University Of Glasgow School of Engineering Department of ...userweb.eng.gla.ac.uk/philip.harrison/Teaching/2011 Bruce Miller... · 1 University Of Glasgow School of Engineering Department

1

University Of Glasgow

School of Engineering

Department of Mechanical Engineering

Final Year Project

Manufacture and Characterisation of Magneto-Rheological Elastomers

By Mr Bruce Miller

Supervised by Dr Philip Harrison and Ms Gerlind Schubert

1 Abstract

This report deals with the manufacturing, testing and characterisation of Magneto

Rheological Elastomers (MRE’s). MRE’s are a set of smart composite materials consisting of

an elastomeric matrix with magnetic particles dispersed in said matrix. When a magnetic

field is applied the stiffness of the material changes instantaneously and reversibly. This is

due to the interaction of the magnetic particles dispersed in the matrix. This report deals

with the manufacturing processes and how to optimize them for the best mechanical

properties and most time efficient methods. Furthermore the method by which these

materials are compression tested while a uniform magnetic field is applied will be dealt

with. Finally the results from experiments will be used to compare the mechanical

properties of MRE’s with different volume percentages of magnetic particles, samples with

Isotropic and Anisotropic particle structures and finally samples with applied magnetic

fields. These results will be used in future work to generate a general constitutive model for

these materials.

List of Objecticves:

Design a test setup to create uniform magnetic field on samples while compression

testing

Compression tests on samples with different curing times to optimize manufacturing

technique

Compression Tests on anisotropic and isotropic samples with different Volume

percentage of Carbonyl magnetic particles (10%,20%,30%)

Compression tests on anisotropic and isotropic samples under the influence of a

magnetic field

Model material behaviour using Abaqus FEA

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Table of Contents

List of Figures ........................................................................................................................................ 3

List of Equations.................................................................................................................................... 3

List of Tables ......................................................................................................................................... 4

Glossary of Nomenclature .................................................................................................................... 4

Acknoledgements ................................................................................................................................. 5

Introduction .......................................................................................................................................... 5

Background Information ....................................................................................................................... 5

Manufacturing Process ......................................................................................................................... 6

Test Method ......................................................................................................................................... 9

Test Setup ........................................................................................................................................... 10

Test Results ......................................................................................................................................... 13

Pure Rubber, 10%, 20%, 30% Isotropic samples cured for 24 Hours at 25oC .................................. 14

Compression of Pure Rubber with different curing conditions ....................................................... 17

Compression of 10% volume Isotropic samples with different curing conditions .......................... 18

Compression of 10%, 20% and 30% Anisotropic samples ............................................................... 19

Compression of 10%, 20% and 30%, Anisotropic and Isotropic Samples with applied magnetic

fields ............................................................................................................................................... 22

10% Isotropic Samples ................................................................................................................ 23



10% Anisotrpic Samples .............................................................................................................. 26

20% Anisotropic Samples ............................................................................................................ 27

30% Anisotropic Samples ............................................................................................................ 28

Modelling of MREs .............................................................................................................................. 29

Modelling of 10% Isotropic Samples ........................................................................................... 30



Modelling of Pure Rubber ........................................................................................................... 42

Conclusions ......................................................................................................................................... 43

Bibliography ........................................................................................................................................ 44

Appendix A : Calculation for Solenoids ............................................................................................... 45

Appendix B: Faulty test setup results .................................................................................................. 47

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List of Figures

Figure 1 Picture of Heating Plates ......................................................................................................... 8

Figure 2 Picture of Electromagnet with mould in between poles ......................................................... 9

Figure 3 Picture of Electromagnet ........................................................................................................ 9

Figure 4 Original Magnetic Setup ........................................................................................................ 11

Figure 5 Revised Magnetic Setup ........................................................................................................ 11

Figure 6 Rendered Drawing of Test Setup........................................................................................... 12

Figure 7 Picture of Test Setup ............................................................................................................. 12

