DESIGN, FABRICATION AND OPTIMIZATION OF SHEAR TEST RIG

(DOUBLE SHEAR TYPE)

MOHD FAKRUL RADZI BIN MOHD MAWARDZI

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 2008

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:

Date: 15th November 2008

…………………................

Name of Panel:

Position:

Date:

i

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 concurently submitted for award of other degree.

…………………………......

Name: Mohd Fakrul Radzi Bin Mohd Mawardzi

ID Number: MC04009

Date: 15th November 2008

ii

ACKNOWLEDGEMENTS

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

‘Alhamdulillah’ to Allah the Almighty for completion of my final year project.

I would like to express my gratitude and appeciation to my final year project

supervisor, Dr Ahmad Syahrizan bin Sulaiman for his irreplaceable encouragement

and guidance to finish this project. A person of innumerable skills, he has eased the

way through a demanding project during a busy time in my life.

I also like to express my admiration to my lovely family, my labmates,

mechanical’s lab staff, my friend and many other personnel I have spoken with about

this project. Thanks to all of them for sharing their helpfulness, ideas and kindness.

Last but not least, I want to take these favorable 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 finish.

iv

ABSTRACT

Shear stress-strain relationship is an important material property of sheet

metals. The property is difficult to measure compared to a more commonly used

tensile stress-strain relationship. The objective of this project is to design and

fabricate a rig that can be use to measure shear stress-strain relationship and test its

workability. The rig has to be mounted in a tensile test machine and utilise the

machine capability of measuring load and displacement progression. The data of load

versus displacement will have to be converted into shear stress-strain relationship

based on an oblique parallelepiped deformation theory.

v

ABSTRAK

Hubungan antara ricihan tegasan dan ricihan terikan ialah sifat bahan yang

sangat penting bagi kepingan besi. Sifat tersebut sukar untuk dikira jika dibandingkan

dengan kebiasaan hubungan tegangan antara tegasan dan terikan. Objektif projek ini

ialah untuk mereka dan membuat satu alat yang boleh digunakan untuk mengira

ricihan tegasan dan ricihan terikan dengan menguji kebolehannya menggunakan

mesin uji tegangan. Alat tersebut akan dipasangkan pada mesin uji tegangan dan

menggunakan keupayaan mesin tersebut untuk mengira beban dan perubahan jarak

bahan uji. Data beban dan perubahan jarak akan ditukarkan kepada hubungan antara

ricihan tegasan dan ricihan terikan berasakan kepada teori kecacatan iaitu ‘oblique

parallelepiped’.

