FINITE ELEMENT METHOD MODELING FUKUI SHEET METAL

FORMABILITY TEST

AMMAR BIN ISMAIL @ MUKHTAR

A report submitted in partial fulfilment of the requirements

for the award of the degree of

Bachelor of Mechanical Engineering

Faculty of Mechanical Engineering

UNIVERSITI MALAYSIA PAHANG

NOVEMBER 2009

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SUPERVISOR’S DECLARATION

We hereby declare that we have checked this project and in our opinion this project is

satisfactory in terms of scope and quality for the award of the degree of Bachelor of

Mechanical Engineering.

…………………................

Name of Supervisor: DR. AHMAD SYAHRIZAN BIN SULAIMAN

Position: Lecturer

Date: 24 NOVEMBER 2009

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STUDENT’S DECLARATION

I hereby declare that the work in this thesis is my own except for quotations and

summaries which have been duly acknowledged. The thesis has not been accepted for

any degree and is not concurrently submitted for award of other degree.

…………………………......

Name: AMMAR BIN ISMAIL @ MUKHTAR

ID Number: MA06103

Date: 24 NOVEMBER 2009

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To my beloved mother and father,

Wan Hasenah Wan Yacob

Ismail @ Mukhtar Salleh

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ACKNOWLEDGEMENTS

First of all I would like to express my fully gratitude and praise ‘Alhamdulillah’

to Allah the Almighty for completion of this research. To my flexible, dedicated guider

and supervisor Dr Ahmad Syahrizan bin Sulaiman, I would like to express my

appreciation to my final year project supervisor for his irreplaceable encouragement and

guidance. A person of innumerable skills, he has eased the way through a demanding

project during a busy time in my life.

I would like to express my admiration to my lovely family especially my parent

Ismail @ Mukhtar and Wan Hasenah Wan Yacob for their love, dream and sacrifice

throughout my life, my project mates, my friend and many other personnel I have

spoken with about this project. I thank all of them for sharing their helpfulness, ideas

and kindness.

Last but not least, I want to take these favourable moments to express

gratefulness to all of them again which are very much appreciated as friends and

mentors. Without them, this project will not be perfect.

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ABSTRACT

The main objective of this project is to create Fukui conical cup model using finite

element method to investigate the formability of sheet metal. The Fukui testing involved

both deformation drawing and stretching. The elastic and plastic material properties are

testing with plane stress and axis symmetric. There are three types of material

aluminium, brass and steel are used to this project. The project begins with die design

with AutoCAD and Solidworks. The project is further to modeling finite element with

Algor FEA. The simulation started with elastic and plastic material model with plane

stress. Then the material model is changed to axis symmetric with elastic and plastic

material. The data collection taken to making graph of displacement. The simulation

taken different time for each material. The variables for this project are variety of sheet

metal and geometry type plane stress and axis symmetric. The constant of this

simulation are thickness of sheet metal and displacement of the indenter to deform the

material. All the data from Algor’s software will show the different value of

displacement when transferred to Microsoft Excel. The axisymmetric geometry type

shown the data are not too overlapping each other compare to plane stress. From the

data documentation, the discussion and result were conclude for making the developing

Fukui conical cup sheet metal formability modeling.

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ABSTRAK

Tujuan utama projek ini adalah untuk membina model cawan berbentuk kon Fukui

menggunakan kaedah elemen hingga untuk menyiasat kadar kebolehan logam untuk

penraikan dan lembaran logam. Percubaan Fukui yang terlibat baik deformasi

menggambar dan peregangan. Elastik dan sifat bahan plastik uji pada regangan dan

paksi simetri. Ada tiga jenis bahan berlainan dari kepingan logam iaitu seperti

aluminium, tembaga dan besi digunakan untuk projek ini. Projek ini bermula dengan

lakaran pada perisian AutoCAD dan Solidworks. Simulasi bermula dengan bahan

plastik elastik dan model regangan. Kemudian model bahan berubah menjadi paksi

elastik dan simetris dengan bahan plastik. Pengumpulan data diambil untuk membuat

graf perpindahan. Masa yang diambil untuk simulasi berbeza untuk setiap jenis bahan.

