COMPOSITE HONEYCOMB CORE SANDWICH PLATE WITH FACESHEET

INDENTATION MODEL SUBJECTED TO LOW-VELOCITY IMPACT

SITI HASYYATI BINTI DRAHMAN

A project report submitted in partial fulfillment of the

requirements for the award of the degree of

Master of Engineering (Civil-Structure)

Faculty of Civil Engineering

Universiti Teknologi Malaysia

JANUARY 2015

iii

This project report is dedicated to my beloved parents.

iv

ACKNOWLEDGEMENT

I wish to express my deepest gratitude to ALLAH SWT, the Most Gracious

and the Most Merciful, for His blessings that enrich me with more health and

wisdom in completing this study on time.

I would like to express my sincere gratitude towards my supervisor, Dr.

Ahmad Kueh Beng Hong for his advices, guidance, supervision, motivation and

encouragement along the way in completing this project. Also, I am very thankful to

Mr Saddam Hussein Ali and Mr Kam Chee Zhou for their help and assistance during

this study.

I would also like to thank my father, Mr Drahman Amit, and my mother,

Mdm Fatimah Lau Abdullah, as well as my brothers and sisters for their continuous

encouragement, understanding, advices, and support. Last but not least, my thanks to

my friends, especially Siti Noordiana, Siti Nur Amiera and Firdaus, and also those

who help and support me during this study.

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ABSTRACT

The composite sandwich structures are applied in many engineering fields

due to their high strength and stiffness but lightweight properties. The purpose of

this study is to obtain the top facesheet indentation and strain failure of a fixed-end

composite sandwich plate with honeycomb core when it is subjected to low-velocity

impact by using MATLAB software. The faceheets are made from Hercules

AW193-PW prepreg consisting of AS4 fibers in a 3501-6 matrix (carbon/epoxy)

with fiber orientation of [0/90]. The honeycomb core is made from HRH 10 1/8-3.0

Nomex honeycomb (Ciba-Geigy). Type of the impactor used in this study is flat-

ended cylinder, which is made from case-hardened steel. The composite sandwich

plate is modeled as a two-dimensional problem with five and three degree-of-

freedom per node for the facesheets and honeycomb core, respectively. Only the

stiffness matrix, [ ], and the mass matrix, [ ], are considered in determining the

responses of the plate. The force is applied at the center of the plate only. Responses

in terms of indentation, strain failure and displacement are explored. It was found

that the most efficient stacking sequence of facesheet is [±45]. Also, the most

effective parameter in improving the strain failure of the top facesheet is crushing

resistance of the core.

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ABSTRAK

Struktur sandwic komposit banyak diaplikasikan dalam bidang kejuruteraan

kerana mempunyai kekuatan dan kekakuan yang tinggi serta ringan. Kajian ini

dilakukan bertujuan untuk mendapatkan lekukan di lapisan atas dan kegagalan

ketegangan pada plat sandwic komposit berteraskan heksagon yang hujungnya diapit

apabila terdedah kepada impak halaju rendah dengan menggunakan perisian

MATLAB. Lapisan atas dan bawah struktur sandwic komposit diperbuat daripada

prepreg Hercules AW193-PW yang terdiri daripada serat AS4 dalam matriks 3501-6

(karbon/epoksi) dengan orientasi serat [0/90]. Teras heksagon pula diperbuat

daripada HRH 10 1/8-3.0 Nomex heksagon (Ciba-Geigy). Jenis beban yang

digunakan dalam kajian ini adalah silinder yang rata pada hujungnya dan diperbuat

daripada keluli yang keras. Plat sandwic komposit dimodelkan sebagai masalah dua-

dimensi dengan lima darjah kebebasan bagi setiap nod untuk lapisan atas dan bawah,

manakala tiga darjah kebebasan bagi setiap nod untuk teras heksagon. Hanya

matriks kekukuhan, [ ] , dan matriks jisim, [ ] , yang dipertimbangkan dalam

memodelkan plat. Daya dikenakan di tengah plat sahaja. Variasi dalam parameter

lapisan atas dan bawah serta teras heksagon diperhatikan untuk mendapatkan tindak

balas plat. Tindak balas yang dikaji adalah dari segi lekukan, kegagalan ketegangan

dan anjakan. Kajian mendapati bahawa turutan lapis yang paling efisien untuk

lapisan atas adalah [±45]. Selain itu, parameter yang paling berkesan dalam

memperbaiki kegagalan ketegangan pada lapisan atas adalah ketahanan

penghancuran teras.