vi

TABLE OF CONTENTS

Page

SUPERVISOR’S DECLARATION i

STUDENT’S DECLARATION ii

DEDICATION iii

ACKNOWLEDGEMENTS iv

ABSTRACT v

ABSTRAK vi

TABLE OF CONTENTS vii

LIST OF TABLES x

LIST OF FIGURES xi

LIST OF SYMBOLS xiv

LIST OF ABBREVIATIONS xv

CHAPTER 1 INTRODUCTION

1.1 Introduction 1

1.2 Peoject Background 2

1.3 Problem Statement 3

1.4 Project objectives 3

1.5 Project scopes 3

CHAPTER 2 LITERATURE REVIEW

2.1 Introduction 4

2.2 Shear Stress 5

2.3 Shear Strain 6

vii

2.4 Current Design 8

2.4.1 Simple Shear Device 8

2.4.2 Three-Rail Shear Test 11

2.4.3 Trellis Frame Or Picture Frame 14

2.5 Material Properties Of Shear Modulus 20

2.6 Problem Of Current Shear Test Frame 20

2.6.1 Encountered Problems 20

CHAPTER 3 METHODOLOGY

3.1 Introduction 23

3.2 Project Methodology Flow Chart 24

3.3 Design And Analysis 25

3.4 Material Selection 26

3.5 Machining 27

3.5.1 Milling and Drilling 28

3.5.2 Turning 29

3.6 Joining Process 30

Testing And Equation Modeling 31

CHAPTER 4 RESULTS AND DISCUSSION

4.1 Introduction 33

4.2 Result 33

4.2.1 Data Of Load And Displacement 34

4.2.2 Graph Of Shear Stress Against Shear Strain 35

4.2.3 Example Calculation Of Shear Modulus 36

4.2.4 Result Of Shear Modulus 37

4.3 Discussion 38

4.3.1 Slot 38

4.3.2 Drilling Holes 39

4.3.3 Fabrication 40

viii

4.3.4 Specimen Preparation 41

4.3.5 Specimen Alignment and Gripping 41

CHAPTER 5 CONCLUSION AND RECOMMENDATIONS

5.1 Introduction 43

5.2 Conclusion 43

5.3 Recommendation 44

REFERENCES 45

APPENDICES

A Shear Test Rig 47

B Part 1 48

C Part 2 48

D Part 3 49

E Part 4 49

F Recommendation For Future Design 50

ix

LIST OF TABLES

Table No. Page

2.1 Shear modulus of material 20

4.1 Shear modulus from the testing 37

x

LIST OF FIGURES

Figure No. Page

1.1 Shear stress and shear strain 2

2.1 Shear stress and shear strain on a rod 5

2.2 The displacement after the shear stress and shear strain 6

2.3 Shear stress-strain curve 7

2.4 Simple shear device 9

2.5 Schematic representation of a simple shear test along the x-axis. L

and h are respectively, the current length and thickness of the

gauge area and mδ is the relative displacement of two grips

9

2.6 (a) The design of three-rail, mounted on the tensile test. (b)

Vertical cross-section of the grip, indicating some general

dimensions

12

2.7 Principle of the three-rail shear test: (a) the setup and (b) the

induced deformation

13

2.8 Representation of the deformation state on Mohr’s circle 13

2.9 Fabric shearing 14

2.10 Trellising-shear test apparatus 15

2.11 UML shear frame: (a) starting position and (b) deformed position.

Note that the top hinge has traveled from bottom of the slot in the

undeformed position (a) to the top of the slot in the deformed

position (b)

15

2.12a Picture frame designed, fabricated, and used by Hongkong

University of Science & Technology (HKUST)

16

2.12b Picture frame designed, fabricated, and used by Katholieke

Universiteit Lauren (KUL, Belgium)

16

xi

2.12c Picture frame designed, fabricated, and used by University of

Massachusetts Lowell (UML)

17

2.12d Picture frame designed, fabricated, and used by University of

Twente (UT, Netherlands)

17

2.12e Picture frame designed, fabricated, and used by Laborative de

Mecanique des systems et des procedes (LMSP)

18

2.12f Picture frame designed, fabricated, and used by University of

Nottingham (UN)

18

2.13 Schematic of picture frame (KUL) 19

2.14 Additive decomposition of the relative displacement mδ of two

pairs of grips into the effective shear displacement uδ and a sliding

movement under the grips gδ

21

2.15 Failure and buckling occurrence in simple shear 22

3.1 Project methodology flow chart 24

3.2 Design of shear test rig 25

3.3 Rectangular mild steel from waste mold 27

3.4 Round bar mild steel 27

3.5 Horizontal sand-saw machines 28

3.6 Milling machine 29

3.7 Lathe machine 30

3.8 Screw and nut 30

3.9 Bolt and nut 31

3.10 Tensile test machine 32

4.1 Specimens before experiments 33

4.2 Specimens after experiments 34

4.3 Graph of load against displacement 34

xii

4.4 Graph of shear stress against shear strain 35

4.5 Graph of shear stress against shear strain 36

4.6 Comparison frame with and without slot 38

4.7 Comparison frame with and without holes 39

4.8 Comparison of precise 40

4.9 Specimen with and without clamping 41

4.10 Difference between the uses of bolts in standard (a) and without

use the bolts (b)

42

5.1 The recommendation design 44

xiii

LIST OF SYMBOLS

F Force

γ Shear strain

τ Shear stress

L Height, length

x∆ Distance

L∆ Horizontal distance

G Shear Modulus

aveτ Average shear stress

t , e Thickness

uδ Effective shear displacement

gδ Sliding movement under the grips

mδ Relative displacement

maxσ Maximum shearing stress

xiv

LIST OF ABBREVIATIONS

Al Aluminium

ASTM American Society for Testing and Materials

mm Milimeter

rpm Revolution per minutes

xv

CHAPTER 1

INTRODUCTION

This chapter explain a surface about shear stress-strain and the view of this

project. In this chapter, the project background, problem statements, objectives,

scopes and thesis outline are included.

