Low velocity impact behavior of fiber metal laminates

LOW VELOCITY IMPACT BEHAVIOUR

OF FIBER METAL LAMINATES

A PROJECT REPORT

Submitted by

CB.EN.U4AEE09002 ADARSH HARIPRASAD

CB.EN.U4AEE09019 MANOJ SHANMUGHOM

CB.EN.U4AEE09027 NIKHIL MOHAN

CB.EN.U4AEE09061 LALITYA DHAVALA

In partial fulfillment of the award of the degree of

BACHELOR OF TECHNOLOGY

IN

DEPARTMENT OF AEROSPACE ENGINEERING

This is to certify that the thesis entitled ‘LOW VELOCITY IMPACT BEHAVIOUR OF

FIBER METAL LAMINATES’ submitted by

CB.EN.U4AEE09002 ADARSH HARIPRASAD

CB.EN.U4AEE09019 MANOJ SHANMUGHOM

CB.EN.U4AEE09027 NIKHIL MOHAN

CB.EN.U4AEE09061 LALITYA DHAVALA

In partial fulfillment of the requirement for the award of the Degree of Bachelor of Technology

in AEROSPACE ENGINEERING is a bonafide record of the work carried out under my

guidance and supervision at the Amrita School of Engineering, Ettimadai, Coimbatore

(SIGNATURE)

Dr. V. Sivakumar

(Project Guide)

Associate Professor

Department of Aerospace Engineering

This report was evaluated by us on :

INTERNAL EXAMINER EXTERNAL EXAMINER

AMRITA VISHWA VIDYAPEETHAM

AMRITA SCHOOL OF ENGINEERING, COIMBATORE - 641105

DEPARTMENT OF AEROSPACE ENGINEERING

DECLARATION

We, ADARSH HARIPRASAD (CB.EN.U4AEE09002), MANOJ SHANMUGHOM

(CB.EN.U4AEE09019), NIKHIL MOHAN (CB.EN.U4AEE09027) and LALITYA DHAVALA

(CB.EN.U4AEE09061) hereby declare that this project report entitled ‘LOW VELOCITY

IMPACT BEHAVIOUR OF FIBER METAL LAMINATES’ , is a record of original work done

by us under the guidance of Dr. V. Sivakumar, Associate Professor, Department of Aerospace

Engineering, Amrita School of Engineering, Coimbatore. This work has not formed the basis of

any degree/ diploma/ fellowship or a similar award to any candidate in any university, to the best

of our knowledge.

ADARSH HARIPRASAD

MANOJ SHANMUGHOM

NIKHIL MOHAN

LALITYA DHAVALA

Place: Coimbatore

Date:

COUNTERSIGNED:

( SIGNATURE)

Dr. V. Sivakumar

( Project Guide )

Associate Professor

Department of Aerospace Engineering

Amrita School of Engineering

Ettimadai , Coimbatore.

i

ACKNOWLEDGEMENT

Firstly, we express our sincere thanks to Dr.J.Chandrasekhar, Chairman, Department of

Aerospace Engineering, for giving us an opportunity to do this project.

Then, we express our heartfelt gratitude to our project guide, Dr. V. Sivakumar, Associate

Professor, Department of Aerospace Engineering. The motivation and inspiration that he

provided to us were just an added benefit to the invaluable guidance and support that he has

given throughout the duration of the project. He has kindly cleared all the doubts and queries that

we had without which we wouldn’t have been able to complete this project.

We thank the entire faculty who have supported us with immense knowledge and helped us

always.

We are also grateful to our friends and parents who were always there for us with encouraging

words and generous wisdom.

Finally, we thank the Almighty, who though in different forms, has showered us with His

blessings, strength and courage to complete this project.

ii

ABSTRACT

Fiber Metal Laminates are a class of hybrid composites which are layers of metal and fibre

reinforced composites stacked alternatively together. These materials are being increasingly used

in the aircraft industry in the form of fuselage skins, wing skins and cargo floors. Impact loading

behaviour has to be analyzed because it forms an important load factor on the cargo floors.