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TABLE OF CONTENTS

CHAPTER TITLE PAGE

DECLARATION ii

DEDECATION iii

ACKNOWLEGEMENT iv

ABSTRACT v

ABSTRAK vi

TABLE OF CONTENTS vii

LIST OF TABLES x

LIST OF FIGURES xi

1 INTRODUCTION 1

1.1 General 1

1.2 Problem Statement 3

1.3 Objectives 4

1.4 Scope of Study 4

1.5 Significance of the Study 5

1.6 Significance of the Study 5

2 LITERATURE REVIEW 7

2.1 General 7

2.2 Composite Sandwich Structures 7

2.2.1 Facesheets 8

2.2.2 Core 10

2.2.3 Advantages and Disadvantages 11

2.2.4 Failure Behaviour 12

2.3 Types of Impact/Loading 15

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2.4 Previous Researches 16

2.5 Conclusions 19

3 METHODOLOGY 20

3.1 General 20

3.2 Modeling 21

3.3 Analysis of Composite Sandwich Plate 23

3.4 Formulations of the Composite Sandwich Plate 25

3.4.1 Formulations for Facesheets Stiffness 26

3.4.2 Formulations for Honeycomb Core

Stiffness

32

3.4.3 Formulations for Composite Sandwich

Plate Stiffness

36

3.4.4 Computation of Mass Matrix 38

3.5 Boundary Condition 39

3.6 Formulation of the Composite Sandwich Plate

Displacement

40

3.7 Formulation of Indentation 42

3.8 Formulation of Strain Failure 43

3.9 An Overview of the MATLAB Source Code 46

4 RESULTS AND DISCUSSION 53

4.1 Introduction 53

4.2 Convergence Study 53

4.3 Source Code Verification 55

4.4 Strain Failure 56

4.5 Parametric Study for Facesheets 57

4.5.1 Number of Ply 57

4.5.2 Fiber Orientation 58

4.5.3 Ply Thickness 60

4.6 Parametric Study for Honeycomb Core 61

4.6.1 Core Thickness 62

4.6.2 Young’s Modulus of Core 62

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4.6.3 Crushing Resistance of Core 63

4.6.4 Relationship between Thickness and

Young’s Modulus of Core

64

4.6.5 Relationship between Crushing

Resistance and Thickness of Core

66

4.6.6 Relationship between Crushing

Resistance of Core and Ply Thickness

67

4.7 Improvement on Strain Failure 69

5 CONCLUSIONS AND RECOMMENDATIONS 75

5.1 Conclusions 75

5.2 Recommendations 76

REFERENCES 77

APPENDICES A – D 79

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LIST OF TABLES

TABLE NO. TITLE PAGE

3.1 The properties of the facesheets 21

3.2 The properties of honeycomb core 21

3.3 The properties of the impactor 22

4.1 Convergence study 54

4.2 The strain failure of lamina of the top

facesheet

57

4.3 Constant parameters for analysis of

relationship between thickness and

Young’s modulus of core

65

4.4 The ply thickness, and extensional

stiffness matrix, A11 of the top facesheet

69

4.5 The effect of number of ply of top

facesheet to the strain failure

71

4.6 The effect of ply thickness of the top

facesheet to the strain failure

72

4.7 The effect of crushing resistance of the core

to the strain failure

74

xi

LIST OF FIGURES

FIGURE NO. TITLE PAGE

1.1 Composite sandwich structure 1

2.1 Construction of Apollo capsule using

sandwich shells

8

2.2 Various types of fibers distribution 9

2.3 The laminate with different fibers

orientations

9

2.4 Examples of core layer of the composite

sandwich structure

10

2.5 Failures occur at the simply supported

sandwich panel

13

2.6 The sequences of damages that occur in

the sandwich plates for both thick and

thin core when subjected to low-velocity

impact

14

2.7 Indentation of a naval-type sandwich

plate with a polymeric foam core

14

2.8 Large and small mass impact with

different impact responses in composite

sandwich structure

15

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2.9 Verification of the damage initiation loads 17