Pemboleh ubah dalam projek ini adalah seperti pelbagai jenis logam dan geometri jenis

regangn dan paksi simetri. Pemalar untuk simulasi ini adalah ketebalan dari lembaran

logam dan perpindahan penujah untuk menjalankan proses keboleh lanturan kepingan

loga mengikut penarikan dan lembaran. Semua data dari perisian Algor akan

menunjukkan nilai yang berbeza dan dipindahkan ke perisian Microsoft Excel. Jenis

geometri yang dipaparkan axisymmetrik tidak terlalu menindih antara satu sama lain

berbanding dengan model regangan.

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TABLE OF CONTENTS

Page

TITLE PAGE i

SUPERVISOR’S DECLARATION ii

STUDENT’S DECLARATION iii

DEDICATION iv

ACKNOWLEDGEMENT v

ABSTRACT vi

ABSTRAK vii

TABLE OF CONTENTS viii

LIST OF TABLES xi

LIST OF FIGURES xii

LIST OF SYMBOLS xiv

LIST OF ABBREVIATIONS xv

CHAPTER 1 INTRODUCTION

1.1 Sheet Formability Test 1

1.2 Project Background 2

1.3 Problem Statement 2

1.4 The Objective of The Research 3

1.5 Scope of The Project 3

CHAPTER 2 LITERATURE REVIEW

2.1 Sheet Metal 4

2.2 Formability Test 5

2.3 Drawing 5

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2.4 Stretching 7

2.5 Finite Element Method 8

2.5.1 Types of Analysis 9

2.5.2 Application 10

2.6 Fukui Conical Cup 11

2.7 Plane Stress 15

2.8 Axisymmetric 16

CHAPTER 3 METHODOLOGY

3.1 Introduction 18

3.2 Flow Chart 19

3.3 Conceptual Design 20

3.4 Die Design and Drawing 20

3.5 Material Properties 22

3.5.1 Material for sheet metals 22

3.5.2 Material for die 22

3.6 Finite Element Analysis Software 23

3.6.1 Model Building 23

3.6.2 Surface Contact 24

3.6.3 Prescribed Displacement 24

3.6.4 Simulation 25

3.6.5 Data Collection 29

3.7 Variables 29

3.8 Constant 30

CHAPTER 4 RESULT AND DISCSSION

4.1 Introduction 31

4.2 Result of Modeling Algor Simulation 31

4.2.1 Result of Elastic Plane Stress Material Model 32

4.2.2 Result of Plastic Plane Stress Material Model 34

4.2.3 Result of Elastic Axisymmetric Material Model 37

4.2.4 Result of Plastic Axisymmetric Material Model 39

4.3 Discussion 42

4.3.1 The Elastic Plane Stress Material Model

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4.3.2 The Plastic Plane Stress Material Model