The main objective of this project was to analyze the behavior of a FML under low velocity

impact load. For this, a FML of Aluminum/ Glass Fiber Reinforced Polymer/Aluminum was

considered and modeled in ABAQUS. Pre-processing, analysis and post processing were

performed in ABAQUS CAE itself. The study was repeated for different orientations of the

fibers of GFRP and the results were compared.

The stress variation across the thickness for all the three configurations considered was studied.

Then using appropriate failure criteria, the maximum load that can be taken by the FML plate

was compared to the maximum load that the pure metal plate can sustain. It was found that FML

offers higher strength to weight ratio. This result was then extended to find the maximum weight

of the projectile that can be dropped onto a hypothetical cabin floor made of the FML

considered.

iii

TABLE OF CONTENTS

ACKNOWLEDGEMENT i

ABSTRACT ii

TABLE OF CONTENTS iii

LIST OF FIGURES v

LIST OF TABLES vi

LIST OF SYMBOLS AND NOTATIONS vii

1. INTRODUCTION 1

1.1 BACKGROUND INFORMATION 1

1.2 FIBER METAL LAMINATES 2

1.3 IMPACT LOADING 5

2. LITERATURE REVIEW 8

3. FINITE ELEMENT MODELLING 9

3.1 INTRODUCTION TO FINITE ELEMENT ANALYSIS 9

3.2 VALIDATION OF ABAQUS RESULTS FOR THE PRESENT 10

CASE

3.3 MODELLING OF FML IN ABAQUS 13

3.4 STRESS VARIATION IN FML 15

3.5 FAILURE CRITERIA MODELLING 16

4. RESULTS AND DISCUSSION 18

4.1 MAXIMUM STRESS EXPERIENCED BY THE FML 18

4.2 FAILURE BEHAVIOUR 19

4.3 COMPARISON OF ALUMINIUM vs. FML 20

4.4 APPLICATION 21

4.5 LIMITATIONS 21

iv

5. CONCLUSION 22

6. REFERENCE viii

7. APPENDIX x

v

LIST OF FIGURES

Fig 1.1 Usage of composites in aircrafts 1

Fig 1.2 Fiber Metal Laminates 2

Fig 1.3 Impact behavior of GLARE 2

Fig 1.4 Improved fatigue behavior of GLARE 3

Fig 1.5 Residual strength diagram of aluminum 3

Vs. GLARE

Fig 1.6 Usage of different types of composites 5

in the aircraft industry

Fig 1.7 Use of FMLs in A380 5

Fig 1.8 Areas on aircraft where impact loading 6

has to be investigated

Fig 3.1 Deformed shape of Aluminum plate 10

Fig 3.2 Deformed shape of GFRP plate 11

Fig 3.3 (a) Specimen of FML used 13

Fig 3.3(b) Layup depicting two aluminum layers 14

and one GFRP layer

Fig 3.4 Variation of stress across thickness 16

Fig 4.1 von Mises stress distribution of FML 18

Fig 4.2 Specimen made of Aluminum 19

Fig 4.3 S11 stress variation across thickness of 20

three different configurations considered

Fig 4.4 S13 stress variation across thickness of 20

three different configurations considered

vi

LIST OF TABLES

Table 1.1 Mechanical Properties of GLARE 4

Table 1.2: Range of velocities of projectile impact 6

Table 3.1: Table depicting stress values at different values 15

of thickness

Table 4.1: Results of the stress analysis 18

Table 4.2: Comparison of strength of Aluminium and FML 19

plates

vii

LIST OF SYMBOLS AND ACRONYMS

Al Aluminium

ARALL Aramid Aluminium Laminate

CFRP Carbon Fiber Reinforced Polymer

FML Fiber Metal Laminate

FRP Fiber Reinforced Polymer

GLARE Glass Laminate Aluminium Reinforced Epoxy

GFRP Glass Fiber Reinforced Polymer

a side of the plate m

g acceleration due to gravity ms-2

h height m

i , j material direction ( i , j = 1,2,3)

p Momentum kgms-1

q Load applied Pa

t Thickness m

v velocity ms-1

Deflection m

A Area m2

D Flexural rigidity of plate Nm

E Young’s Modulus Pa

F Force applied N

G Shear modulus Pa

M Mass kg

Q1* Equalent Flexural rigidity Nm

Strength of the stress along different material direction Pa

Stress along the material direction Pa

υ Poisson’s ratio

1

CHAPTER 1

INTRODUCTION

1.1 Background information:

Composite materials or composites, in short, are a combination of two or more materials

