(FML), Steel and Composite Beams

12 Pages·2017·0.44 MB·English

International Journal of Pure and Applied Mathematics
Volume 114 No. 11 2017, 325-335
ISSN:1311-8080(printedversion);ISSN:1314-3395(on-lineversion)
url:http://www.ijpam.eu
SpecialIssue
ijpam.eu

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 F1M L. 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.

325
International Journal of Pure and Applied Mathematics Special Issue
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.

[1]
Figure 1: FML Layup
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
2
be sensitive to delamination buckling, which occurs when a partially
delaminated panel is subjected to a compressive force.

326
International Journal of Pure and Applied Mathematics Special Issue
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. 3
Fiber Angle Orientations and stacking sequence for different Sets.

327
International Journal of Pure and Applied Mathematics Special Issue
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
4
-6.26646E-08 2.80628E-07 0.00000E+00
0.00000E+00 0.00000E+00 3.58566E-07

328
International Journal of Pure and Applied Mathematics Special Issue
Deflection Max (mm) = 19.9172 mm
As mentioned above ABD Matrix, Inverse ABD Matrix and deflection
were obtained and mentioned in the following table.

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

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 ana5l ysis 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

329
International Journal of Pure and Applied Mathematics Special Issue
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.
6

330
International Journal of Pure and Applied Mathematics Special Issue

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.

7

331
International Journal of Pure and Applied Mathematics Special Issue

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.
8

332
International Journal of Pure and Applied Mathematics Special Issue

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. Laminate/Bea Thickness,
Weight (kg)
No m mm
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
9
The optimum design for the fiber metal laminated beam is evaluated by
using various combinations of fiber and metal layers and also using different

333
International Journal of Pure and Applied Mathematics Special Issue
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. 10
[7] ANSYS APDL Basic Analysis Guide, Release 15.0, November 2013

334