1.1 INTRODUCTION

The shear modulus is the elastic modulus used for the deformation which

takes place when a force is applied parallel to one face of the object while the

opposite face is held fixed by another equal force. [3]

When an object likes a block of height L and cross section, A experiences a

force, F parallel to one face, the sheared face will move a distance x∆ . The shear

stress is defined as the magnitude of the force per unit cross-sectional area of the face

being sheared (F/A). The shear strain is defined as x∆ /L. [3]

The shear modulus S is defined as the ratio of the stress to the strain.

xA

FL

L

xA

F

nShearStrai

sShearStresS

∆=

∆=≡ (1.1)

2

Figure 1.1: Shear stress and shear strain [3]

The bigger the shear modulus the more rigid is the material since for the same

change in horizontal distance (strain) need a bigger force (stress). This is why the

shear modulus is sometimes called the modulus of rigidity.

To a first approximation there is no change in volume in this deformation.

The planes of atoms merely slide sideways over one another. That is why the area A

(which determines the number of atomic bonds) is important in defining the stress

and not just F. [3]

Note that in the diagram, since the block is not moving, there is a force F to

the left on the bottom face which is not shown.

1.2 PROJECT BACKGROUND

Shear stress-strain relationship is an important material property of sheet

metals. Mechanical properties of sheet metals can be altered by giving a load to the

sheet metals. But the property is difficult to measure compared to a more commonly

used tensile stress-strain relationship. It is very important aspect to analysis and

design the rig or frame relates to the shear stress-strain of sheet metals caused by the

loads applied to the rig. The rig has to be mounted in a tensile test machine and

3

utilise the machine capability of measuring load and displacement progression. The

data of load versus displacement will have to be converted into shear stress-strain

relationship based on an oblique parallelepiped deformation theory. This project will

study about the shear modulus of aluminum. By getting the shear stress-strain

relationship, it will be then used to determine the modulus of rigidity or shear

modulus. The project is succeeding if the shear modulus of the aluminum from the

experimental value is same to the theoretical value.

The planar simple shear test has proved to be a very efficient technique to

evaluate the mechanical properties of flat samples. Previous studies of this

mechanical test can be found in Genevois, Liu and Miyauchi. Briefly, the planar

simple shear test device consists of two rigid parts subjected to a parallel movement.

[8]

1.3 PROBLEM STATEMENT

Shear modulus is influenced by the shear stress-strain relationship. But plane

shear load is difficult to apply on sheet metals. So, it is very important to design a

new test rig with established standard.

1.4 PROJECT OBJECTIVES

1.4.1 Design a new shear test rig.

1.4.2 Determine shear modulus of aluminum using shear-stress relationship.

1.5 PROJECT SCOPES

1.5.1 Fabricate the design using mild steel part.

1.5.2 Fit the prototype when mounted to the tensile test machine.

1.5.3 Test with Aluminum 1.5mm width as a benchmark.

1.5.4 Optimisation of the shear test rig

4

CHAPTER 2

LITERATURE REVIEW

2.1 INTRODUCTION

Tensile tests are performed for several reasons. The results of tensile tests are

used in selecting materials for engineering applications. Tensile properties frequently

are included in material specifications to ensure quality. Tensile properties often are

measure during development of new materials and processes, so that different

materials and processes can be compared. Finally, tensile properties often are used to

predict the behavior of a material under forms of loading other than uniaxial tension.

The strength of a material often is the primary concern. The strength of interest

maybe measured in terms of either the stress necessary to cause appreciable plastic

deformation or the maximum stress that the material can withstand. [5]

These measures of strength are used, with appropriate caution (in the form of

safety factors), in engineering design. Also of interest is the material is ductility,

which is a measure of how much it can be deformed before it fractures. Rarely is

ductility in corporate directly in design; rather, it is included in material

specifications to ensure quality and toughness. Low ductility in a tensile test often is

accompanied by low resistance to fracture under other forms of loading. Elastic

properties also may be of interest, but special techniques must be used to measure

these properties during tensile testing, and more accurate measurements can be made

by ultra sonic techniques. [5]

5

2.2 SHEAR STRESS

In additional to axial (or normal) stress and strain, it is known as shear stress

and shear strain. In Figure 2.1 there is a metal rod which is solidly attached to the

floor. After a force, F exerted and acting at angle theta with respect to the horizontal

on the rod, the component of the force perpendicular to the surface area will produce

an axial stress on the rod given by Force perpendicular to an area divided by the area,

or:

AF /sinθσ = (2.1)

The shear stress is produced because of the effect of the component of the

Force parallel to the area, defined as Force parallel to an area divided by the area, or:

AF /cos θτ = (2.2)

where the Greek letter, Tau, is used to represent Shear Stress. The units of

both Axial and Shear Stress will normally be lb/in2 or N/m

2. [7]

Figure 2.1: Shear stress and shear strain on a rod [7]

6

2.3 SHEAR STRAIN

Shear strain is produced by the change in the length divided by the original

length of the member. Both Axial Strain and Shear Strain are shown in Figure 2.2.