whose properties vary from the properties of its constituents. Examples of composite

materials are fibre reinforced polymers, ceramic composites and metal composites. Today

composites are extensively used in various industries such as construction, heavy structures

such as bridges and ships, race car bodies but the most advanced applications have been in

the aerospace industry. This has been attributed to their high strength to weight ratio, lesser

maintenance costs, improved corrosion resistance, better fatigue resistance, lesser thermal

expansion and tailor-able mechanical properties. The most commonly used composites in

aerospace are Fibre reinforced polymers of several types, like CFRP (Carbon FRP) and

GFRP (Glass FRP) .

Figure 1.1: Usage of composites in aircrafts[1]

The graph above shows the increase in use of composites in the aircraft industries. Though

initially used only in military and business class aircrafts, the trend shows increasing usage of

composites across all domains of aircraft industry. It is predicted that the next generation

narrow-body transport aircraft will contain more than half of its structural weight as

2

composites. Currently, the Boeing 787 Dreamliner is the aircraft with maximum usage of

composites.

1.2 Fiber Metal Laminates:

Fibre Metal Laminates are a special class of composites known as hybrid composites. Hybrid

composites contain pure metal paired with already existent composite materials.

Figure 1.2: Fiber Metal Laminates[2]

Fibre metal laminates are a pairing of fibre reinforced composites and metal laminates. They

consist of several layers of varying layups and orientations, designed to offer higher strength

and fatigue tolerance than existing metals. Typical FML includes several layers of aluminium

and glass fibre reinforced composites stacked alternatively and this combination is known as

GLARE (GLass Reinforced). This material is proven to have improved fatigue

characteristics, good fire resistance, good resistance to impact and improved damage

behaviour when subjected to impact than conventional metals for a lesser weight. This is

illustrated in the following figures.

Figure 1.3: Impact behaviour of GLARE[8]

3

Figure 1.4: Improved fatigue behaviour of GLARE[8]

Figure 1.5: Residual strength diagram of aluminum vs. GLARE[8]

4

Table 1.1 : Mechanical properties of GLARE[8]

Commonly used in aircrafts, aluminum 2024 has a maximum tensile strength of 200-470

MPa and maximum yield strength of no more than 96-280 MPa, depending on the temper and

the type of alloy being used.[3]

Thus, from the above tabulation, it can be observed that

GLARE offers higher strength. These properties make FML an excellent choice for aircraft

structures where the need to reduce weight is directly translated into significant cost savings.

They are typically used for the skin of primary structures such as fuselage and wings and for

smaller applications like cargo floors, engine cowlings and stringers.

In 1982, the first commercial FML was produced under the name ARALL( Aramid

Reinforced Aluminum Laminates). Though GLARE was patented first in 1987, it was

commercially used in aircrafts only in 2005 and more recently on the A380 and B787.

5

Figure 1.6: Usage of different types of composites in the aircraft industry[1]

Figure 1.7: Use of FMLs in A380 [2]

1.3 Impact loading:

It has been observed that two- thirds of the aircraft accidents in Canada in the seventies

occurred within narrow speed ranges during take-off and landing. This can be safely extended

to other aircraft as well. For example, runway debris caused impact loading on a Concorde

aircraft resulting in its infamous explosion and 113 deaths.

6

When crash data was throughout the world was analysed, low to medium velocity impact

loads were the most prominent ones.

Table 1.2: Range of velocities of projectile impact[10]

Description Energy

(J)

Mass

(g)

Velocity

(m/s)

Circumstances

Tool drop 6 330 6 Maintenance work

Removable element drop 4 220 6 Cargo handling

Maintenance component 16 910 6 Maintenance work

Hail(up to 51 mm diameter) 43 62 37.3 Take-off and landing,

flight, taxiing

Bird strike 3.8-81(kJ) 1800 65-300 Take-off and landing,

flight, taxiing

Runway debris 2-40 9 20-94 Take-off and landing,

flight, taxiing

Concentrated load 50 - Static Maintenance cargo

handling

Figure 1.8: Areas on aircraft where impact loading has to be investigated[9]

Thus, it can be inferred that impact studies are necessary for any material being used in

aircraft. This is why it had been decided to study the low velocity (up to 20m/s) impact

behaviour of fibre metal laminates.

