Investigations on Stress and Deflection Analysis of …...1 Investigations on Stress and Deflection...

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Investigations on Stress and Deflection Analysis of Fiber Metal

Laminated (FML), Steel and Composite Beams

Rohit R. Ghadge and Dr.S.Prakash

School of Mechanical Engineering, Sathyabama

University, Chennai, Tamil Nadu,India.

[email protected]

Abstract

Fiber Metal Laminates (FML) are the class of hybrid materials comprising of thin metal sheets adhesively bonded together with fiber reinforced composite layers. These are widely used in aerospace industry for structural applications. In this paper the end point deflection and maximum equivalent stress of FML cantilever beam made of aluminum sheets and E-Glass fibers have been investigated by considering the effect of varying fiber angle orientation, stacking sequence and number of layers. Theoretical investigations were performed using Classical lamination theory. Six different parameter sets of FML with total eighteen stacks out of which four stacks are of aluminum and remaining fourteen stacks are of E-Glass fibers are analyzed and compared with steel beam for the same boundary conditions using commercially available FEA tool. Finally FEA results are validated by analytical results. It has been found that the tip displacement is inversely proportional to the material index and thickness. Considerable amount of weight reduction is achieved in comparison with steel beam for the same boundary conditions. With little increase in thickness of FML it gives better results compared to steel beam with minimum stress values and higher weight reduction.

Key Words and Phrases: Fiber laminated composite, Fiber angle orientation; stacking sequence. Stress Deflection characteristics,

1 Introduction

With increase in demands for more fuel efficient vehicles, there is need to replace

the heavy steel components by some other material which will reduce the weight

and will possess same or more strength than the steel material. In western

countries in many of the aircraft applications metal parts are either replaced or

repaired by composite materials or FML. For automobiles if we use such materials

or laminates instead of metals that will help to reduce the weight as composites

possess less mass density than the metals and high strength to weight ratio.

International Journal of Pure and Applied MathematicsVolume 114 No. 11 2017, 325-335ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version)url: http://www.ijpam.euSpecial Issue ijpam.eu

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Currently considerable amount of research has been done to replace the metal

components with that of fiber laminated composites. In the present research three

different configurations (FML, Composite and steel) have been analyzed and

compared. It is found that composites exhibits higher weight reduction but shows

more deflection than steel. Whereas FML shows higher weight reduction and

lesser deflection than composites and shows more potential than composites.

Figure 1: FML Layup

[1]

Fiber-reinforced metal laminates (FML) are hybrid composites consisting of

alternating thin layers of metal sheets and fiber reinforced epoxy. The most

commonly used metal for FML is aluminum, and the fibers can be Kevlar or

glass. The FML with glass fibers (tradename GLARE), and Kevlar fibers

(trade name ARALL) have been evaluated for applications in aircraft

structures. More recently, GLARE has been selected for the upper fuselage

skin structure of Airbus A380. The combination of metals and composites

results in a new family of hybrid laminates with an ability to impede and

arrest crack growth caused by cyclic loading, with excellent impact and

damage tolerance characteristics and a low density. [2] FMLs offers excellent

fatigue strength, impact resistance, residual and blunt notch strength, flame

resistance, high strength/stiffness and good damage tolerance, etc. The fiber

layers act as barriers against corrosion of inner metallic sheets, whereas the

metal layers protect fiber layers from picking up moisture. Composite material

provides low weight and excellent strength. FML take advantage of metal and

fiber reinforced composites, provides improved mechanical properties over

conventional lamina made up of only fiber reinforced lamina or metal alloys.

H. Esfandiar et al. (2011)[ 3], done case study on the elastic and plastic

behavior of the fiber metal laminates subjected to tensile loading. In his

research work he used two laminates GLARE4 (Al/00/900/00/Al) having

thickness 0.2-0.5 mm for per aluminum layer and 0.375 mm for per fiber

layer, GLARE5 (Al/00/900/900/00/Al) having thickness 0.2-0.5 mm for per

aluminum layer and 0.5 mm for per fiber layer. They concluded that GLAREs

are stronger than aluminum alloy and stress-strain relations are almost bilinear

in both longitudinal and transverse directions.