Figure 8 ............................................................................................................................................... 14

Figure 9 Microscopic Picture of 10% Isotropic Sample ....................................................................... 15

Figure 10 Microscopic Picture of 20% Isotropic Sample ..................................................................... 15

Figure 11 Graph of all Isotropic Sample Configurations ...................................................................... 16

Figure 12 Graph of Pure Rubber with different Curing Conditions ..................................................... 17

Figure 13 Graph of 10%v CIP samples with different curing conditions.............................................. 18

Figure 14 Microscopic Picture of 10% Anisotropic Sample ................................................................. 19

Figure 15 Buckling Samples ................................................................................................................. 20

Figure 16 Graph of all volume percentages of CIP for Anisotropic and Isotropic structures ............... 21

Figure 17 Graph of 10% Isotropic CIP Samples with different applied magnetic fields ....................... 23

Figure 18 Graph of 20% Isotropic CIP Samples with different applied magnetic fields ....................... 24

Figure 19 Graph of 30% Isotropic Samples with different applied magnetic fields ............................. 25

Figure 20 Graph of 30% Anisotropic Samples with different applied magnetic fields ........................ 26

Figure 21Graph of 20% Anisotropic samples with different applied magnetic fields .......................... 27

Figure 22 Graph of 30% Anisotropic samples with different applied magnetic fields ......................... 28

Figure 23 10% Isotropic Samples with 400mT applied magnetic field ................................................ 30


Figure 25 10% Isotropic samples no applied magnetic field ............................................................... 32

Figure 26 20% Isotropic Sample with 400mT applied magnetic field .................................................. 34


Figure 28 20% Isotropic Samples with no applied magnetic field ....................................................... 36



Figure 31 30% Isotropic Samples with no applied field ....................................................................... 40

Figure 32 Pure Rubber Modelling Curves............................................................................................ 42

List of Equations

Equation 1 Equation for Mass of CIP[] ................................................................................................... 8

Equation 2 Standard Ogden Model ..................................................................................................... 29

Equation 3 Standard Mooney Rivlin Model ........................................................................................ 29

Equation 4 Standard Neo Hookean Model ......................................................................................... 29

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List of Tables

Table 1 Rubber Poperties ...................................................................................................................... 6

Table 2 CIP properties ........................................................................................................................... 7

Table 3 Calculation of Masses ............................................................................................................... 7

Table 4 Youngs Moduli for all Isotropic Sample Configurations .......................................................... 16

Table 5 Youngs Moduli of Pure Rubber with different Curing Times .................................................. 17

Table 6 Youngs Moduli of 10%v CIP samples with different curing times ........................................... 18

Table 7 Youngs Moduli for Anisotropic Samples ................................................................................. 21

Table 8 Table of Youngs Moduli for 10% Isotropic Samples ................................................................ 23

Table 9 Table of Youngs Moduli for 20% Isotropic Samples ................................................................ 24

Table 10 Table of Youngs Moduli for 30% Isotropic Samples .............................................................. 25

Table 11 Table of Youngs Moduli for 10% Anisotropic samples .......................................................... 26

Table 12 Table of Young’s Moduli for 20% Anisotropic Samples ........................................................ 27

Table 13 Table of Youngs Moduli for 30% Anisotropic samples .......................................................... 28

Table 14 Table of Coefficients for Mooney-Rivlin Model .................................................................... 33

Table 15 Table of Coefficients for Neo-Hookean Model ..................................................................... 33

Table 16 Table of Coefficients for Neo-Hookean Model ..................................................................... 37

Table 17 Table of Coefficients for Mooney-Rivlin Model .................................................................... 37

Table 18 Table of R2 values for 30% Isotropic Samples ...................................................................... 41

Table 19 Youngs Modulus for 30% Isotropic Samples for Neo-Hookean Model ................................. 41

Table 20 Youngs Modulus for 30% Isotropic Samples for Mooney-Rivlin Model ................................ 41

