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ANALYSIS AND SIMULATION OF MATERIALS FOR THE FRONT

IMPACT ZONE OF THE UJ SOLAR CAR

By

JULES DAVID DE PONTE - 200901524

A mini-dissertation submitted to the Faculty of Engineering and the Built Environment in

partial fulfilment of the degree of

BACCALAUREUS INGENERIAE

In

MECHANICAL ENGINEERING SCIENCE

At the

UNIVERSITY OF JOHANNESBURG

SUPERVISOR: N. Janse van Rensburg

October 2012

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Declaration

I, Jules David de Ponte, hereby declare that this mini-dissertation is wholly my own work and

has not been submitted anywhere else for academic credit by myself of another person. I

understand what plagiarism implies and declares that this mini-dissertation is my own ideas,

words, phrases, arguments, graphics, figures, results and organisation except where reference

is explicitly made to anothers work.

I understand further that any unethical academic behaviour, which includes plagiarism, is

seen in a very serious light by the University of Johannesburg and is punishable by

disciplinary action.

Signed: Date:

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If we knew what we were doing it wouldn't be research.

Albert Einstein

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Acknowledgements

I would like to thank the following people, without whom, this project would have been

unsuccessful.

- God For the ability, intellect and strength of will to complete this project. - My Family For motivating and encouraging me, and also financial support during

my degree.

- N. Janse van Rensburg Whose efforts has made the UJ Solar Team a reality. Also, for providing practical advice on how to best complete this project.

- Dr PFJ Henning For granting permission to use the drop test rig and other associated equipment

- The UJ Solar Team I would like to acknowledge the good job that was done during the 2012 Sasol Solar Challenge. May the 2014 race be even better for us.

My deepest gratitude goes out to these individuals.

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Abstract

The aim of this research is to determine which material is most suitable to use as a crash

structure for the front impact zone of the UJ solar car. The two materials investigated will be

AISI 4130 chrome-moly and 6063-T6 aluminium. The most suitable material will be chosen

based on its energy absorption properties, more specifically, how much energy it can absorb,

and the rate of the absorption.

The study will include a finite element analysis component, whose primary purpose is to

compare the real world laboratory tests to a numerical solution. Its secondary purpose is to

expose the experimenter to the finite element method, and increase the skill set of the UJ

Solar Team moving forward.

Literature on impact testing was reviewed, including buckling, impact loading, and a cursory

review on stress wave propagation. The finite element method is reviewed, explaining how it

works, as well as how one should create a finite element study. The experimental setup

consists of two parts. The first being the setup of the laboratory test, and the second being on

the setup of the finite element analysis.

The samples investigated are AISI 4130, 19.051.25mm, 600mm long, and 6063-T6, 31.763.18mm, 600mm long. They are subjected to an impact load; the impacting trolley has a mass of 150kg, and is moving at 7.74m/s. This is equal to a kinetic energy of 4 500J.

The finite element analysis modelled only the first 85mm of deformation, due to limitations

in computing power. After the first 85mm of deformation, the mass impacting the AISI 4130

sample experienced an acceleration of -49.34m/s2 due to impact, and it absorbed 644.4J of

energy. The mass impacting the 6063-T6 sample experienced and acceleration of -95.41m/s2

due to the impact, and it absorbed 1317.63J. The aluminium sample absorbed 49.6% more

energy than the steel, during the first 85mm of deformation. Based on the finite element

analysis, the aluminium is the better material to use for the front impact zone.

The experiments were conducted using the University of Johannesburgs drop test rig. In total, 6 samples were tested, but one of the samples was an outlier and had to be excluded

from the analysis. The aluminium samples absorbed, on average, 64.4% of the total kinetic

energy of the trolley, overall. The chrome-moly samples absorbed, on average, 54.04% of the

total kinetic energy of the trolley. Thus, the aluminium absorbed 14.4% more energy than the

steel samples.

Comparing the finite element analysis to the laboratory tests, the following data was found:

The finite element analysis overestimated the energy absorption of the aluminium samples by

20%, over the first 85mm of deformation. The finite element analysis underestimated the

energy absorption of the steel by 17%, over the first 85mm of deformation. The deformed

shapes of the finite element models were similar to those obtained in the laboratory tests.

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Table of Contents

List of Figures ............................................................................................................................ 8

List of Tables ........................................................................................................................... 10

List of Symbols and Nomenclature.......................................................................................... 11

1. Problem Formulation Background to the Investigation ................................................ 12

1.1 Problem Statement .................................................................................................... 14

1.2 Hypotheses ................................................................................................................ 14

1.3 Scope of the Experiments .......................................................................................... 15

1.4 Required Resources ................................................................................................... 15

1.4.1 Available Resources........................................................................................... 16

1.4.2 Equipment to be sought ..................................................................................... 16

1.5 Experimental Variables ............................................................................................. 16

1.5.1 Independent Variables ....................................................................................... 16

1.5.2 Dependent Variables .......................................................................................... 17

1.5.3 Extraneous Variables ......................................................................................... 17

1.6 Reviewing the Results ............................................................................................... 17

1.6.1 Accelerometer Results ....................................................................................... 17

1.6.2 Footage Results .................................................................................................. 17

1.7 Finite Element Analysis ............................................................................................ 18

2. Literature Review............................................................................................................. 19

2.1 Materials .................................................................................................................... 19

2.1.1 Material Classes ................................................................................................. 19

2.1.2 Metals ................................................................................................................. 19

2.1.3 Material Properties ............................................................................................. 21

2.2 Current State of Impact Testing ................................................................................ 24

2.3 Finite Element Analysis ............................................................................................ 25

2.4 Governing Regulations .............................................................................................. 28

2.5 Buckling .................................................................................................................... 29

2.6 Impact Loading and Strain Energy............................................................................ 30

2.7 Stress Wave Propagation ........................................................................................... 32

2.8 Energy Absorption of Dynamically Loaded Members ............................................. 33

3. Experimental Setup .......................................................................................................... 34

3.1 Laboratory Experiment ............................................................................................. 34

3.1.1 Sample Fixture ................................................................................................... 34

3.1.2 Samples .............................................................................................................. 35

3.1.3 Experimental Matrix .......................................................................................... 37

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3.2 Finite Element Analysis Setup .................................................................................. 38

3.2.1 Samples .............................................................................................................. 38

3.2.2 Analysis Setup AISI 4130 ............................................................................... 39

3.2.3 Experimental Matrix .......................................................................................... 40

4. Finite Element Analysis Results ...................................................................................... 41

4.1 Results AISI 4130 .................................................................................................. 44

4.2 Results 6063-T6 ..................................................................................................... 45

4.3 Discussions ................................................................................................................ 46

4.3.1 Discussion of AISI 4130 Simulation ................................................................. 46

4.3.2 Discussion of 6063-T6 Simulation .................................................................... 48

4.3.3 Comparison of AISI 4130 and 6063-T6 ............................................................ 50

5. Experimental Results ....................................................................................................... 53

5.1 Equipment and Calibration........................................................................................ 53

5.2 Results ....................................................................................................................... 56

5.3 Discussion of the Experiment ................................................................................... 67

5.3.1 Practical Oversights ........................................................................................... 67

5.3.2 Buckling Modes of the Samples ........................................................................ 70

5.3.3 Difficulties with the Equipment ......................................................................... 73

6. Comparison between Finite Element Analysis and Experimental Results ...................... 76

7. Conclusion ....................................................................................................................... 78

7.1 Problem Statement .................................................................................................... 78

7.2 Hypotheses ................................................................................................................ 79

7.3 Recommendations for Future Trials .......................................................................... 79

7.3.1 Finite Element Analysis ..................................................................................... 79

7.3.2 Laboratory Experiment ...................................................................................... 79

7.4 Recommended Future Work ..................................................................................... 80

7.5 Closing ...................................................................................................................... 80

Bibliography ............................................................................................................................ 81

Appendix A Finite Element Analysis ................................................................................... 84