4.3.3 The Elastic Axisymmetric Material Model

4.3.4 The Elastic Axisymmetric Material Model

4.3.5 The Comparison of Elastic and Plastic Plane Stress Material Model

4.3.6 The Comparison of Elastic and Plastic Axisymmetric Material Model

CHAPTER 5 CONCLUSION AND RECOMMENDATIONS

5.1 Conclusion 44

5.2 Recommendations 44

REFERENCES 46

APPENDICES

A1 Drawing Die Design General Part 48

A2 Drawing Die Design Top Die Part 49

A3 Drawing Die Design Bottom Die Part 50

A4 Drawing Die Indenter 51

A5 Drawing Die Inner Cylinder 52

B Gannt Chart for PSM2 53

C1 Solid Drawing Fukui Cup 1 54

C2 Solid Drawing Fukui Cup 2 55

D1 Graph Elastic Plane Stress Material Model 56

D2 Graph Plastic Plane Stress Material Model 57

D3 Graph Elastic Axisymmetric Material Model 58

D4 Graph Elastic Axisymmetric Material Model 59

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LIST OF TABLES

Table No. Title Page

3.1 The table of variables for the simulation modeling in this project 29

3.2 Table of constant value for the simulation modeling in this project 30

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LIST OF FIGURES

Figure No. Title Page

2.1 Some fracture from drawing 6

2.2 550 Ton Capacity Deep Drawing 7

2.3 Metal drawing food services food buffet pan 8

2.4 Simulation by using FEM in how car deform in asymmetrical crash 11

2.5 The schematic of Fukui Conical Cup Test redraw based on reference 12

2.6 The schematic of Fukui Conical Cup Test redraw based on reference in

3D Cross sectional view 13

2.7 The flat and spherical cup after forming 14

2.8 The sample of deformation from Fukui testing 15

2.9 Components in plane stress 15

2.10 Cross section through the axis of a body of revolution 16

2.11 The visualization models in 3D visualization 17

3.1 Flowchart 20

3.2 The schematic die design of Fukui draw using AutoCAD 21

3.3 The cross sectional view of die design using Solidworks 21

3.4 Plot of Load Curve 25

3.5 Load curve setting 25

3.6 Fukui modeling drawing shows the presribed displacement 26

3.7 The 2D drawing of axisymmetric at Z and Y plane 27

3.8 The model while deformation running 28

3.9 The blank with indenter with hiding the die to show the blank deformed 28

4.1 Aluminum 6063 –T6 Elastic Plane Stress Material Model 32

4.2 Steel (AISI 1015) Annealed Elastic Plane Stress Material Model 32

4.3 Brass, red Elastic Plane Stress Material Model 33

4.4 Graph the Elastic Plane Stress Material Model 33

4.5 Aluminum 6063 –T6 Plastic Plane Stress Material Model 34

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4.6 Steel (AISI 1015) Annealed Plastic Plane Stress Material Model 35

4.7 Brass, red Plastic Plane Stress Material Model 35

4.8 Graph the Plastic Plane Stress Material Model 36

4.9 Aluminum 6063 –T6 Elastic Axisymmetric Material Model 37

4.10 Brass, red Elastic Axisymmetric Material Model 37

4.11 Steel (AISI 1015) Annealed Elastic Axisymmetric Material Model 38

4.12 Graph the Elastic Axisymmetric Material Model 38

4.13 Aluminum 6063 –T6 Plastic Axisymmetric Material Model 39

4.14 Brass, red Plastic Axisymmetric Material Model 39

4.15 Steel (AISI 1015) Annealed Plastic Axisymmetric Material Model 40

4.16 Graph the Plastic Axis symmetric Material Model 40

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LIST OF SYMBOLS

Stress

Shear

t Time

mm Milimeter

r Radius

A Area

F Force

P Load

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LIST OF ABBREVIATIONS

AISI American Iron and Steel Institute

ASTM American Society for Testing and Materials

2D Two dimensional

3D Three dimensional

CCV Conical Cup Value

FEA Finite Element Analysis

FEM Finite Element Model

CAD Computer Aided Drawing

CHAPTER 1

INTRODUCTION

1.1 SHEET FORMABILITY TEST

Formability is a measure of the amount of deformation a material can withstand

prior to fracture or excessive thinning. Sheet metal forming ranges from simple bending,

to stretching, to deep drawing of complex parts. Therefore, determining the extent to

which a material can deform is necessary for designing a reproducible forming

operation. Mechanical properties greatly influence formability, and forming properties

may vary from coil to coil, it is essential to test incoming sheet material. However, the

outcome of a forming process depends on both material characteristics and process

variables such as strain, strain rate and temperature. In fact, stress and strain fields are

so diverse during a forming process that no single test can reliably predict the

formability of materials in all situations.

The important point to bear in mind is that they change gradually and

predictably as the yield strength of the steel increase. No discontinuous drop in

formability is experienced. Certain formability modes are insensitive to yield strength.

Therefore, knowing the charge in formability parameters expected, compensation can be

made in part design, tool design, lubricant selection and press parameters [1]. Sheet

metal parts are usually made by forming in a cold condition, although many sheet metal

parts are formed in a hot condition because the material when heated has a lower

resistance to deformation. Strips or blanks are very often used as initial materials, and

are formed on presses using appropriate tools. The shape of a part generally corresponds

to the shape of tool.

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Sheet metal forming process is used for both serial and mass production. Their

characteristics are high productivity, highly efficient use of material, easy servicing

machines, the ability to employ workers with relatively less basic skills and other

advantageous economic aspects. Parts made from sheet metal have many attractive

qualities: good accuracy of dimension, adequate strength, light weight and a broad range

of possible dimensions.

However it is not possible to evaluate accurately the formability of the materials

in terms of these parameters. The complete assessment of the formability, the direct

methods, such as the Ericksen test, Swift cup test, and Fukui conical cup test have been

used for determination of formability [2].

1.2 PROJECT BACKGROUND

The sheet metal is a very important thing nowadays, because of many

applications use this material. Even though, there are limitation of sheet metal

formability and many cases while deforming the sheet metal, the component fractures at

certain point. The causes of failure are parameters related to forming process. The

project is expected to find the sheet formability by using finite element method. The

project is using finite element modeling of Fukui Sheet Metal Formability Test to

investigate the ability of sheet metal to be shaped.