7

This study can be broadly performed in three categories:

1. Experimental study- most common. Numerous studies have been done on the low

velocity impact behaviour of different types of fibre metal laminates, generally using

drop weight impact apparatus and different specimens and impactors. Due to cost

limitations, this approach was not an option to a bachelors’ level project.

2. Analytical study-a failure model for the FML is proposed and compared with

experimental approach. Though many papers have been published in this area, there

has been no officially identified failure model for FML yet.

3. Numerical analysis- this is mainly through finite element analysis using soft-wares

like ABAQUS and LS-DYNA. ABAQUS Implicit was chosen for this project and

FML layers have been modelled in it.

8

CHAPTER 2

LITERATURE REVIEW

Several papers on the analysis of FML were studied and an overview of the current research

development in this field is presented below.

Studies on energy distribution in GLARE and 2024-T3 aluminium during low

velocity impact were conducted by F.D. Morinière, R.C. Alderliesten, and R.

Benedictus [4]

and in this; an analytical model was developed to predict the impact

behaviour of FMLs. Also, absorbed energy, impact force, maximum deflection and

impact velocity were predicted within 5% of test results. The conclusion of the papers

is that GLARE 5-2/1-0.4 is 72% more resistant than its monolithic 2024-T3

aluminium counterpart of the same thickness.

Studies on the low velocity impact resistance of aluminium/carbon-epoxy fibre metal

laminates were conducted by Jarosław bieniaś and Patryk jakubczak[5]

. This study

researches the resistance to low-velocity impact of hybrid laminates based on

aluminium alloys and a carbon/epoxy composite (Al/CFRP).The inter-relation

between the damage zone area, maximum depth of the deformation and the layer

configurations and energy level was investigated. It was noted that Al/CFRP

laminates have high impact damage resistance (at low-velocity) because of the

superior properties of both metals and fibrous composite materials with strong

adhesion bonding. In particular the FML with (0/90) ply sequence in the carbon fibre

was observed to have the best behaviour.

Numerical modelling of low-velocity impact damage in fibre-metal-laminates was

done by Jeremy Laliberté and Cheung Poon and Paul. V. Straznicky[9]

. The most

important part of this paper was the development of a user defined material subroutine

in LS-DYNA for the FRP in one type of FML and it was hence showed that

delamination is not a critical damage mode in FMLs under low velocity impact loads.

Low-velocity impact response of fibre–metal laminates was studied by both

experimental approach and finite element analysis by Shengqing Zhu and Gin Boay

Chai.[11]

The impact dynamic response and failure modes of fibre–metal laminated

panels subjected to low velocity impact were investigated and presented. The

experiments were conducted using a standard drop-weight test machine and the finite

element analysis was carried out using ABAQUS.

9

CHAPTER 3

FINITE ELEMENT MODELLING

3.1 Introduction to Finite Element Analysis:

Finite Element Analysis (FEA) was first developed in 1943 by R. Courant, who utilized

the Ritz method of numerical analysis and minimization of variational calculus to obtain

approximate solutions to vibration systems.

In practice, a finite element analysis usually consists of three principal steps:

Pre-processing: The user constructs a model of the part to be analysed in which the

geometry is divided into a number of discrete elements connected at discrete points

called nodes. This can be constructed using commercially available soft wares like

CAD, Hypermesh etc.

Analysis: The dataset prepared by the pre-processor is used as input to the finite

element code itself, which constructs and solves a system of linear or nonlinear

algebraic equations

Kijuij=fi

where u and f are the displacements and externally applied forces at the nodes.

The formation of the K matrix is dependent on the type of problem. Commercial codes

may have very large element libraries, with elements appropriate to a wide range of

problem types. One of FEA's principal advantages is that many problem types can be

addressed with the same code, merely by specifying the appropriate element types from

the library.