Appendix B Finite Element Analysis Tables ........................................................................ 85

Appendix C SolidWorks Simulation Drop Test Setup ......................................................... 88

C.1 Simulation Setup AISI 4130 .................................................................................. 89

C.2 Analysis Setup 6063-T6 ......................................................................................... 91

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List of Figures

Figure 1-1 Drinks bottle with a crude 'crumple zone' [8] ..................................................... 13

Figure 2-1- Microscopic Image of Low Carbon Steel Grains [15] .......................................... 20

Figure 2-2 - Microscopic Image of High Carbon Steel Grains [16] ........................................ 20

Figure 2-3 - Side view of Ilanga I ............................................................................................ 25

Figure 2-4 - Straight line and polynomial interpolation functions [30] ................................... 26

Figure 2-5 - Simple finite element analysis [31] ..................................................................... 26

Figure 2-6 - Sinusoidal Bucking Modes [35] .......................................................................... 29

Figure 2-7 - Columns with Different End Conditions subjected to Buckling Loads [36] ....... 30

Figure 3-1 General Sample Fixture....................................................................................... 34

Figure 3-2 - General Sample .................................................................................................... 35

Figure 3-3 - Sample being inserted into the fixture ................................................................. 36

Figure 3-4 - Fixture and Sample in the Drop Test Rig ............................................................ 37

Figure 3-5 - General FEM Sample........................................................................................... 39

Figure 4-1 Simulation Sample (a) AISI 4130, (b) 6063-T6. Both images are to scale ........ 41

Figure 4-2 Stress-Strain Curve of AISI 4130, Normalised ................................................... 42

Figure 4-3 Acceleration of the block of mass, AISI 4130 sample ........................................ 44

Figure 4-4 Load-Displacement curve, AISI 4130 ................................................................. 45

Figure 4-5 Acceleration of Block of Mass 6063-T6 Sample ............................................. 45

Figure 4-6 Load-Displacement curve - 6063-T6 .................................................................. 46

Figure 4-7 Deformed Result of the AISI 4130 at Plot Steps 1, 20, 40, 60, 80 and 100........ 48

Figure 4-8 Deformed Result of 6063-T6 at Plot Steps 1, 20, 40, 60, 80 and 100 ................ 49

Figure 4-9 Plot Step 2, 6063-T6 ........................................................................................... 49

Figure 4-10 Area where the Sample is Buckling .................................................................. 50

Figure 4-11 Aliasing is present in the AISI 4130 Acceleration Graph ................................. 51

Figure 4-12 Energy Absorption Comparison ........................................................................ 52

Figure 4-13 Acceleration Comparison .................................................................................. 52

Figure 4-14 Deformation Comparison .................................................................................. 52

Figure 5-1 Drop Test Rig showing the components used to calculate the average velocity.53

Figure 5-2 - Average Speed laser light and receiver ................................................................ 53

Figure 5-3 (a) Average Speed Sensor, (b) National Instruments Data Logger ..................... 54

Figure 5-4 Calibration of the Accelerometer [40] ................................................................ 54

Figure 5-5 - Accelerometer Calibration Data Card.................................................................. 55

Figure 5-6 - Accelerometer, displaying the Model Number .................................................... 55

Figure 5-7 - Average Speed Sensor Test ................................................................................. 56

Figure 5-8 Acceleration vs. Time, Aluminium Sample Number 1, Full Drop ..................... 57

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Figure 5-9 Acceleration vs. Time, Aluminium Sample Number 2, Full Drop ..................... 57

Figure 5-10 Acceleration vs. Time, Aluminium Sample Number 3, Full Drop ................... 58

Figure 5-11 Acceleration vs. Time, Steel Sample Number 1, Full Drop.............................. 59

Figure 5-12 Acceleration vs. Time, Steel Sample Number 2, Full Drop.............................. 59

Figure 5-13 Acceleration vs. Time, Steel Sample Number 3, Full Drop.............................. 60

Figure 5-14 Acceleration vs. Time, Aluminium Sample 1 ................................................... 61

Figure 5-15 Acceleration vs. Time, Aluminium Sample 2 ................................................... 61

Figure 5-16 - Acceleration vs. Time, Aluminium Sample 3.................................................... 62

Figure 5-17 Acceleration vs. Time, Steel Sample 1 ............................................................. 62

Figure 5-18 Acceleration vs. Time, Steel Sample 2 ............................................................. 63

Figure 5-19 Acceleration vs. Time, Steel Sample 3 ............................................................. 63

Figure 5-20 - Aluminium Sample 3 ......................................................................................... 65

Figure 5-21 - Percentage Energy Absorption Comparison ...................................................... 65

Figure 5-22 - Average Acceleration Comparison .................................................................... 66

Figure 5-23 - Acceleration Multiplied with Time Duration .................................................... 67

Figure 5-24 - Deformed Aluminium Fixture, this fixture could not be reused........................ 68

Figure 5-25 - Sample Holding Fixture ..................................................................................... 68

Figure 5-26 - Experimental Setup; the planks of wood were meant to arrest the trolley before

it damage the sample fixture .................................................................................................... 69

Figure 5-27 - Deformed Steel Sample #2 which could not be removed from its fixture ........ 70

Figure 5-28 - Image showing the buckling mode of the aluminium FEM sample .................. 71

Figure 5-29 - Buckling mode schematic for all of the samples tested ..................................... 71

Figure 5-30 - Aluminium Sample #1, deformed as if it had a clamped-pinned end condition 72

Figure 5-31 - Steel Sample #3 deformed as if it had a clamped-pinned end condition ........... 72

Figure 5-32 - Top end of the aluminium sample #1 ................................................................ 73

Figure 5-33 - Drop Test Rig Trolley and Cage ........................................................................ 74

Figure 5-34 - Broken leg of the cage ....................................................................................... 75

Figure 6-1 Comparison between the deformed shapes of the Chrome-moly (a) and (b), and the aluminium (c) and (d) ........................................................................................................ 76

Figure 6-2 - Energy absorption of the samples after 85mm of deformation ........................... 77

Figure 0-1 - AISI 4130 Material Setup .................................................................................... 89

Figure 0-2 AISI 4130 Mesh Control ..................................................................................... 90

Figure 0-3 AISI 4130 Drop Test Setup ................................................................................. 90

Figure 0-4 AISI 4130 Result Options ................................................................................... 91

Figure 0-5 - 6063-T6 Material Setup ....................................................................................... 91

Figure 0-6 - 6063-T6 Result Options ....................................................................................... 92

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List of Tables

Table 2-1 - AISI 4130 Steel, normalized at 870C (1600F) Properties [19] ......................... 22

Table 2-2 - 6063-T6 Properties [21] ........................................................................................ 23

Table 2-3 Side-by-Side Comparison between AISI 4130 and 6063-T6 ............................... 24

Table 3-1 Experimental Matrix, Camera Results ................................................................. 38

Table 3-2 Experimental Matrix, Accelerometer Results ...................................................... 38

Table 3-3 - Experimental Matrix, FEM Analysis .................................................................... 40

Table 4-1 - Finite Element Analysis Results, AISI 4130......................................................... 44

Table 4-2 Finite Element Analysis Results, 6063-T6 ........................................................... 45

Table 5-1 Aluminium Samples Energy Absorption.............................................................. 64

Table 5-2 Steel Samples Energy Absorption ........................................................................ 64

Table 6-1 - percentage Comparison between the FEA and Lab Results ................................. 77

Table B-1 - AISI 4130 Chrome-Moly Finite Element Analysis Results ................................. 86

Table B-2 6063-T6 Aluminium Finite Element Analysis Results ........................................ 87

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List of Symbols and Nomenclature

Abbreviation Definition Explanation

CAD Computer Aided

Design

The use of computers to aid in the design and

analysis of components.

CFD Computational

Fluid Dynamics Computer aided fluid dynamics software.

Chrome-moly Steel Alloy Chrome-moly is a steel alloy with the agents

chromium and molybdenum.