The displacement of the rod as indicated in the right drawing in Figure 2.2 produced

by shear stress. The edge of the rod is displaced a horizontal distance, L∆ from its

initial position. This displacement (or horizontal deformation) divided by the length

of the rod L is equal to the shear strain. Examining the small triangle made by L∆ , L

and the side of the rod, the shear strain, LL /∆ is also equal to the tangent of the

angle gamma, and since the amount of displacement is quite small the tangent of the

angle is approximately equal to the angle itself. Or it can be writing as:

Shear Strain = γγ ==∆ tan/ LL (2.3)

Figure 2.2: The displacement after the shear stress and shear strain [7]

As with axial stress and strain, shear stress and strain are proportional in the

elastic region of the material. This relationship may be expressed as, G = Shear

7

Stress/Shear Strain, where G is a property of the material and is called the Modulus

of Rigidity (or at times, the Shear Modulus) and has units of lb/in2. [7]

If a graph is made of shear stress versus shear strain in Figure 2.3, it will

normally exhibit the same characteristics as the graph of axial stress versus axial

strain. There is an elastic region in which the stress is directly proportional to the

strain. The point at which the elastic region ends is called the elastic limit, or the

proportional limit. In actuality, these two points are not quite the same. The elastic

limit is the point at which permanent deformation occurs, that is, after the elastic

limit, if the force is taken off the sample, it will not return to its original size and

shape, permanent deformation has occurred. The proportional limit is the point at

which the deformation is no longer directly proportional to the applied force (Hooke's

Law no longer holds). Although these two points are slightly different, it will treat as

same in this course. There is a plastic region, where a small increase in the shear

stress results in a larger increase in shear strain, and finally there is a failure point

where the sample fails in shear.

Figure 2.3: Shear stress-strain curve [7]

To summarize the shear stress/ strain/ Hooke's Law relationships up to this

point: [7]

Shear Stress: ( ) AFparallel /=τ (Ib/in2, or N/m

2) (2.4)

Shear Strain: γγγ ==∆= tan/ LL (2.5)

8

Hooke’s Law: γτ /=G (Ib/in2, or N/m

2) (2.6)

A materials shear modulus is the coefficient of elasticity for a shearing force.

It is defined as “the ratio of shear stress to the displacement per unit sample length”.

[6]

2.4 CURRENT DESIGN

2.4.1 Simple Shear Device

The first equipment referred in the literature was that developed by Miyauchi.

The specimen has two symmetrically sheared zones and is acted on an axial load. By

turning over the device Bauschinger tests can be carried out. The main advantage of

this arrangement is that the shear forces to which is subjected the central grip of the

device are equilibrating each other. Therefore, the slides are less loaded and the

friction forces decrease, thus allowing a better estimate of the shearing forces. A

second version of the simple shear device was proposed by G’Sell for polymers and

subsequently adapted for metallic materials by Rauch and G’Sell. An improved

version of this device was developed by Genevois (Figure.2.4), where the rotation of

the specimen under the action of the shearing forces is impeded by a very stiff frame.

The specimens easy to prepare because have a simple rectangular shape. [8] To avoid

any eventual hardening due to drilling, they can be eventually cut out by electro-

erosion in order. The specimen is firmly clamped by the fixed and moving grips of

the shearing device (Figure.2.5). The shear test is not sensitive to small shape

imperfections of the sample, with the possible exception of thickness variations

related to the rolling process. [8]

9

Figure 2.4: Simple shear device [8]

In order to impose the condition h=constant the moving grips of the device

presented in Figure 2.4 can also move laterally (along the y-axis in Figure 2.5). In the

former case, a supplementary load cell and/ or a motorization can be added in order

to super impose a controlled lateral tension or compression on the shear deformation.

Figure 2.5: Schematic representation of a simple shear test along the x-axis. L and h

are respectively, the current length and thickness of the gauge area and mδ is the

relative displacement of two grips. [8]