoxy pressure vessel for different orientation angles.

Angle of fibre

orientation

Principal Stress MPa Equivalent Stress MPa Deformation

mm

[+15/-15/-15/+15] 130.68 314.41 27.44

[+30/-30/-30/+30] 103.65 248.75 16.49

[+45/-45/-45/+45] 63.42 137.80 9.912

[+60/-60/-60/+60] 61.79 171.91 33.95

[+75/-75/-75/+75] 70.82 155.23 44.74

[+90/-90/-90/+90] 89.84 139.45 45.96

Table.5. comparison of mass, weight, density, volume and surface area of the structural steel

and carbon/epoxy pressure vessel.

Properties Structural Steel Carbon/Epoxy

Mass 42202 Kg 8010.3 Kg

Weight 413860.240 N 78578.10 N

Density 7.85 x 10-6 Kg/mm3 1.49 x 10-6 Kg/mm3

Volume 5.376 x 109 mm3 5.376 x 109 mm3

Surface Area 1.0752 x 108 mm2 1.0752 x 108 mm2



153

Table 6. Composite Ply angle upper and lower bound for 1st and 4th layer.

Table.7. Composite Ply angle upper and lower bound for 2nd and 3rd layer.

Table.8. Ply Thickness upper and lower bound.



154

Table. 9. DOE Runs.

Run

No

Modeling Ply angle

1

Modeling

Ply angle 2

Modeling

Ply angle

3

Modeling ply angle

4

Thickness

mm

Equivalent stress

MPa

1 45 -45 -45 45 12.5 137.8024

2 0 -45 -45 45 12.5 214.7312

3 90 -45 -45 45 12.5 241.2867

4 45 -90 -45 45 12.5 157.5614

5 45 0 -45 45 12.5 122.8908

6 45 -45 -90 45 12.5 155.0172

7 45 -45 0 45 12.5 111.4963

8 45 -45 -45 0 12.5 184.5386

9 45 -45 -45 90 12.5 225.6497

10 45 -45 -45 45 5 345.7434

11 45 -45 -45 45 20 85.08644

12 32.25 -57.75 -57.75 32.25 14.62505 122.1557

13 57.75 -57.75 -57.75 32.25 10.37495 300.0916

14 32.24 -32.25 -57.75 32.25 10.37495 183.1427

15 57.75 -32.25 -57.75 32.25 14.62505 145.4567

16 32.25 -57.75 -32.25 32.25 10.37495 171.3436

17 57.75 -57.75 -32.25 32.25 14.62505 164.456

18 32.25 -32.25 -32.25 32.25 14.62505 197.801

19 57.75 -32.25 -32.25 32.25 10.37495 199.9963

20 32.25 -57.75 -57.75 57.75 10.37495 291.5513

21 57.75 -57.75 -57.75 57.75 14.62505 143.9549



155

Table. 10. Optimization of stress.

Table. 11. Result for optimized design of pressure vessel.

REFERENCES

1. Lekhnitskii, S. G. (1981). Theory of Elasticity of an Anisotropic Body, Mir Publishers, Moscow.

2. Roy, A. K., Massard, T. N.(1992). A Design Study of Multilayered Composite Spherical

Pressure Vessels, Journal of Reinforced Plastic and Composites, VII, 479-493

22 32.25 -32.25 -57.75 57.75 14.62505 191.4392

23 57.75 -32.25 -57.75 57.75 10.37495 172.8128

24 32.25 -57.75 -32.25 57.75 14.62505 141.8791

25 57.75 -57.75 -32.25 57.75 10.37495 172.4225

26 32.25 -32.25 -32.25 57.75 10.37495 227.2353

27 57.75 -32.25 -32.25 57.75 14.62505 106.582



156

3. Sayman, O. (2005). Analysis of Multi-Layered Composite Cylinders Under Hygrothermal

Loading, Composites Part A, 1-11.

4. Mackerle, J. (2002). Finite Elements in the Analysis of Pressure Vessels and Piping, an

Addendum: a Bibliography (1998-2001), International Journal of Pressure Vessels and Piping,

79, 1-26.

5. Rao, V. V. S. & Sinha, P. K. (2004). Dynamic Response of Multidirectional Composites in

Hygrothermal Environments, Composite Structures, 64, 329-338.

6. Adali, S., Verijenko, V. E. et al.(1995). Optimization of multilayered composite pressure

vessels using exact elasticity solution, Composites for the Pressure Vessels Industry, PVP-V302,

ASME, 203-312.

7. Jacquemin, F. & Vautrin, A. (2002). The Effect of Cyclic Hygrothermal Conditions on the

Stresses near the Surface of a Thick Composite Pipe, Composite Science and Technology, 62,

567-570.

8. Mirza, S., Bryan, A., Noori, M. (2001). Fiber-Reinforced Composite Cylindrical Vessel with

Lugs, Composite Structures, 53, 143-151.

9. Sun, X. K., Du, S. Y. & Wang, G. D. (1999). Bursting Problem of Filament Wound Composite

Pressure Vessels, International Journal of Pressure Vessels and Piping, 76, 55-59.

10. Hwang, T. K., Hong, C. S., & Kim, C. G. (2003). Size Effect on the Fiber Strength of Composite

Pressure Vessels, Composite Structures, 59, 489-498.

11. S.K. Roychowdhury, B. Maiti, G. Chakraborty. Design of machine elements.

12. K. Mahadevan, K. Balaveera Reddy. Design data hand book, for mechanical engineers, 2008.

13. Medhavi Sinha, Dr. S. N. Pandit. Design and Burst Pressure Analysis of CFRP Composite

Pressure Vessel for Various Fiber Orientations Angles.

14. Javad Marzbanrad, Amin Paykani, Amir Afkar, Mostafa Ghajar, 2012. Finite element analysis

of composite high-pressure hydrogen storage pressure vessels.

15. Deniss R. Moss. Pressure vessel design manual, gulf professional publishers, 2004.

16. McGrew- Hill. Machine design databook, the McGrew Hill companies, 2004.

carbon epoxy

Documents

composite vessel

matrix materials

different materials

constituent materials

carbonepoxy composite

carbon fibers

machine design

design project