Euro NCAP

European New Cap

Assessment

Programme

This organisation tests new cars for crash safety for

drivers and passengers.

FEA/FEM

Finite Element

Analysis/Finite

Element Method

used

interchangeably

Computer software used for complex strength of

material simulations and calculations.

FIA

Federation

Internationale de

lAutomobile

Governing body for the South African Solar

Challenge.

Ilanga: isiZulu Word for Sun Ilanga I and Ilanga II are the University of

Johannesburgs first and second solar cars respectively.

SACS 2012

South African

Solar Challenge

2012

Cross-country race around South Africa for

alternative fuelled vehicles, to promote the research

and development of alternative energy.

UJ University of

Johannesburg.

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1. Problem Formulation Background to the Investigation

The University of Johannesburg (UJ) has endeavoured to participate in the South African

Solar Challenge 2012 (SASC). This is an alternative fuels race around South Africa, covering

a distance of over 5 000km. UJ has already built one car for the race, Ilanga I; Ilanga is the isiZulu word for sun. Ilanga I was built by a team [then] final year mechanical and electrical engineering students. The team has since graduated and are studying their Masters degrees. They are currently designing the next generation solar vehicle, Ilanga II. A new team of final

year undergraduate engineering students have begun optimisation work on Ilanga I. In this

text, the senior students will refer to the students currently working on Ilanga II, and the undergrads will refer to those working on Ilanga I.

After testing Ilanga I, it was found that the single motor would not provide enough power to

drive the car at a reasonably competitive speed. The car was redesigned to have four wheels;

the two rear wheels each powered by hub motors. The decision was made to use AISI 4130

chrome-moly for the chassis of the updated Ilanga I-I, instead of the 6063-T6 aluminium

alloy used in Ilanga I.

Ilanga I presents a rich source of final year design and research project for the undergrads to

work on. Some of the design work involves reconfiguring and optimising the front and rear

suspension, updating the rear drive system and implementing an updated braking system.

Some of the research projects include researching new methods of solar cell encapsulation,

computational fluid dynamics (CFD) of the body and finite element analysis (FEA) of the

chassis and front impact zone. The main purpose of doing this design and research work on

Ilanga I is to build a team of engineers who are skilled and capable to compete in the SASC.

Ilanga I may be seen as the proving ground for the students involved. The knowledge and

skills gained working on Ilanga I will be used to good effect in carrying this initiative further.

Safety in any form of sport or industry is paramount. There ethical and legal issues that come

into effect should an individual be harmed or killed; thus, the ever-present need to pursue

safety in mechanical engineering through scientific research. The European New Cap

Assessment Programme (Euro NCAP) subjects new European motor vehicles to crash tests to

evaluate safety. The car is then awarded a certain star rating, based on its performance, where one star is the worst performance, and a five star rating is the best [1]. This system

rates the cars for driver, passenger (front and rear) and pedestrian safety. The Federation

Internationale de l'Automobile (FIA) set standards for occupant safety for the motorsports

events they govern. The SASC is an event governed by the FIA; they have regulations

pertaining to the safety of the competing vehicles. Included in the regulations are rules

concerning the front impact safety of a solar car. This implies the front impact structure must

be made from a suitable material, in a particular configuration to achieve the standards

necessitated by the FIA [2,3].

The importance of developing cars with a good crash structure cannot be overstated. It is first

instructive to know what Newtons First Law is and how it applies to the current investigation. The First Law states that if a body is on motion, it will continue with that

motion in a straight line unless acted upon by some net external force [4]. So if a vehicle is

moving at a certain speed, the occupants are moving at that same speed. If the vehicle should

suddenly stop, the occupants will want to continue moving, unless they themselves are

brought to rest by some restraint (seat belts or airbags). Their internal organs will however,

still want to continue in the same line of motion. This is how internal injuries occur during a

collision [5].

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The field of crash testing is a vitally important one in automotive design. Essentially, energy

management is the core focus of crash testing [6]. As a vehicle is traveling, it has a certain

amount of kinetic energy, according to the equation [4]:

(1.1)

Where:

- = the kinetic energy of the moving vehicle - m = the mass of the vehicle - v = the velocity at which it is travelling

According to the law of the Conservation of Energy [4], one of the most fundamental laws of

nature, energy cannot be created nor destroyed. The implication for a vehicle collision is that

the kinetic energy the car has when moving has to be conserved throughout the accident. This

means that, during the collision, any deformation of the structure of the vehicle will absorb

energy. This is desirable since this energy will not be transmitted to the occupants. During the

collision, the rate at which energy is converted from kinetic energy of the moving vehicle, to energy used to deform the structure should be as slow as is practically reasonably, i.e. while still absorbing an appreciable amount of energy. According to Newtons Second Law, the force acting on an object is equal to the mass of the object multiplied by the acceleration

that object is subjected to [4]. Therefore, the magnitude of the acceleration of a vehicle

during a collision should be made as small as possible.

Engineers have tried to make cars safer by including crumple zones in their designs. A

crumple zone is a part of the chassis specifically designed to deform in a controlled manner

during an impact, absorbing energy [7]. These structures are typically placed at the front and

rear of the car. Their design can be likened to that of a fruit juice bottle. The ridges on the

outside of a fruit juice bottle are not there merely to facilitate gripping of the bottle, but they

are there to make it easier for the user to crush the bottle so it takes up less space in a waste

basket. See Figure 1-1. It is worth mentioning that any destructive event that happens to a

vehicle during a collision serves to dissipate energy windscreen shattering, wheels detaching or bodywork deforming. Crumple zones deform in a controlled and predictable

manner, absorbing energy This is why many times in motor racing, a driver will walk away

unscathed from a seemingly terrible accident.

Figure 1-1 Drinks bottle with a crude 'crumple zone' [8]

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One could argue that if the main goal is to dissipate energy, way not make the entire car a

crumple zone? There is one section of the car that is built rigidly. The passenger compartment

is built to not deform to provide a survivable area within the vehicle where the passengers

will be relatively unharmed [7].

With the preceding statements kept in mind, the objective of the investigation is brought to

light. The materials used to construct vehicles participating in the SASC have to be

investigated. The front impact zone should ideally be constructed from a material which can

absorb a large amount of energy. All the energy absorbed by the crash structure would not be

transmitted to the occupants. The research undertaken in this report serves to determine

which material is better suited for the front impact zone.

There are two primary functions this research will serve to achieve. The first objective will be

to determine which material is best suited for the construction of the front impact zone. This

will be determined by the rate and amount of energy dissipation of the material, under an

impact loading condition. The second objective will be to determine how closely the real

world tests compare to finite element analysis (FEA) simulations of the crash test. This

Report will detail the process followed during the design of the experiment, the experimental

results, discussions and conclusions. The information and skills gleaned from the subsequent

experiments can be used to design and test more intricate front impact zones in the future.

1.1 Problem Statement

The experiments conducted are meant to:

1. Determine the most suitable materials to use for the front impact zone of Ilanga I. This will be based on the energy dissipation characteristics of the different materials,

when subjected to an impact load. The two materials under consideration are 6063-T6

aluminium and AISI 4130 chrome-moly.

2. Compare the results obtained from FEA simulations to those obtained in real world

lab tests. This will form the basis for future work when simulating the entire front

crash zone of future solar cars.

1.2 Hypotheses

1. The aluminium will absorb more energy than the steel samples. 2. The steel samples will result in a greater acceleration of the drop test rigs trolley than

the aluminium.

3. The FEA results will be accurate to within 60% of the laboratory tests, in terms of energy absorption comparisons between the aluminium and the chrome-moly.

FEA is used in many fields of engineering to model situations where hand calculations would

be impractical. It is a method for computing strength of materials properties (stresses, strains

and deformations) using numerical techniques [9]. The plastic deformation of a material

under an impact load is just such a case. Knowing how to perform a finite element analysis

may prove to be an important skill for an engineer, it would be beneficial to incorporate such

a study into this research project.