J.J.C. Remmers et al. (2001)[4], observed that the fiber metal laminate can

be sensitive to delamination buckling, which occurs when a partially

delaminated panel is subjected to a compressive force.

International Journal of Pure and Applied Mathematics Special Issue

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A. Pourkamali Anaraki et al. (2012)[5], experimented the tensile behavior

of the cracked aluminum plates repaired with fiber metal laminated composite

patches. The paper concluded that decrement of crack length in more crack

angle, show less effect on the increment of ultimate load of repaired

specimens.

B.S.Sugun et al. (2008)[6], presented the work which discusses on

improved process for manufacturing of fiber metal laminates. For bonding in

the conventional process, the cure consolidation and bonding of the metal and

prepeg layers are carried out in autoclave.

In the present paper instead of using alternating layers of Fiber and metals

laminates, authors tried to minimize the number of metal layers so as to

reduce the stresses induced at the interface of metal and fibers due to

differences of elastic modulus of metal and fibers.

2 Problem Statement

To investigate stress deflection characteristics of fiber metal laminated

(FML) cantilever beam with point load at the free end considering different

ply angles and stacking sequence. It is also required to compare the results of

stress and deflection of the beam with the results of steel beam under same

boundary conditions.

Objectives

• The primary objective of this study is to find the stress and deflection

of the FML composite beam considering it as cantilever beam.

• It is required to estimate the effect of variation of fiber angle and

stacking sequence on stress and deflection of the FML beam.

Beam specifications are as shown in following figure 2:

Figure 2 : FML beam specifications

Classical lamination theory is used as the base for numerical solution. The

load range is from 500 N to 1000 N. Symmetric layup is selected for FML and

composites.

Fiber Angle Orientations and stacking sequence for different Sets.


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Set 1 : [Al(0)/Eg(0)7/Al(0) ]s