Post processing: A typical post-processor display overlays colored contours

representing stress levels on the model, showing a full-fledged picture similar to that of

photo-elastic or more experimental results.

10

3.2 Validation of ABAQUS results for the present case:

Case 1: A rectangular plate made of aluminium was modelled in ABAQUS and a uniformly

distributed load of 10Pa was applied to it under fixed- fixed boundary conditions. The plate

was analysed and maximum deflection was found to be 1.975*102 mm.

Figure 3.1: Deformed shape of aluminium plate

This was compared to the theoretically predicted maximum deflection for this case through

the use of theory of elasticity.

Flexural rigidity,

Where E is the Young’s modulus of Aluminum, 70 GPa

11

t is the thickness of aluminum plate, 3mm

υ is the Poisson’s ratio of Aluminum, 0.3

Maximum deflection,

Where q is the applied load, 10 Pa

a is the side of the plate, 100 mm

The error between the numerical and theoretical calculation was found to be 0.5%.

Case 2: A rectangular plate made of GFRP was modelled in ABAQUS and a uniformly

distributed load of 10Pa was applied to it under fixed- fixed boundary conditions. The plate

was analysed and maximum deflection was found to be 6.921*102 mm.

Figure 3.2 : Deformed shape of GFRP plate

This was compared to the theoretically predicted maximum deflection for this case through

the use of theory of elasticity.

12

Flexural rigidity,

D1 = νDx = 466.893 Nmm

Dxy = D(1-ν/2) =739.247 Nmm

Effective torsional rigidity, H=D1+2Dxy =1945.388 Nmm

Equivalent rigidity,Q1*

Deflection,

The error between the numerical and theoretical calculation was found to be 4.62%.

CONCLUSION: ABAQUS results were validated for the case in consideration and this can

be extended to the modeling of FML plates.

13

3.3 Modeling of FML in ABAQUS:

The FML plate was modelled in ABAQUS as follows:

Figure 3.3(a): Specimen of FML used

Preprocessing

Part: Rectangular, 300x300x3mm

Section: Solid, Composite Layup

Materials: Aluminium, GFRP

Analysis

Mesh: Uniform,square, 5x5 mm

Load:40.6 MPa in time step of 0.1s

Boundary conditions: Fully fixed

14

Figure 3.3(b): Layup depicting two aluminum layers and one GFRP layer

Material properties were defined as follows:

FOR ALUMINUM: The material is isotropic, which means that its material properties

remain constant along all directions. Only the elastic behavior was considered and the

material data were given as: Young’s Modulus E= 70000Mpa and Poisson’s ratio

ν=0.3.

FOR GFRP: The material is orthotropic; its properties vary according to the

orientation of its fibers. Only elastic behavior was considered and Engineering

Constants were used to define the material behavior.

E1 = 24000, E2 = 22000, E3 = 22000(all units in MPa)

ν12 = 0.24,ν13 = 0.24,ν23 = 0.24

G12 = 4500, G13 = 4500, G23 = 4500(all units in MPa)

15

3.4 Stress variation in FML:

The stress variation across the thickness of the FML was investigated using a static

concentrated load. This calculation was repeated for various layups with different 0/0/0,

0/45/0 and 0/90/0, i.e. the orientation of the fibers in GFRP is changed.

Then the stress value at each thickness of the specimen is tabulated according to the values

given by ABAQUS output requests.

Table 3.1: Stresses at different thickness for different configurations

Thickness (mm)

Stress for the

configuration, 0/0/0

(MPa)

Stress for the

configuration , 0/45/0

(MPa)

Stress for the

configuration, 0/90/0

(MPa)

1.5 -97.7631 -97.6623 -97.6638

1.4 -84.6475 -84.5591 -84.5583

1.3 -71.8099 -71.7364 -71.7326

1.2 -58.9798 -58.9221 -58.9154

1.1 -46.1653 -46.1237 -46.1141

1 -33.3705 -33.3455 -33.3329

0.9 -20.5964 -20.5882 -20.5725

0.8 -7.84094 -7.84991 -7.83093

0.7 4.89996 4.87373 4.896

0.6 17.6317 17.5882 17.6138

0.5 30.3605 30.2997 30.3286

0.4 43.0923 43.0142 43.0464

0.3 55.8328 55.7376 55.7732

0.2 68.5873 68.4746 68.5141

0.1 81.3598 81.2293 81.2735

0 94.2478 94.0996 94.1495

16

These results can be plotted in a graph as follows:

Fig 3.4: Variation of stress across thickness

From the above, it is clearly seen that the pattern follows the typical stress variation curve of

an elastic material.