Euro NCAP and FIA crash tests both use high speed cameras to film their tests. This gives

the testers an additional resource to use in order to ensure quality in their investigations.

According to Ref. [10], high speed cameras can be used in many fields of university research.

Use of high speed cameras would be greatly beneficial to the current investigation. High

speed cameras could be used to film an impact test and useful results velocity, deceleration, deformation and the like can be gained from its use.

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As was previously stated, the chassis of Ilanga I was constructed using 6063-T6 aluminium

alloy. The new car, Ilanga I-I would use AISI 4130. As such, the front impact zone would be

constructed using either one of these two materials. Since the chassis has a modular design, it

would be possible to use one material for the chassis, and a different material for the nose

section.

1.3 Scope of the Experiments

The scope of the experiment is as follows:

1. Samples of continuous diameter, hollow tubes of 6063-T6 aluminium and AISI 4130 chrome-moly will be used. The diameters of these tubes will be the same as those

being used on Ilanga I ( 31.761.8mm aluminium) and on the updated Ilanga I-I ( 19.051.25mm AISI 4130 steel). The sample will be attached to a rig which will subject the sample to a longitudinal impact loading. UJ has a piece of equipment

which can be used to facilitate a vertical drop test. The rig will be positioned to the

correct height and the appropriate mass will be fixed to ensure a certain potential

energy is achieved. The mass will be released from this height, it will fall and impact

the sample; in the process, energy will be absorbed. An accelerometer will be fixed to

the mass to measure the rate of deceleration. This measurement will be used to

calculate the amount of energy that was dissipated and the rate of this energy

dissipation by the sample. This process will be repeated, both for the aluminium and

the chrome-moly sample. Thus, a comparison can be made between the two materials

to determine which one produces the slower rate of deceleration and which material

absorbs more energy. These experiments will be filmed using high speed cameras; an

additional set of data can be used to verify the results.

2. The abovementioned samples will be modelled using a finite element analysis package, SolidWorks Simulation. The material properties will be programmed into

the software package for both the materials to be tested. The FEA samples will be

subjected to the same loading condition as the one described for the lab test, and the

simulation will be run. A comparison can be made between the energy dissipation

results obtained between the real world tests and the FEA simulation. This will then

give an indication as to how accurately the FEA simulates the real world, and then a

decision can be made as to whether FEA can be used to model the entire front impact

zone in the future.

The FEA simulation serves another purpose, that is, to expose the experimenter to finite

element analysis, and thus increase the skillset and knowledge available to the UJ Solar

Team.

Items which are not covered in the scope of this investigation include:

1. Testing of composite materials. 2. Testing of the fibreglass nose cone of the solar car during a frontal impact. 3. Testing/analysing the survival cell of the chassis of the solar car. 4. Determining the deflection of the solar array during a frontal collision. 5. Testing what effect welding has on the energy absorption.

1.4 Required Resources

The experiment has to be designed in such a way as to be cost effective, as a budget of only

R1 200 has been allocated. With this budget, the materials must be purchased and any other

costs must be covered. The University has the some resources and equipment at their

disposal; their use will be free of charge, once permission to use them has been granted.

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1.4.1 Available Resources

- Drop Test Rig: This rig has a trolley which can be loaded with gym weights. The maximum weight of the rig is 200kg (including the trolley). The sample is loaded at

the bottom and once ready, the weight is raised up to the desired height and released.

Use of this equipment will be invaluable to the experiment.

- High Speed Camera: The University has a film studio on campus, whose main role is to film the construction and testing of the two solar cars UJ is building. They have

sophisticated camera equipment that can film at an increased frame rate, thus allowing

the footage to be slowed down, while maintaining high picture quality. If they would

agree, they could film the experiment. Along with accelerometers, this footage could

be used to determine the deceleration of the sample. This will add an additional set of

data to the results.

- Computers to perform the FEA: UJ has a centre for mechanical design, the SMO, which has the necessary software to perform the FEA of the experiments. They have

also obtained academic Editions of SolidWorks 2011-2012 and Abaqus which they

have supplied to the final year students. The Solar Lab, the labs where the cars are

being built, has Creo available. With these software packages, a decent FEA can be

conducted.

1.4.2 Equipment to be sought

- Material Samples: If it falls within the budget, ideally at least three samples each of the AISI 4130 chrome-moly and the 6063-T6 aluminium alloy should be purchased.

Ilanga Is current front crash structure is made from 31.73mm 6063-T6 tube. This is a standard size available in South Africa. The steel alloy used in the updated

suspension is AISI 4130 19.051.25mm tube. These two materials will be used in the experiments. The lengths of these samples will be 500mm, plus an additional

100mm which will be fitting in the fixture.

- Accelerometers: In order to ultimately obtain the energy dissipation, the deceleration has to be measured. This will be done in part be the high speed footage, on the one

hand, and on the other, by accelerometers placed on the rig.

1.5 Experimental Variables

Any experiment essentially compares the relationship between variables. In order to answer

the question set out in the problem statement, the variables which affect the experiment

should be identified and classified. They can be grouped into independent, dependent and

extraneous variables [11]. More about the experimental setup and design will be covered in

later sections, but the following lists the variables identified for the present investigation.

1.5.1 Independent Variables

Independent variables are those over which the experimenter has control. This includes the

material of the samples and amount of potential energy of the mass in the drop test rig. The

values and/or characteristics of these variables have been added in italics. The variables are:

- Dimensions of the material samples. This includes length, diameter and wall thickness. This also includes whether or not the material will be of a constant

diameter.

o AISI 4130 19.051.25mm, 600mm long o 6063-T6 31.763.18mm, 600mm long

- The potential energy of the mass that will be dropped onto the sample to provide the impact load. The potential energy includes both the mass to be dropped and the height

Page | 17

from which it will be dropped. The potential energy can be set be changing the mass

and/or height above the sample.

o Potential energy will be set at 4 500J The mass will be 150kg The height above the sample will be 3.06m above the sample.

- Frame rate of the cameras filming the experiment. The higher the frame rate, the more frames (points of reference) there will be when analysing the footage. Increasing the

frame rate by 2-3 times would be acceptable.

o Maximum frame rate of the Sony EX3 = 60fps - Increment marking of the scale. The scale (which will ultimately be used to measure

the speed of the falling mass) will have to be marked using some convenient

increment. It should be such that it can be seen easily by the camera. This variable,

and the one stated above will not influence the deformation of the material specimen,

but it will be important in evaluating that data obtained.

o Increments will be 20mm

1.5.2 Dependent Variables

The value that will change as a result of changing the above variables will be:

- The deceleration. - The energy absorption.

1.5.3 Extraneous Variables

Noise may affect the readings of the accelerometer somewhat; although, it will be subjected

to a very large force, which will stand out above the noise. Nevertheless, noise has to be

taken into consideration. It is thought that drift will not be a major issue when conducting this

experiment. Despite this, the tests will be done in a random order, thus ensuring that what

drift may exist, does not affect the results. That is, the first test may be of the steel sample,

the next test of a truss sample, and the following one of an aluminium sample. Randomisation

in the experimental procedure will mitigate the influence of drift.

1.6 Reviewing the Results

The experiments will be conducted using the resources and equipment mentioned above. The

use of accelerometers and high speed footage would yield two sets of data; each has to be

analysed in a different way.

1.6.1 Accelerometer Results

The mass impacting the sample will come to a stop, inevitably, and all of the energy would

have been dissipated. The salient issues are the average deceleration for a given amount of

deformation, and the average deceleration for a given amount of energy absorption. Ideally,

the magnitude of the deceleration should be as small as possible, while absorbing the highest

amount of energy.

The material samples will be fully defined in Section 3, along with the mass to be used in the

drop test rig. Target values for deceleration and energy absorption are set out by the FIA for

Formula One [12]; however, achieving the targets set out for Formula One will not be goal of

this investigation. They are included for the sake of completeness.