2.10 Verification of the indentation force

against top facesheet deflection (load-

indentation curve)

18

2.11 The indentation force against top

facesheet deflection for different stacking

sequence

18

3.1 Model arrangement

21

3.2 Finite element analysis procedure for

composite sandwich plate with

honeycomb core under low-velocity

impact

24

3.3 The degrees-of-freedom per node for the

composite sandwich plate

25

3.4 Combination of plies to form a laminate

26

3.5 The distance between mid-planes of ply k

and composite sandwich plate

28

3.6 The process of the facesheets assembly

(2×2 discretised elements)

32

3.7 The process of the honeycomb core

assembly (2×2 discretised elements)

36

3.8 The formation of the global stiffness

matrix of the composite sandwich plate

(2×2 discretised elements)

37

3.9 Rearrangement of sub-elements nodes

from local to global stiffness matrix

37

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3.10 The nodes arrangement for global

stiffness matrix of composite sandwich

plate with 2×2 discretised elements

38

3.11 The side view of the indented composite

sandwich plate

44

3.12 The distance between mid-planes of ply k

and top facesheet

45

3.13 Input the engineering properties of the

composite sandwich plate

47

3.14 Stiffness matrix of the facesheets 48

3.15 Mass matrix of the facesheets 48

3.16 Stiffness matrix of the honeycomb core 49

3.17 Mass matrix of the honeycomb core 49

3.18 Global stiffness and mass matrices of the

composite sandwich plate

50

3.19 Boundary condition of the composite

sandwich plate

50

3.20 The computations of the impact force,

global displacement and indentation

51

3.21 The computation of the strain failure 52

4.1 The cross-section of the composite

sandwich plate subjected to the low-

velocity impact

54

4.2 Graph of the convergence study 55

4.3 Graph of contact force against indentation 56

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4.4 Graph of indentation/total thickness

against number of ply for [0/90]

58

4.5 Graph of indentation/total thickness

against number of ply for [0/90], [±60],

[±45] and [±15]

59

4.6 Graph of indentation against number of

ply for [0/90], [±60], [±45] and [±15]

60

4.7 Graph of indentation against ply thickness 61

4.8 Graph of displacement against core

thickness

62

4.9 Graph of displacement against young’s

modulus of core

63

4.10 Graph of indentation against crushing

resistance of core

64

4.11 Non-dimensional graph of d/L against

(Ec/A11)*h

65

4.12 Non-dimensional graph of δ/L against

(q/A11)*h

67

4.13 Non-dimensional graph of δ/L against

(q/A11)*

68

4.14 Graph of strain after impact against ply

thickness for first ply (0o)

72

4.15 Graph of strain after impact against

crushing resistance of core for first ply

(0o)

73

CHAPTER 1

INTRODUCTION

1.1 General

Composite structure is a combination of two or more components as one

structure which makes it better than that of individual components. A structure that

consists of two facesheets that are separated by a core is known as composite

sandwich structure (Figure 1.1). The facesheets are also known as composite skins.

The facesheets and core component are bonded by matrix/adhesive materials such as

resin. The core layer is usually made of lightweight and thick but less stiff materials,

such as Nomex honeycomb cores, fiberglass reinforced thermoplastic, aluminium

and foam-type cores. The top and bottom facesheets are commonly thin but stiff

material from light alloys, e.g., aluminium and fibre-reinforced composites (Chai and

Zhu, 2011).