3.5 Failure criteria modelling:

Failure criteria have to be considered for the metal and composite separately.

For aluminium, the von Mises damage criteria can be used which can be stated as

follows:

Where 1,2 and 3 refer to the body axes.

For GFRP, the damage has to be addressed as a combination on matrix failure and

fibre failure. When the matrix cracks, the failure of the laminate starts. Then the first

fibre breaks and it propagates to all the nearby fibres. The laminate loses its load

carrying capacity. Also interlaminar damage has to be considered for multi-ply

composites.

Hashin damage criteria is used to evaluate the behaviour of GFRP.

17

Absolute

If ≥ 0, then the Tensile Fibre Failure Criterion is:

(

)

(

)

If < 0, then the compressive Fibre Failure Criterion is:

(

)

If ≥ 0, then the Tensile Matrix Failure Criterion is :

(

)

(

)

If < 0, then the compressive Matrix Failure Criterion is :

(

)

*(

)

+

(

)

In an FML, the aluminium is responsible for the impact loading whereas the GFRP is

responsible for carrying the tensile loading. Thus, it is sufficient that aluminium is tested for

failure against an impact loading.

18

CHAPTER 4

RESULTS AND DISCUSSION

4.1 Maximum stress experienced by the FML

Case 1: The modelled FML was analysed for maximum stress and maximum displacement

before failure. This was repeated for three different orientations.

Figure 4.1: von Mises stress distribution of FML

The results are tabulated as follows:

Table 4.1: Results of the stress analysis

FML LAYUP MAXIMUM DISPLACEMENT(mm)

MAXIMUM STRESS(MPa)

0/90/0 3.977 336.3

0/0/0 3.978 336.5

0/45/0 3.981 337.3

Case 2: A specimen made entirely of aluminum with the same dimensions as the FML was

also analyzed. Its yield strength was found to be 414 MPa.

19

Figure 4.2: Specimen made of Aluminum

4.2 Failure behaviour:

Since aluminium is the component responsible for carrying the impact load, the mises stress

experienced by the FML is compared with the maximum strength of aluminium. It is found

that the stress experienced is far lesser than that experienced by pure aluminium.

Table 4.2: Comparison of strength of Aluminum and FML plates

FML LAYUP S11(MPa) S13(MPa)

TENSILE STRENGTH of

Al(MPa)

RESULT SHEAR STRENGTH of

Al(MPa)

RESULT

0/90/0 428

234.158 246

130.253

0/0/0 234.324 130.203

0/45/0 234.743 130.356

20

Figure 4.3: S11 stress variation across thickness of three different configurations considered

Figure 4.4: S13 stress variation across thickness of three different configurations considered

4.3 Comparison of aluminium vs. FML:

Through trial and error approach, we found that:

Maximum load Aluminium plate can withstand without failure= 40.6 MPa

Maximum load FML plate can withstand without failure = 50.05 MPa

This clearly indicates that FML withstands higher load.

Increase in load bearing capacity of the material = (50.05-40.6)/ 40.6 = 23.3%

We know that

Density of GFRP = 1.8g/cm3

Density of aluminium= 2.7 g/cm3

From the specimen volume, we find

Mass of aluminium plate= 270g

Mass of FML plate = 189g

21

Reduction in weight by the use of FML= (270-189)/270 =11.11%

This clearly shows that FML has a higher strength-to-weight ratio than aluminium.

4.4 Application:

This result was extended to the real time case of cargo falling on the floor deck inside the

passenger cabin

Assuming the smallest area on which load is applied, A = 1cm2

Force , F = P x A= 50.05 x 1x10-4

x 106 = 5005 N

Time of impact, t =0.1s

Change in momentum, Δp = F x t = 5005 x 0.1 = 500.5 kgms-1

Considering the height from which the weight is dropped to be 2 m( average cabin height ),

Velocity of the load at the time of impact = √ = √ = 6.264 ms-1

p = M x v

M =

=

Thus 80 kg is the maximum weight that can be dropped onto the FML from a height of 2 m.