This research will overcome this problem with finite element analysis with find

the elastic and plastic deformation of sheet metal with four different materials with

same thickness. The aluminum, brass, steel and iron are the variables of this simulation

with the constant thickness.

1.3 PROBLEM STATEMENT

In many cases, while deforming sheet metal, the causes of failure are related to

forming process. This developing the Fukui finite element modeling will solve and

investigates the performance of sheet metal with the simulation testing. According the

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three different of sheet metal will give the different of formability each sheet metal. It

solve sheet metal forming problem with identify where a forming process is predicted to

fail. The Fukui sheet metal involved both deformation stretching and drawing.

1.4 THE OBJECTIVE OF THE RESEARCH

Create the working finite element model of Fukui Sheet Metal Formability Test.

1.5 SCOPES OF THE PROJECT

This modeling is focus on the elastic and plastic material model. The scopes of

this project are:

(i) The material that used in this project which is divided with three materials like

aluminum, brass, and steel

(ii) Design and simulate the modeling of Fukui Sheet Metal Testing

CHAPTER 2

LITERATURE REVIEW

2.1 SHEET METAL

Sheet metal is one of the most important semi finished products used in the steel

industry, and sheet metal forming technology is therefore an important engineering

discipline within the area of mechanical engineering. Sheet metals are characterized by

a high ratio of surface area to thickness. Sheet metal forming is basically conversion of

a flat sheet metal into a product of desired shape without defect like fracture or

excessive localised thinning [3].

The products made by sheet-forming processes include a large variety of shapes

and sizes, ranging from simple bends to double curvatures with shallow or deep

recesses. Typical examples are metal desks, appliance bodies, aircraft panels, beverage

cans, auto bodies, and kitchen utensils. In many cases while deforming the sheet metal,

the component fractures at certain point. The causes of failure are parameters related to

forming process. The sheet metal is available as flat pieces. The sheet metal are formed

by running a continuous sheet of metal through a roll slitter. The sheet metal thickness

is called gauge. The gauge of sheet metal ranges from 30 gauge to 8 gauge. The thinner

the metal is, the higher of gauge.

There are many application that using sheet metal like car bodies, airplane

wings, roofs, lab table and so on. In automobiles the sheet metal is deformed into the

desired and brought into the required form to get car part body pressings like bonnet,

bumpers, doors, etc. In aircraft’s sheet metal is used for making the entire fuselage

wings and (body). In domestic applications sheet metal is used for making many parts

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like washing machine body and covers, iron tops, timepiece cases, fan blades and

casing, cooking utensils etc.

2.1.1 FORMABILITY TEST

Sheet metal formability is undergoing a transition from art to science.

Formability within each forming mode can be related to specific metal formability

parameters [4]. The successful sheet metal forming process which is can convert

initially from flat to desired shape. There many major failures that always happened

such as splitting, wrinkling or shape distortion. The formability test is use to access of

sheet to be deformed into a useful part [5]. The testing can divided into two types:

intrinsic and simulative. The intrinsic tests measure the basic material properties under

certain stress strain states, for example the uniaxial tensile test and the plane strain

tensile test. Traditional evaluation of formability is based on both intrinsic tests and

simulative tests. The intrinsic tests measure the basic characteristic properties of

materials that can be related to their formability. These tests provide comprehensive

information that is insensitive to the thickness and surface condition of the material.

Uniaxial tensile test, Plane strain tensile test, Marciniak Biaxial Stretching test,

Examples of intrinsic tests are Hydraulic Bulge test, Marciniak In-Plane Sheet torsion

test, Miyauchi shear test, Hardness test. The simulative test can provide limited and

specific information that may be sensitive to factors other than the material properties

like the thickness, surface condition, lubrication and many more. subject the material to

deformation that closely resembles the deformation that occurs in a particular forming

operation. Examples of these tests include Ericksen, Olsen, Fukui, Swift tests.

2.3 DEEP DRAWING

Formability of sheet metal generally understood to mean capability of being

extensively deformed into desired shape without any fracture or defects in the finished

part. This process is called deep drawing or press forming. The deep drawing process is

the most common sheet metal forming method. Generally, this process is involved with

a flat blank is formed into a finished shape between a pair of matched dies. A blank of

sheet metal is restrained at the edges, and the middle section is forced by a punch into a

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die to stretch the metal into a cup shaped drawn part. This drawn part can be circular,

rectangular or just about any cross-section. Drawing can be either shallow or deep

depending on the amount of deformation. Shallow drawing is used to describe the

process where the depth of draw is less than the smallest dimension of the opening;

otherwise, it is considered deep drawing.