Figure 1.1: Composite sandwich structure (Engineered Materials Inc., 2012)

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The application of composite sandwich structure is very beneficial in

engineering field especially in aircraft and aerospace industries. This is because of

their excellent properties, which are high in strength and stiffness as well as low in

weight (lightweight), e.g., the airplanes are mainly built from composite sandwich

structures. Besides that, this lightweight structure is widely used due to its cost

effectiveness and environmental friendly. For example, a vehicle fabricated from

lightweight structures will require less energy to move and indirectly consume less

fuel. This means that the use of lightweight vehicle will reduce environmental

impact as well as service cost of the vehicle. In construction field, the application of

composite sandwich structure is widely used in the lightweight construction.

The composite sandwich structures may expose to several types of impact

such as static impact, velocity impact, blast impact, quasi-static impact, vibration and

so on. These impacts will result in the damage of the structure and indirectly reduce

its strength. Different types of impact will result in different impact responses or

failures. One of the impact responses is indentation. Indentation can occur during

construction and maintenance of the structure. For example, the composite sandwich

structure may experience indentation due to the low-velocity impacts of tools drop,

machineries mishandling, heavy materials falls and so on (Hosseini and Khalili,

2013).

Velocity impact is divided into two types, i.e., low-velocity and high-velocity

impacts. Both impacts give different responses on the composite structures. In

presence of low-velocity impact, an apparent damage is observed in the structure, in

which the structural strength and stiffness may reduce by 50% (Ivanez and Saez,

2013). The low-velocity impact response of the composite structure can be

categorized on the basis of the impact mass, which are small, medium and large. The

larger mass impact will produce longer impact duration as well as larger

displacement. Chai and Zhu (2011) mentioned that the response of composite

structures due to small mass impact will result in larger delaminations than that of

large mass impact with the same kinetic energy.

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1.2 Problem Statement

The research on composite sandwich structure is usually done experimentally

or numerical modeling using application software, such as ANSYS, ABAQUS, etc.

Compared to those approaches, implementing MATLAB software is more efficient.

This is because the application of MATLAB software is time and cost effective

compared to the experimental study. Also, the application of finite element method

in MATLAB software can enhance the basic fundamental and knowledge of those

who studied on that particular research compared to the use of the application

software.

So far, not many researches consider indentation in composite sandwich

plate. Although there was a study on indentation of composite sandwich plate, but it

did not consider the strain failure of the structure. Strain failure is related to the

indentation in determining the failure of the structure in terms of strain. The

occurrence of indentation on the composite sandwich plate does not mean that there

will necessarily be a failure in strain. Hence, in this research, the main concerns

include:

(i) The formulation that can be used to model the composite sandwich plate.

(ii) The verification of the composite sandwich plate with the model from

previous research using MATLAB software.

(iii) Investigation on strain failure, indentation and global displacement of

composite sandwich plate.

(iv) Parametric studies on composite sandwich plate.

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1.3 Objectives

The objectives of this research are:

(i) To obtain the finite element formulation of composite sandwich plate with

facesheet indentation description under low velocity impact.

(ii) To produce the MATLAB code for aforementioned formulation and verify it

with the existing model.

(iii) To conduct parametric study on indentation and global displacement for

numerous facesheet stacking sequences and core properties.

1.4 Scope of Study

The followings are the scopes of the study:

(i) Formulation for composite sandwich plate considers only the core with a

honeycomb layout.

(ii) MATLAB software is used as the programming language.

(iii) Only point load at the center of the plate is considered.

(iv) Only low-velocity impact responses are considered.

(v) The impact responses that will be discussed are only global displacement,

indentation and strain failure.

(vi) Only flat-ended cylinder impactor is considered.

(vii) Only one type of materials of facesheets and honeycomb core are analysed.

(viii) Only fixed-end composite sandwich plate is considered.