Set 2 : [Al(0)/Eg(0)4/Eg(45)3/Al(0)]s

Set 3 : [Al(0)/Eg(0/45/0/45/0/45/0)Al(0)]s

Set 4 : [Al(0)Eg(45/90/45/45/90/45/0)Al(0)]s

Set 5 : [Eg(0/0/45/0/45/0/45)Al(0)2]s

Set 6 : [Al(0)2/Eg(45/0/45/0/45/0/0)]s

Composite : [Eg(0/45/0/45/0/45/45/90/0/45/0)]s

Composite_0 : [Eg (0)11]s

Steel : [S(0)3]s

3 Analytical Solution

The analytical solution for nine different set of parameters were obtained

based upon classical lamination theory. ‘Autodesk Helius composite’ is used

to obtain the ABD matrix and deflections of all different sets. E-glass/epoxy

material and aluminium A 1050 are selected and material properties are taken

accordingly. The properties of the aluminium are takes as: Young’s modulus,

E = 70 GPa, Poisson’s ratio, μ = 0.33 and Density, ρ = 2.71 g/cm3. The

properties of E-glass/epoxy material are taken as: Young’s modulus along

direction 1, E1 = 43.36 GPa, Young’s modulus along direction 2, E2 = 7.923

GPa , Poisson’s ratio, μ = 0.24, Density, ρ = 1.90 g/cm3

ABD Matrices of FML Set 1

[A] Matrix : 5.90292E+05 1.15799E+05 0.00000E+00

1.15799E+05 3.64664E+05 0.00000E+00

0.00000E+00 0.00000E+00 2.59335E+05

[B] Matrix: 0.00000E+00 0.00000E+00 0.00000E+00

0.00000E+00 0.00000E+00 0.00000E+00

0.00000E+00 0.00000E+00 0.00000E+00

[D] Matrix: 5.52138E+06 1.23293E+06 0.00000E+00

1.23293E+06 3.83876E+06 0.00000E+00

0.00000E+00 0.00000E+00 2.78889E+06

ABD Inverse Matrices

[A] Inverse Matrix

1.80662E-06 -5.73692E-07 0.00000E+00

-5.73692E-07 2.92442E-06 0.00000E+00

0.00000E+00 0.00000E+00 3.85602E-06

[B] Inverse Matrix

0.00000E+00 0.00000E+00 0.00000E+00

0.00000E+00 0.00000E+00 0.00000E+00

0.00000E+00 0.00000E+00 0.00000E+00

[D] Inverse Matrix

1.95107E-07 -6.26646E-08 0.00000E+00

-6.26646E-08 2.80628E-07 0.00000E+00

0.00000E+00 0.00000E+00 3.58566E-07


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Deflection Max (mm) = 19.9172 mm

As mentioned above ABD Matrix, Inverse ABD Matrix and deflection

were obtained and mentioned in the following table.

Table 1 : Analytical results ( Using Helicus Composite )

4 Finite Element Analysis A finite element model of a FML composite cantilever beam is developed to

validate the analytical results of stress and deflection using ANSYS 16.2

APDL. Shell 181 element is selected for the analysis as it is suitable for

analyzing thin to moderately-thick shell structures. It is a four-node element

with six degrees of freedom at each node: translations in the x, y, and z

directions, and rotations about the x, y, and z-axes. The accuracy in modeling

composite shells is governed by the first-order shear-deformation theory

(usually referred to as Mindlin- Reissner shell theory). Maximum number of

layers that can be analyzed under SHELL181 element is limited to 250 layers.

Figure 3: SHELL 181 Element [7]

Modeling and Meshing

The dimensions selected for the analysis of beam are 350 × 70 × 10 mm. Al of

1 mm thickness and UD glass fiber of thickness 0.45 mm each are considered.

2-D model of the beam is modeled by using rectangular area command. The

Set No Deflection (mm)

Set 1 19.91

Set 2 20.95

Set 3 22.66

Set 4 26.43

Set 5 24.27

Set 6 18.86

Composite 46.38

Composite_0 19.91

Steel 27.39


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modeled rectangular beam is then meshed for the formation of finite elements

by using mesh tool option. In mesh tool option firstly the meshing attribute is

selected as global. For better and quick results size of element edge length is

selected as 5. Free meshing option is selected to mesh the entire beam. Figure

4 shows the layup of Set 2 configuration

Figure 4: Set 2 Layup

Application of loads and boundary conditions

After meshing is done the next part is to apply the boundary conditions and

loads on the beam. As for this research work beam is considered as cantilever

beam, for this purpose one side is selected that is to be fixed. All nodes along

this side are selected and on displacement of all these nodes is fixed by giving

the degree of freedom value as zero in all directions. Other end of the beam,

which is freely suspended all nodes are selected and load of 500 N is applied

by distributing it over 16 nodes. Same procedure is followed at the time of

applying the load of 1000 N.

5 Results Nonlinear finite element analysis is performed on around nine different

parameter sets of beams. The analysis results of this are plotted using x-

component stresses. The results are demonstrated for the maximum deflection,

maximum stress and minimum stress acting on the beam. The pictorial view

of the beam shows the high stress location i.e. stress concentration area of the

beam.


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Figure 5 : Deflection (mm) Vs Length of Beam (mm)

For all the sets, deflection is nonlinear from 0 mm to 200 mm of the length

and linear from 200 mm till the end. Range of deflection at the end of the

beam is found to be 16.8 mm (for Set 6) to 36.7 mm (for Composite).

Composite material shows maximum deflection almost double than that for

Set 2, 3 & 6.

Figure 6:Von Mises Stress (MPa) Vs Length of Beam (mm)

Range of Von Mises stress at the fixed support of beam is found to be 400

MPa (for Steel) to 140 MPa (for Set 6). It is found decreasing towards the end

of beam. Beam with Steel exhibits maximum stress & Set 6, Set 3, Set 5, &

Composite _0 shows minimum stress effects as compared to steel beam.