Other forming methods exist, but in all of them two principal kinds of

deformation, drawing and stretching are involved [4]. This drawing process, the

clamping force of the hold down dies is just sufficient to permit the material to flow

radially into the die cavity without wrinkling. Drawing leads to wrinkling and puckering

at the edge where the sheet metal is clamped. This is usually removed by a separate

trimming operation.

Figure 2.1: Some fracture from drawing [6]

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Figure 2.2: 550 Ton Capacity Deep Drawing Press [7]

Figure 2.3: Metal drawing food services food buffet pan [8]

2.4 STRETCHING

A wavy piece of sheet metal can be straightened by gripping it at two opposite

sides and stretching it a bit beyond its elastic limit. It will come out straight, flat and

undistorted. Sheet metal so treated by a mill is termed stretcher leveled, and is supplied

to meet flatness requirements.

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Parts blanked from aluminum and other soft metals can also be stretched if

product designers and tooling designers agree that it is needed. In the operation

sequence, one or more stations before the blanking station, a station is provided for

impressing a grid of closely-spaced pinpoint indentations on both sides of the material.

These indentations, although tiny, shallow and barely visible, have the same effect as

stretching. They flatten and stiffen the metal in the area where the blanking will occur,

so that the finished part will have the required flatness, yet with the indentations hardly

noticeable.

The periphery of the tray has a short vertical rim and a narrow horizontal flange.

When this part is draw-formed, an unequal compressive stress builds up along the rim

and flange, and continues down into the bottom panel. This stress sometimes warps a

part like this and introduces the objectionable "snap" action. To avoid this defect, the

bottom of the tray is stretched a little in a way that cancels the compression stress there.

This gives the metal a new granular orientation, eliminates the objectionable twist and

allows the tray to lie steady on the table.

The stretching that is introduced could be designed into the drawing die, or it

could be done as a second operation after the part is completed. In the first method, the

blank is drawn and the bottom stretched in one operation. In the second, the drawing

only is performed in the first of two dies. The stretching is done later in another die.

Both methods produce the same results. Depending upon the ingenuity and discretion of

the die designer, the stretching could comprise a pattern of shallow rectangular

depressions pressed into the bottom panel to stretch the excess metal, remove stress, and

prevent it from twisting. Unfortunately, it is the nature of these procedures to render

unpredictable results, so they must be worked out experimentally in each case.

2. 5 FINITE ELEMENT METHOD

Finite element method (FEM) is originated from the solving complex elasticity

and structural analysis problems. The finite element method is a numerical technique for

finding approximate solutions of partial differential equation as well as of integral

equation. The finite element method is one of a good technique for solving partial

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differential equations over a complex domain. Finite element analysis allows detail

visualization of where structures bend or twist. This software gives wide range of

simulation for controlling the complexity of both modeling and analysis of a system.

There are generally two types of analysis that are used in industry: 2-D modeling, and 3-

D modeling. Within each of these modeling schemes, the programmer can insert

numerous algorithms (functions) which may make the system behave linearly or non-

linearly. Linear systems are far less complex and generally do not take into account

plastic deformation. Non-linear systems do account for plastic deformation, and many

also are capable of testing a material all the way to fracture.

The solution approach is based either on eliminating the differential equation

completely (steady state problems), or rendering the PDE into an approximating system

of ordinary differential equations, which are then numerically integrated using standard

techniques such as Euler's method, Runge-Kutta, etc.

There are many ways of doing FEM, this is because of the advantages and

disadvantages. The FEM is a good choice for solving partial differential equations over

complex domains like cars and oil pipelines, when the domain changes as during a solid

state reaction with a moving boundary, when the desired precision varies over the entire

domain, or when the solution lacks smoothness. For instance, in a frontal crash

simulation it is possible to increase prediction accuracy in "important" areas like the

front of the car and reduce it in its rear (thus reducing cost of the simulation)

2.5.1 Types of Analysis

Sheet Metal Analysis: The thin bodies, a different type of meshing approach is

required. For sheet metal parts, the sheet metal can extract and mesh a mid-surface

using 2D plate elements instead of 3D solid elements. These structures are represented

much more efficiently using 2D elements without compromising accuracy, with

minimal solution time and use of computer resources. We use sheet metal mid-surface

for both static and modal analysis.