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1.5 Significance of the Study

The application of composite sandwich structure has been widely used since

many years ago. Many researches on the composite sandwich structure have been

conducted experimentally and numerically. The purposes of these researches are to

understand the behaviours and failure mechanisms of the composite sandwich

structure as well as to improve it. Numerical analysis is used worldwide since it is

more economical and not time-consuming. Besides that, the behaviours and failure

mechanisms of the composite sandwich structure can be obtained before

manufacturing it. And, the parametric study can be done in a much easier way.

The indentation on the composite sandwich structure due to the low-velocity

impact can be very small or very large or even penetrate through the composite

sandwich plate. Although the indentation is very small, it may also experience the

local strain failure. The local strain failure is obtained in order to know whether the

indented part is failed or not. If the indented part is failed, further impact on it will

make the damaging of the composite sandwich structure more severe. Hence, it is

necessary to conduct analysis considering simultaneously both indentation and strain

failure together.

1.6 Report Outline

The main topic in this report consists of five categories namely introduction,

literature review, methodology, results and discussion, and conclusion.

Chapter 1 introduces the main topic for this report generally. The problem

statement, objective and scope of work are explained in this chapter.

6

Chapter 2 explains more on composite sandwich structures including their

advantages and disadvantages. Besides that, this chapter includes several previous

researches that are related to the composite sandwich structures.

Chapter 3 is devoted to research methodology. The model of composite

sandwich plate used in the analysis will be discussed in detail in this chapter. All the

formulations that will be used in the analyses will also be gathered in this chapter.

Also, an overview of MATLAB source code will be included here.

Chapter 4 includes all the results obtained from the MATLAB software. The

discussion on MATLAB result verification with previous study as well as the strain

failure and parametric study of composite sandwich plate will be covered in this

chapter.

Chapter 5 covers the conclusion and recommendation. All the results will be

concluded in this chapter. The conclusion is made with respect to the objectives of

this report. The recommendation for future research is also outlined in this chapter.

REFERENCES

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velocity impact on sandwich panels with honeycomb core and comparison

with F.E.M results.

Bazant, Z.P., Gattu, M. and Vorel, J. (2012). Work conjugacy error in commercial

finite-element codes: its magnitude and how to compensate for it,

Proceedings A, vol. 471, 2174.

Chai, G.B. and Zhu, S. (2011). A review of low-velocity impact on sandwich

structures, Proceedings of the Institution of Mechanical Engineers, Part L:

Journal of Materials Design and Applications, 207-230.

Davies, J.M. (2001). Lightweight Sandwich Construction. London: Blackwell

Science Ltd.

Engineered Materials Inc. (2012). Structural composites and sandwich panels.

Retrieved Dec 27, 2014, from

http://www.engineeredmaterialsinc.com/products/structural-composites-and-

sandwhich-panels/

Foo, C.C., Seah L.K. and Chai, G.B. (2007). A model to predict low-velocity impact

response and damage in sandwich composites, Composite Science and

Technology, vol. 68, 1348-1356.

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Hoo Fatt, M.S. and Park, K.S. (2001). Dynamic models for low-velocity impact

damage of composite sandwich panels – Part B: Damage initiation.

Composite Structure, vol. 52, 353-364.

Hosseini, M. and Khalili, S.M.R. (2013). Analytical prediction of indentation and

low-velocity impact responses of fully backed composite sandwich plates.

Journal of Solid Mechanics, vol 5, 278-289.

Ivanez, I. and Saez, S.S. (2013). Numerical modelling of the low-velocity impact

response of composite sandwich beams with honeycomb core, Composite

Structures, vol. 106, 716-723.

Jones, B. (1985). Design, Fabrication and Mechanics of Composite Structures.

United States of America: Technomic Publishing Company, Inc.

Meidell, A. (2009). Minimum weight design of sandwich beams with honeycomb

core of arbitrary density. Composites: Part B, vol 40, 284-291.

Reddy, J.N. (2004). Mechanics of Laminated Composite Plates and Shells: Theory

and Analysis. United States of America: CRC Press LLC.

Williamson, J.E. and Lagace, P.A. (1993). Response mechanism in the impact of

graphite/epoxy honeycomb sandwich panels.