Beyond this weight, the FML will fail because it exceeds the yield strength of aluminium.

4.5 Limitations:

1) Delamination effects in the FML were not considered.

2) Only elastic portion of the material properties was used to find the yield strength.

3) Complete momentum transfer was assumed when the impactor hits the FML.

22

CHAPTER 5

CONCLUSION

A study was done on the low velocity impact behaviour of Fibre Metal Laminates. A simple

layup of Al/GFRP/Al was considered and modelled in ABAQUS. The maximum stress

experienced by the FML was compared against the yield strength of the constituent materials

to find the maximum impact load that the FML can sustain without failure.

After a thorough study of the current research developments in this field, it was decided to go

for the numerical analysis approach due to the limitations of a bachelors’ level project.

The approach of ABAQUS analysis used was validated by the use of theoretical comparison.

Then the FML was modelled in ABAQUS and stress variation across the thickness of the

plate was plotted. It was observed to be behaving like a typical elastic material.

From this, using the failure criteria condition, the maximum stress that the FML can take

without failure was found. This was repeated for three different configurations/ orientations

viz. 0/0/0, 0/45/0, 0/90/0. It was found that the orientation of the fibres of GFRP did not have

a marked significance in the maximum stress that can be applied.

The maximum load that can be taken by the aluminium in the FML before failure was found

to be 50.05MPa and from this, the maximum weight of a projectile that can be dropped onto

the FML was found. It was seen that a weight of 80 kg can be dropped onto the FML from a

height of 2 m without any significant damage to itself.

This height of 2 m is the average height from the cabin floor to the overhead stowage bins in

an aircraft. However the maximum weight of carry-on baggage allowed internationally is

always equal to or less than 10 kg per person, indicating the use of a high factor of safety.

viii

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1) Tomblin J., Overview of Composite Material Trends in Aviation Manufacturing, National

Institute of Aviation Research, Wichita State University

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University of Technology, www.tudelft.nl

3) Aluminum 2024, Wikipedia-the free encyclopedia

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and 2024-T3 Aluminum during low velocity impact, 28th

International Congress of

aeronautical sciences , Delft University of Technology, 2012

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x

APPENDIX

CALCULATION FOR MAXIMUM DEFLECTION OF ALUMINIUM RECTANGULAR

PLATE WITH FIXED EDGES UNDER UNIT LOAD AT THE CENTER :

α = 0.0056

Load, P = 1N

Side of plate, a = 100 mm

Young’s modulus, E =70 GPa

Poisson’s ratio, = 0.3

Flexural rigidity,

= 6410.256 Nmm

Deflection,

w= 8.736E-03 mm

Result from abaqus, w= 8.748E-03 mm

Analytical Numerical Error

Deflection 8.736E-03 8.748E-03 0.14%

MAXIMUM DEFLECTION OF ALUMINIUM RECTANGULAR PLATE WITH FIXED

EDGES UNDER UNIFORMLY DISTRIBUTED LOAD OF 10PA :

Load ,q =10Pa

a=100mm

Flexural rigidity,

= 6410.256 Nmm

= 1.965E02 mm

xi

Analytical Numerical Error

Deflection 1.965E02 1.975E02 0.5%

MAXIMUM DEFLECTION OF GFRP RECTANGULAR PLATE WITH FIXED EDGES

UNDER UNIFORMLY DISTRIBUTED LOAD OF 10PA :

Load, = 10Pa

Side , a = 100mm

Aspect ratio , c = b/a = 1

= 0.24

Flexural rigidity,

= 2122.24 Nmm ;

= 1945.388Nmm

D1 = = 466.893 Nmm

Dxy = D(1- = 739.247 Nmm

Effective torsional rigidity, H=D1+2Dxy =1945.388 Nmm

Equivalent rigidity, = 7 = 36254.948 Nmm

Deflection,

= 6.599E02mm

Analytical Numerical Error

Deflection 6.599E02 6.921E02 4.6%