1.6.2 Footage Results

The mass impacting the sample will have a certain velocity and kinetic energy. Once the

mass impacts the sample, it will begin to decelerate. The deceleration of the mass can be

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obtained by observing the difference in speed values between each frame. Using this direct

observation, the deceleration can be measured, and consequently, the energy absorption can

be measured. Once these results, and those obtained by the accelerometer have been found,

they can be compared against each other to determine if they agree.

1.7 Finite Element Analysis

Either SolidWorks Simulation or Abaqus were considered to be used in these experiments finite element representations. Therefore, a very brief overview of each is given. After

reviewing these packages in more detail, it was found that, although Abaqus is superior in

terms of functionality, in has a very high learning curve. SolidWorks Simulation, on the other

hand, has reasonable capabilities, while being much user friendlier. The authors familiarity with SolidWorks is an additional advantage.

- SolidWorks Simulation: SolidWorks has been made available to the students, in the form of the 2011-2012 Education Edition. SolidWorks Simulation, as with

SolidWorks itself, is very user friendly. Thus, for an experimenter with little

experience using this type of software, this is a useful asset. SolidWorks Simulation

has the capability to model a non-linear analysis, which is what this type of

experiment calls for.

- Abaqus: This is a dedicated finite element package, specifically designed to model both linear and non-linear studies. This is one of the primary FEA programs on the

market. It would be ideal to use this package; however, there are a few key concerns.

Firstly, the University has the academic version, which limits mesh size of the models

to 1 000 elements. This may result in a mesh which is too coarse to yield accurate

results. The second concern is that Abaqus has a steep learning curve, much more so

than SolidWorks. If Abaqus is to be used, then access to a full version is required, as

well as a FEA course. Time and budget are the limiting factors, which rule Abaqus

out.

The following methodology is to be followed:

- The material sample is to be inputted into the program. This is easy to do in SolidWorks.

- The material properties have to be inputted. Since the material will undergo plastic deformation, the appropriate stress-strain behaviour is required. SolidWorks allows

the user to enter a tangent modulus, which is a simplification of the stress-strain

behaviour once the material has yielded. Alternatively, one could enter a series of

stress-strain relations, thus drawing an approximate stress-strain curve for the

material. Both packages allow the user to enter a strain hardening factor.

- The boundary conditions are to be inputted. In SolidWorks, this is simply a case of selecting the appropriate face. The drop test simulation allows the user to enter the

velocity of the sample at impact, as well as the direction and strength of gravity.

- The mesh will have to be generated. A mesh control will be applied to the sample, netting a finer mesh on the sample, and a courser mesh on the weight subjecting the

sample to the load.

- The step time for the simulation has to be defined. - The simulation can be run after all the prerequisites have been met, and the results can

be analysed and compared to the real world tests.

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2. Literature Review

This Literature Review will look in-depth at all the aspects of this investigation, how to

perform it and the current state of technology in materials and impact testing. The materials

will be reviewed first, after which, the current state of technology concerned with impact

testing and finite element analysis will be reviewed. Strength of materials aspects, such as

buckling and stress wave propagation will subsequently be reviewed.

2.1 Materials

The two materials under consideration in this investigation are 6063-T6 aluminium and AISI

4130 chrome-moly. It is therefore necessary to review these materials, their properties,

alloying agents and crystal structure. A cursory mention of the other fundamental engineering

materials will be made, before looking in-depth into metals.

Ilanga I currently has a crash structure made from aluminium. The updated Ilanga I-I will use

chrome-moly. This steel is used for aircraft, and is approximately three times stronger than

the aluminium (ultimate tensile strength); it is also three times heavier. The most appropriate

material will be selected from these two.

2.1.1 Material Classes

Ashby, et. al. [13] states that there are five fundamental engineering materials. These are:

Ceramics, Metals, Polymers, Elastomers and Glasses. These materials can be combined

together in certain proportions to obtain some hybrid material. These groups of materials are

known as families. Each member of a certain family of materials will have certain traits in

common with the other members. Each one of these families can be subdivided into classes,

sub-classes and members [13,14]. These members have attributes specific to it. It is these

attributes that are important when selecting a material. Certain materials have attributes in

common with others, but each individual material will have a specific combination of

properties, which makes it unique. When selecting a material, it is important to select the

material which offers the best compromise of attributes. In the following sub-section, the

metals family will be looked at; a metal product will be used for the crash structure.

2.1.2 Metals

Metals generally have a high modulus of elasticity, that is, they are generally stiff. Unless

alloyed with some agent, pure metals will deform quite easily, meaning that they have a low

yield strength. The yield strength can be increased by alloying, or by heat treating. Despite

this, under standard conditions (not extremely low temperatures), the material will remain

ductile, thus alloying to yield a certain amount before failing/fracturing. The resistance the

material has to fracturing in called toughness. Metals will generally corrode if not protected,

either by some surface treatment, of by the introduction of some alloying agent [13].

Metals have many properties that are appealing to an engineer. A wide range of treatments

can be conducted on them to increase strength, corrosion resistance, electrical conductivity

and the like. A full review of the mechanical properties of metals is beyond the scope of this

review, so only some pertinent aspects will be discussed.

2.1.2.1 Grain Structure

Metals are cast when they are in the liquid phase. As the metal begins to cool, the molecules

of the metal start forming bonds with each other. This yields a grain of an almost perfect

crystal structure. This happens at different locations within the cast, concurrently. Eventually,

the metal will contain many hundreds of these crystals within it. The lattice structure of these

crystals has a different orientation from one grain to the next. The yield strength of a material

Page | 20

is based largely of the size, shape and orientation of these grains [14]. The grain itself has a

very high yield strength, but the weakness of the material lies in the grain boundaries. A

crack will propagate along grain boundaries much faster than it would propagate through the

grain itself.

Alloying was mentioned earlier, what some alloying agents, like magnesium, do is promote

grain refinement [14]. What this means is that the grains in the metal become much smaller,

increasing the amount of grain boundaries. It seems counter-intuitive that this would make

the metal stronger, but it does. With smaller grains, the number of grain boundaries increase,

thus increasing the number of discontinuities; this hinders crack propagation [14].

Figure 2-1- Microscopic Image of Low Carbon Steel Grains [15]

In Figure 2-1, the microscopic grain structure is shown. This image shows a low carbon steel.

High carbons steels have a grain structure as shown in Figure 2-2. The dark areas are graphite

flakes imbedded in the metal.

Figure 2-2 - Microscopic Image of High Carbon Steel Grains [16]

Page | 21

2.1.2.2 Strain Hardening

Metals can be strain hardened. This means that if a metal undergoes strain, or a deformation,

it will become harder and stronger [13,14]. The reason for this is that the grains within the

metal become deformed. Thus, the grain boundaries will once again present discontinuities to

impede crack propagation. The amount that a metal will strengthen is depended upon a

quantity known as strain hardening index. Thus, a material can be processed (cold rolled) to

increase strength. For a more in-depth study of this topic, refer to one of the following

references [17,13,14].

Strain hardening is of particular interest for the current investigation, because the material

subjected to the impact load will yield and deform plastically. Therefore, as the material

deforms, its material properties will change, thereby changing the energy absorption rate.

How this has an effect remains to be seen in the investigation.

2.1.2.3 Alloying

Alloying is a key concept in material science. It offers the designer some properties that he

otherwise would not have had. The steel, AISI 4130, for example, has the following

constituents: 0.5-0.95% Chromium, 0.12-0.2% Molybdenum [18]. The chromium serves to

increase corrosion and oxidation resistance, it increases hardenability, increases high

temperature strength, and can combine with carbon to form hard, wear resistant micro-

structures [18]. Molybdenum promotes grain refinement, and improves high temperature

strength [18]. Steels can be combined with many other alloying agents, such as silicon,

vanadium, nickel and others to produce these and other characteristics. Aluminium can be

alloyed in much that same way. 6063-T6 aluminium has been alloyed with magnesium and

silicon. The magnesium in an aluminium alloy serves to improve castability (with used in

conjunction with iron), improves ductility and impact strength. Silicon improves corrosion

resistance, but an excess of silicon, around 13% makes the alloy very difficult to machine

[18].