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Figure 7: Load Vs Stress

Beam with steel material exhibits maximum Von Mises stress, with gradual

increase of load from 500 N to 1000N. Other materials (Set 1, 2, 3, 5 ) shows

sudden rise in stress from 160 MPa to around 390 MPa. Set 4 and Composite

show moderate rise in stress for the same load range.

Figure 8 : Load Vs Deflection

Set 1, 2, 3, 6 are found to have higher stiffness as compared with Set 4, 5,

Steel and Composite_0. Composite shows lower stiffness as compared to

other materials. Set 4, 5 & steel beam show moderate stiffness.


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Figure 9 : Shear stress variation in the different sets.

Maximum shear stress is shown for the Composite_o configuration whereas

lowest shear stress for the set 5.

Figure 10 : Comparison of FEA and Analytical results.

The FEA results are validated by analytical solver and compared as shown in

figure 10. Both results are in close comparison with each other. As 10 mm

thick FML beam results are better than 6 mm thick steel beam, the weight

comparison of these beams is given in following table,

Sr.

No

Laminate/Bea

m

Thickness,

mm Weight (kg)

1 FML 10 0.54

2 Composite 10 0.47

3 Steel 6 1.15

Table.2. Weight comparison

The comparison shows that FML beam is having less weight than the steel

beam and marginally higher weight than composite beam.

Conclusion

The optimum design for the fiber metal laminated beam is evaluated by

using various combinations of fiber and metal layers and also using different


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ply orientations and stacking sequences of the fiber layer.

The results of the analytical analysis are then validated with the finite element

analysis results. From these results following conclusions can be drawn;

1] The FML beam gives better results under given loading conditions

compared to steel beam.

2] Weight reduction of 53 % is achieved by using FML

3] Optimized FML beam is given by Set No1 for minimum Von-

Mises stresses (145.99 MPa) and moderate deflection (16.74 mm). In this Set

all fiber are oriented to 0 degree. But this may cause delamination. Whereas

Set 2 and set 6 shows close results and also uses 45 degree fiber orientation

with less chances of delamination as compared to set 1.

4] Variation in the both result is due to the type of theories applied in

both solvers (Analytical solver is based on Classical Lamination Theory

whereas FEA uses First Order Shear Deformation Theory)

Acknowledgement The authors acknowledge the financial grant received from BCUD, SPPU for

the year 2013-15.

References

[1] Edson C. Botelho, Mirable C. Rezende, Luis Claudio Pardini,

Hygrotermal effects evaluation using the iosipescu shear test for

glare laminates, J. of the Braz. Sco. Of Mech. Sci. & Eng, July-

September 2008, Vol, XXX, No. 3 / 213.

[2] F. L. Mathews and R. D. Rawlings, Composite Materials Engineering

Science, Chapman & Hall, London, 1994.

[3] H. Esfandiar, S. Daneshmand, “Analysis of Elastic-Plastic Behavior

of Fiber Metal Laminates Subjected to In-Plane Tensile

Loading”, International Journal Advanced Design and Manufacturing

Technology, Vol. 5, No. 1, December- 2011.

[4] J.J.C. Remmers, R. de Borst, “Delamination buckling of fiber–metal

laminates”, Composites Science and Technology 61, 2207–2213,

2001.

[5] A. Pourkamali Anaraki, G. H. Payganeh, F. Ashena ghasemi, A. Fallah,

“An Experimental Study on the Tensile Behavior of the Cracked

Aluminum Plates Repaired with FML Composite Patches”, World

Academy of Science, Engineering and Technology, Vol 6(1), 2012.

[6] B.S.Sugun, RMVGK Rao, and D V Venkatsubramanyam, “Cost

effective approach for the manufacture of fiber metal laminates”,

International conference on Aerospace science and technology, 26-28

June, 2008.

[7] ANSYS APDL Basic Analysis Guide, Release 15.0, November 2013


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