The preceding paragraphs provide a very cursory view of metals. For further information, the

reader may consult references [13,14,18]. The purpose of the above sections is to demonstrate

the range of possibilities, and material properties available when choosing a material. The

focus was given to metals, as a metal will be used to construct the components; at this stage

however, it is uncertain as to which metal will be chosen. The following sections will present

a list of material properties and selection criteria. After which, calculations will be made and

the most appropriate material will be selected.

2.1.3 Material Properties

Many materials one can purchase can be prepared in many different ways. AISI 4130 steel

can be purchased in the normalised condition, annealed, cold worked and many more [19].

All of these different processes change the material properties considerably. Therefore, it is

important to request a certificate when purchasing the material, to ensure the correct product

is delivered. The situation is slightly different when it comes to aluminium alloys. The

designation, 6063-T6 for example, includes the alloying agents and heat treatment properties

of the alloy. What follows are the material properties of the two materials under investigation,

and thereafter, the most pertinent material properties will be discussed.

Page | 22

2.1.3.1 AISI 4130 Chrome-Moly Table 2-1 - AISI 4130 Steel, normalized at 870C (1600F) Properties [19]

AISI 4130 Steel, normalised at 870C (1600F)

Physical Properties Metric English

Comments

Density 7.85 g/cc 0.284 lb/in

Mechanical

Properties

Metric

English

Comments

Hardness, Brinell 197 197

Hardness, Knoop 219 219

Hardness, Rockwell

B

92 92

Hardness, Rockwell

C

13.0 13.0

Tensile Strength,

Ultimate

670 MPa 97200 psi

Tensile Strength,

Yield

435 MPa 63100 psi

Elongation at Break 25.5 % 25.5 % in 50 mm

Reduction of Area 60.0 % 60.0 %

Modulus of

Elasticity

205 GPa 29700 ksi

Bulk Modulus 140 GPa 20300 ksi

Poissons Ratio 0.290 0.290 Calculated

Izod Impact 87.0 J 64.2 ft-lb

Machinability 70 % 70 % Annealed and cold drawn

Shear Modulus 80.0 GPa 11600 ksi

The most important properties for this material are the yield strength, tensile strength and the

elastic and bulk moduli. During an impact test, a likely mode of failure is buckling (covered

in more detail later). Buckling is dependent on the elastic modulus of the material, its cross-

sectional area and the eccentricity of loading [17,20]. The bulk modulus is important in the

calculation of the speed of stress waves traveling through the tube. The yield strength is

important; local buckling may occur and this may cause yielding in these areas. The tensile

strength may be exceeded during the impact test, thus, the value of this quantity is important.

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2.1.3.2 6063-T6 Aluminium Table 2-2 - 6063-T6 Properties [21]

Aluminium 6063-T6

Physical

Properties

Metric English Comments

Density 2.70 g/cc 0.0975 lb/in

Mechanical

Properties

Metric English Comments

Hardness, Brinell

Hardness, Knoop

73

96

73

96

500 g load; 10 mm ball

Hardness, Vickers 83 83

Tensile Strength,

Ultimate

241 MPa 35000psi

Modulus of

Elasticity

68.9 GPa 10000

Ultimate Bearing

Strength

434 MPa 62900 psi

Bearing Yield

Strength

276 MPa 40000 psi

Bulk Modulus 68.95 GPa 9.9-10.2 (106) psi [22]

Poissons Ratio 0.330 0.330

Fatigue Strength

Machinability

68.9MPa

50 %

10000 psi

50 %

@# of Cycles 5.00e+8

Shear Modulus 25.8 GPa 3740 ksi

Shear Strength 152 MPa 22000 psi

The quantities mentioned in the preceding section are important here as well. The modulus of

elasticity is lower than that of the steel. This would indicate that the aluminium would have a

lower buckling load, if all else remained equal. The aluminium tube being investigated

though has a great cross-sectional area; the calculation of the buckling loads will be

conducted in Section 5. The bulk modulus is also lower, indicating that the aluminium will

have a different stress wave propagation rate than that of the steel. The tensile and yield

strengths are also lower. Table 2-3 below shows a side-by-side comparison of the two

materials. The pertinent values discussed are present next to each other, for convenience. The

aluminium alloy has a lower yield than the steel, yet, on a strength-to-weight basis, it is

slightly stronger. It remains to be seen how these values will affect the energy absorption

properties of these materials.

Page | 24

Table 2-3 Side-by-Side Comparison between AISI 4130 and 6063-T6

Property AISI 4130 Value 6063-T6 Value AISI 4130/6063-T6 %

Yield Strength 435Mpa 214Mpa 203%

Ultimate Strength 670Mpa 241 278%

Modulus of Elasticity 205Gpa 68.9Gpa 297%

Bulk Modulus 140GPa 68.95GPa 203%

Density 7.85g/cc 2.7g/cc 291%

2.2 Current State of Impact Testing

Impact testing is a widely researched field. The automotive industry in particular has a vested

interest in developing improved crash structures. To this end, different types of energy

absorbing materials, as well as the use of buckling initiators are researched [23,24,25,26].

Much of the literature reviewed focuses on impact testing of aluminium tubes. It was found

that the main method of energy absorption of the aluminium alloys is due to the localised

buckling, and folding of the tubes [23,24]. The pattern of these folds is due to the material

properties, cross-section of the tube, and the method of loading [25].

Henning [23], conducted an investigation of imperfect 6063-T6 aluminium alloy tubes. The

samples are imperfect in the sense that grooves were machined into the walls of the tubes;

some samples had a spiral pattern machine and others had concentric grooves machined. The

aim of this experiment was to determine how these grooves would influence the energy

absorption of the material, compared to a standard, unmodified tube. The findings were that

the imperfections introduced a lower buckling load than was present in the unmodified tubes.

Additionally, unique buckling patterns were observed for the modified tubes; patterns not

previously seen. The energy absorption of the member was decreased as material is removed

to create the grooves. In this experiment, an Instron 250kN hydraulic testing system was

used.

Dong-Kuk, et. al. [24], conducted an experiment into determining the energy absorption of

square extruded aluminium tubes. In this experiment, thicknesses of 1.5, 2.0 and 3.0mm tubes

were investigated using a servo-hydraulic machine. The aim of this research was to determine

which thickness of material to use to promote folding of the member, not bending. It was

found that the 2.0mm sample proved to have the best energy absorption.

Karagiozova and Jones [25], investigated the axisymmetric buckling of circular cylindrical

shells. The aim of their research was to study the initiation of buckling and investigate

buckling as a transient process. Stress wave propagation was mentioned previously;

Karagiozova and Jones research investigating what role stress waves play in the buckling process.

Karagiozova [27], conducted in-depth study on the role stress waves play in the initiation of

buckling. Once again, square tubes were used in this investigation. It was found that the

initial stress state of the material influenced the speed of stress wave propagations. The final

shape of a buckled member can be analysed using an estimation of the speed of the stress

wave.

In many of these experiments, the tubes used are relatively short, on the order of 100-200mm

long. The tubes used in the present investigation are much longer, 600mm. The reason for

this is due to the design of Ilanga I. There is a large gap between the front of the chassis, and

the nose cone of the car. This was designed in this way to accommodate the array of solar

cells. This can be seen in Figure 2-3. So while the energy absorption of aluminium members

may be well documented, the current intended use is slightly different from the scenarios in

the literature presented above. However, Ref. [28] did a study on long-rods, but their

Page | 25

investigation was of high velocity impact (1 500m/s). More detail concerning the issues of

buckling, stress waves and energy absorption will be given in subsequent sections.

Figure 2-3 - Side view of Ilanga I

The front of the chassis is approximately 650mm behind the nose cone.

2.3 Finite Element Analysis

In the analysis of the real world components, the simple strength of materials equations are

generally unable to provide an adequate solution. The designer is then forced to use a

numerical approximation. The numerical solution usually used is called finite element

analysis or FEA. Many CAD software packages incorporate some FEA simulator, although

there are advanced FEA packages available for more intensive design work. These include

ANSYS, NASTRAN and Abaqus [17]. Without the use of numerical methods, like FEA, the

analysis would be subject to idealisations. This may be an idealisation of the boundary

conditions, or the initial value of a system described by a differential equation. In real world

engineering problems however, such idealisations may not be acceptable and the numerical

method should be employed [29].

The finite element method works thus: The field to be evaluated is essentially subdivided into

many smaller, geometrically simple shapes. These simple shapes can be described by the

location of intersecting points, or nodes. This is called the mesh. The governing equations

(either stress or thermal equations) can then be applied to each of these nodes. This result is a

matrix of equations, one equation for each node. If a differential equation were to be

established to describe the domain under evaluation, then the finite element methods solution would be equal to the solution of this differential equation, in the limit; that is when

the number of nodes tends towards infinity [29]. It is simple to think of FEA in the following

way. Suppose a geometrical model were to be subdivided into a number of elements. If the

location of each of the nodes and the angles between them are known, then the links

connecting the nodes can be thought of as beams in a truss, and evaluated as such. It is

important however, to properly consider the boundary conditions, and the load application

conditions. Although the calculation is now simple, there are hundreds, perhaps thousands of

Page | 26

nodes, therefore, a computer is necessary to complete the computation [17]. The method just

describes is the most straightforward and simplest way to grasp the way in which FEM

works.

Interpolation functions describe the distribution of variables (displacement, temperature or

electro-magnetic flux) through each element [9]. The method described in the preceding

paragraph assumes a linear variation of displacement between each node in the model. In

most FEM packages, the interpolation function is a polynomial. Polynomials are prevalent

because their integration and differentiation are easy to implement on a computer. A

polynomial function may also provide more accurate results, merely by increasing its order.

The real life displacement distribution between two nodes may be some curve; a polynomial

interpolation function may approximate this curve more accurately than a straight line

can [9]. Figure 2-4 shows a linear vs. a polynomial interpolation function. The polynomial

interpolation function is much smoother than the linear one; it approximates the sine curve

much closer. Figure 2-5 shows a simple finite element analysis of a cantilever. This study is

using simplex elements, and this can be calculated by hand.

Figure 2-4 - Straight line and polynomial interpolation functions [30]

Figure 2-5 - Simple finite element analysis [31]

After the body to be analysed has been discretised, the governing equations for a specific

analysis type (stress or thermal) have a constant form. All that has to be applied are the

material properties and loading conditions and nodal coordinates. The system of equations

can now be used to form matrices, which describe the entire system. These matrices have the

form [17,29,9]

[ ][ ] [ ] (2.1)

Where

- [k] = the stiffness matrix, i.e. the matrix containing the material properties. - [U] = the displacement matrix. This matrix describes the displacements of the

individual nodes, or the temperature distribution over the body.

- [F] = the force matrix.

Page | 27

The forces and the stiffness matrix are known quantities, and only the displacement vector

has to be found. This is done by inverting the stiffness matrix, and multiplying it with the

forces vector. As was mentioned earlier, the FEA method (also known as the Finite Element

Method, or FEM. FEA and FEM are used interchangeably) essentially simplifies the analysis

from a complex continuous problem, to a simple truss analysis. The material constant of the

body can be thought of as a spring constant between the nodes. Eq. (2.1) is directly

comparable to the equation relating displacement to force in a spring, [9]. The matrix simply represents a system with many equations relating force to displacement.

Loading and boundary conditions are crucial aspects to do correctly to ensure an accurate

solution. In terms of loading the object, care should be taken to not subject the load to a

single node. If this is done, the solution will indicate that that point will experience a very

large stress [32]. Although, it the designer is concerned about the stress condition at points far

away from the load application, then Saint-Venants principle may be employed [17]. Boundary conditions are the most difficult aspect to get right in an FEA simulation.

Oftentimes it is difficult to determine where the boundary conditions are, and what sort of

boundary condition actually exists there. In a situation where the type of boundary condition

is unknown, the designer may try the following approach: He can assume one type of

boundary condition, run the simulation and obtain the results. He can then assume another

plausible boundary condition and obtain those results. This will establish limits as to what the

expected deformations might be [17]. In such a case it is advised that the more conservative

results (that which shows the largest deformations) be employed.

Delving into more detail of how FEM works at a fundamental level is beyond the scope of

this review. The interested reader can consult a variety of sources, [9,31,33] for a more in-

depth explanation.

The preceding paragraphs discuss some of the aspects of a FEM analysis. The general

procedure required to perform such an analysis follows [9,34]:

1. Discretisation of the Problem: Subdivide the region into smaller elements. Each element is connected at nodes. Simplifications can be made in this step. These include

2D simplifications and symmetry. The size of the elements must be chosen. The

smaller the elements are, the larger the computational effort becomes. A compromise

must be reached between the element size and available computing power and time.

This is called known as creating a mesh.

2. Selection of the appropriate shape function: The nodal values are used to define this function for each element. Linear functions are used for simplex element and

higher order elements use polynomial shape functions.

3. Derivation of the basic element equations: The stress-strain relationship between the elements must be known, in order to generate the stiffness matrix. The work or

energy methods can be employed to do this. Ref. [9] details how to do this.

4. Calculation of system equations: Equations for each of the elements are determined. If simplex elements were used, then this is an exact solution, and if higher order

elements were used, then numerical integration is used. This step provides the system

equations.

5. Incorporation of the boundary conditions: The boundary conditions, such as an initial displacement or reaction force, are substituted into the system of equations.

6. Solution of the system equations: Having substituted the boundary conditions, the system of equations can now be solved for the displacements, stresses and strains.

Either the wave-front method or the elimination method is used.

7. Post processing: The results of the analysis are found. These results can now aid in the decision making process for any design/analysis.

Page | 28

8. Presentation and Reporting: The results are presented by means of contour plots. The report is written up; the report includes all assumptions and information

necessary for someone else to conduct the analysis.

In the realm of FEA, when analysing stresses, two situations can be encountered. These are

linear and non-linear. The linear analysis is concerned with finding the deflections within a

body, while it still remains elastic, that is, when Hookes Law is still obeyed. This is much simpler than the non-linear case, in which, the material has yielded, and no longer obeys

Hookes Law. In this case, the theory of plasticity must be taken into account. Analysis of this type requires detailed knowledge of the true strain-strain relationship for that particular

material so the FEA package can accurately simulate the deformation.

2.4 Governing Regulations

Formula One, the top motor-racing enterprise governed by the FIA has very stringent

regulations. Many of these pertain to the safety of a driver, should he be involved in an

accident. The regulations concerning the South African Solar Challenge are not that stringent.

Thus, the Formula One regulations serve to be the best starting point to begin the

investigation.

Article 16: Impact Testing, in the FIA Technical Regulations for Formula One [12] gives the

operating procedure to perform the front impact test. Article 16.2 in [12] details the minimum

requirements to pass the crash test:

- The peak deceleration over the first 150mm of deformation does not exceed 10g; - The peak deceleration over the first 60kJ energy absorption does not exceed 20g; - The average deceleration of the trolley does not exceed 40g; - The peak deceleration in the chest of the dummy does not exceed 60g for more than a

cumulative 3ms, this being the resultant of data from three axes;

Or:

- The peak force over the first 150mm of deformation does not exceed 75kN; - The peak force over the first 60kJ energy absorption does not exceed 150kN; - The average deceleration of the trolley does not exceed 40g; - The peak deceleration in the chest of the dummy does not exceed 60g for more than a

cumulative 3ms, this being the resultant of data from three axes.

The article states that any equipment or bodywork that could possibly affect the impact test

must be fixed to the car for the test. Additionally, the test rig should have a mass of 780kg,

including a 75kg dummy. Using these parameters, the above list of requirements must be met

in order to pass the test. It is worth noting that these regulations apply to a full scale crash

test. This is not the aim of this investigation. This investigation will serve to find a suitable

material that, when incorporated into a chassis, would be able to pass this FIA crash test.

Therefore, a full scale crash test of the solar car will not be conducted.

In addition to the FIA regulations, the SASC has its own regulations to adhere to. Article 3.12

in [3] have the following three conditions for occupant safety:

a) All sharp edges, chains and sprockets must be covered when in use, and internal components or cargo must be secured.

b) Adequate ventilation must be provided to all occupants. c) The design and construction of the vehicle must be such that, in the event of a front-

end collision, any part of the vehicle structure (especially the solar array) will be

deflected away from the driver/passenger compartment. The deflection process should

be modelled and the results presented as part of the Event documentation.

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There are yet more regulations regarding the type of materials allowable for the event. Article

3.7 in [2] prohibits the use of titanium alloys for use in chassis construction. Although there

might be some benefit to using titanium alloys, they will not be considered in this report.

Article 5 in [2] also provides some valuable information regarding safety in general. Article

5.1.1 states that the cars are to be of a condition that would not represent a danger to the

driver or any other participants.

2.5 Buckling

In this investigation, the bulking load of the samples must be known. In strength of materials

textbooks, the critical buckling load is found by [20]:

(2.2)

Where

- P = the critical buckling load - E = Elastic modulus of the material - I = Moment of inertia of the cross-section - L = the length of the material - K = some constant which is dependent on the end conditions of the material.

Some notes can be stated about this equation. Firstly, it is the idealised case, where the load

will be placed exactly along the central axis of the sample; that is, no eccentricity in the

loading exists. Secondly, all else being equal, the buckling load only depends on the elastic

modulus of the material. This equation only describes the linear aspect of the phenomenon of

buckling. As soon as the material does buckle, then the system will be described in terms of

non-linear equations. The buckling process can be described by the material progressively

folding; the deformation occurs locally. This is the quasi-static load case. In the dynamic load

case, due to inertial effects of the load, the deformations occur along the entire length of the

bar [25]. Thus, after buckling, this equation will not provide any useful information, and

therefore, the numerical method must be employed. So although the chrome-moly will have a

higher buckling load than the aluminium [17,20], after buckling, not much can be said about

the energy absorption of either material, in terms of this equation.

When a column buckles, it can assume a number of shapes; each has the form of a

sinusoid [17,20].

Figure 2-6 - Sinusoidal Bucking Modes [35]

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Figure 2-6 shows the sinusoidal buckling modes with half, one, and one and a half periods of

a sinusoid. These buckling modes occur due to the pinned end supports. If the column had

different end conditions, the buckling modes would be different, as seen in Figure 2.7.

(a) (b) (c) (d)

Figure 2-7 - Columns with Different End Conditions subjected to Buckling Loads [36]

When a column is loaded dynamically, as in an impact test, the shape of the buckled column

depends on its geometry, material properties and the loading condition [25]. More

specifically, due to the inertial effects of the load, plastic waves may propagate along the

sample, thus causing different buckling patterns [25].

The experimental setup will be discussed in Section 3; nevertheless, some predictions of the

setup will be discussed presently. The samples to be tested will be fixed at the bottom, and

the top end will be free. Therefore, it is thought that the buckling mode of the sample will be

similar to that of Figure 2-7 (d), that is, one quarter of a period of a sinusoid. Hibbler, [20]

suggests that it is unlikely that a column subjected to a buckling load will buckle with more

than one period of a sinusoid.

2.6 Impact Loading and Strain Energy

A load can be applied to an object (beam/column) either gradually, suddenly, or the load can

impact the object (shock load). Consider a column, onto which a weight is placed. When the

load is applied gradually, mass is brought into contact with column, and released slowly, or

quasi-statically. The load on the column increases gradually; the resultant stress on the

column is then simply given by [17,20]:

(2.3)

For shock loads, Ref.s [17,20] derive a similar, yet subtly different equation, one determines the resultant stress due to the impact load, and the other determines the resultant elongation.

Ref. [17] uses the Law of the Conservation of Energy to determine the stress induced by a

shock load. The resultant equation is:

(2.4)

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Where:

- = Instantaneous stress due to the shock load. - = Stress induced should the load be applied gradually. - =Youngs Modulus for the material. - = Height above the column from which mass was released. - = Length of the column.

Should the height above the column, from which the mass is released, be zero, the

instantaneous stress induced would be:

(2.5)

Ref. [20] derives the maximum instantaneous deformation due to an impact load:

(2.6)

Where:

- = Instantaneous deformation due to shock load. - = Deformation should the load be applied gradually.

As was the case with the maximum stress induced due to a suddenly applied load, where h

equals zero, the deformation in this case is:

(2.7)

Equations (2.4) and (2.6) were both derived assuming that the potential energy of the mass above the

column will be converted into strain energy within the sample being deformed. In practice, there is

not a complete transfer of energy from potential to strain energy. There will always be losses,

including losses to heat or sound. Incidentally, Equation (2.1) is derived in much the same fashion;

utilising the Conservation of Energy Principle [9].

It would be fitting to discuss strain energy in a bit more depth. As was previously mentioned, energy

in a system is conserved, assuming no losses. According to the definition of work, a force acting on an

object which causes that object to displace will do work on that object [20]. In terms of physics, work

is equal to energy [4]. Therefore, the work done on a material Force F, multiplied by displacement x will be equal to the strain energy induced in that material. Following the derivations from Ref.s [9,20], we arrive at the following equation for strain energy induced in a material due to normal strain

[20]:

(2.8)

For the common case of a prismatic member, subjected to an axial load, Equation (2.8) can be

reduced to [20]:

(2.9)

Where:

- = Internal strain energy. - = Stress induced, which causes the strain.

-

= Integration over the volume of the material sample.

- N = Applied load which induces the stress and strain. - L = Length of the prismatic member. - A = Cross-sectional area of the member.

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Both Ref.s [17,20] go into more detail concerning strain energy and shock loads, but that is beyond the scope of this text. The present need is only concerned with find strain energies on axially loaded

members. At least for the elastic region of the deformation of the sample to be tested experimentally,

the equations presented in this section will serve the present purpose well.

2.7 Stress Wave Propagation

When a material is subject to a shock load, a stress wave will propagate through the sample.

According to the laws of physics [4], a disturbance will cause a wave. A wave is a transfer of

energy, without the accompanying transfer of matter. Waves (mechanical waves) require

three things: a source of disturbance, a medium through which to propagate, and a

mechanism by which the particles within the medium can interact with each other [4]. There

are two types of waves, transverse and longitudinal. Transverse waves occur when the

elements disturbed move perpendicularly to the line of action of the disturbance.

Longitudinal waves occur when the elements disturbed move parallel to the line of action of

the disturbance. Stress waves propagate longitudinally, much like sound waves; therefore,

similar theories apply to both sound waves and stress waves.

The speed of a longitudinal wave through a medium is dependent on the bulk modulus of the

material and the density of the material. They are related as follows [4]:

(2.10)

Where:

- v = Wave velocity. - B = Bulk modulus of the material (elastic property).

- = Material density (inertial property).

Technically, the disturbance moving through the material is not a wave, per se, as a wave is

formed by a repeated, periodic disturbance. The disturbance due to a shock load is a pulse.

Stress wave propagation is also dependant on two other factors: the initial stress state of the

sample as well as the direction of propagation through the sample [26].

Stress wave propagation is influenced by factors such as strain hardening as well as shear

stresses [37]. Additionally, the stress wave propagation depends on the stress state of the

materials through which it is propagating. The mechanisms by which the stress waves

propagate, and how they are influenced by the stress state of strain hardening properties of

the materials, are beyond the scope of this text.

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2.8 Energy Absorption of Dynamically Loaded Members

The area under the load vs. displacement curve is the energy absorbed by the material

[20,24]. D. Karagiozova and N. Jones [38] conducted a study to determine the energy

absorption characteristics of cylindrical cross-sections