Table 21 Youngs Moduli for Pure Rubber for Mooney Rivlin Model ................................................... 43

Table 22 Youngs Moduli for Pure Rubber Neo-Hookean model ......................................................... 43

Glossary of Nomenclature

MR effect- Magneto-Rheological effect whereby the stiffness of material increases with an

applied magnetic field

CIP- Carbonyl Iron Powder

Mullins Effect- The instantaneous softening of rubbers when the all time maximum applied

stress is reached

FEA- Finite Element Analysis

Magnetic Flux Density- This is the amount of magnetic field passing through a surface

measured in Teslas

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Acknoledgements

I would like to thank Dr Harrison for helping me out during this project.He has always kept me

organisedand wa always giving me new suggestions and some really good ideas to work on. I would

also like to thank Gerlind Schubert for helping with all backround information on this topic as well as

the analysis parts of the project. I would also like to thank John Davidson the materials lab

technician. He really helped with the testing and the test setup.

Introduction

Magneto Rheological Elastomers are a set of smart composites whose mechanical

properties can be reversibly and instantaneously changed when a magnetic field is applied.

These materials can be used in systems where the ability to vary the stiffness of a

component is required, such as vibration control systems and variable suspension systems

in automobiles. Currently there is no available general constitutive model for these

materials and the aim of Ms Schubert’s PhD research project is to develop a constitutive

model for these materials. The objective of this project is to undertake the preliminary

compression testing of these materials to determine their stress strain behaviour.

Furthermore the manufacturing process and testing procedures will be developed and

refined throughout. The objective is to test all the relevant specimens and all configurations

possible in order to assist with the development of the constitutive model.

Background Information1

Magneto Rheological Elastomers were first studied in 1995 by Toyota Central Research and

Development Laboratories. They tested silicone gels with the magnetic particles aligned

through dynamic shear experiments with small deformations. They noted the change in

moduli due to the effects of the applied external magnetic field. Further research was

carried out by Jolly and Carlsen in 1996 at the Thomas Lord Research Centre where they also

tested silicon gels under small deformation shear with and without magnetic field and noted

the change in storage modulus due to the applied magnetic field. The first applications for

this kind of material were brought forth by the Ford Motor Company. They suggested and

implemented the material as a suspension bushing thats stiffness could be altered to

change ride comfort or handling quality of their motor cars. Kallio2 carried out many

experiments in 2003 in order to discover which materials were best to create an MR effect.

Kallio conducted mainly small strain experiments and found that the best materials are

Silicone Rubber Matrix with CIP magnetic particles. Farshad3 in 2003 conducted

compression testing up to 30% strain, using anistropic samples and isotropic samples for

testing.

1 All Backround information has been researched through Ms Gerlind Schuberts 1st Year Literature Revue 2 M. Kallio Preliminary tests on an MRE device 3 M. Farshad Magnetoactive elastomer composites

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Furthermore testing with an applied magnetic field were conducted, although moving

magnets were used which means further steps are needed in calculations to allow for the

attractive forces of the magnets to be removed from the force measurements. Varga4 in

2005 conducted similar compression testing but chose to use a solenoid coil to apply

magnet fields to the samples. Applications for this material mainly involve vibration control

as the forced response can be controlled by changing the stiffness components in springs.

Manufacturing Process

For this project a silicone rubber has been chosen as the matrix material along with

Carbonyl Iron powder acting as the magnetic particle filler. The silicone rubber was chosen

since has been the most widely used matrix material for MRE’s in past research.

Furthermore it has good mechanical properties and chemical resistance over a large range

of temperatures. The rubber which is being used is defined by the manufacturer as

MM240TV. Like most silicon rubbers it consists of two parts. Part A and Part B where part B

acts as the hardener. The components are mixed at a ratio of 10:1. MM240TV has the

properties defined in Table 1.

Table 1 Rubber Poperties

Figures from data sheet provided by ACC silicones Ltd

Viscosity 96000 mPa.s Tensile Strength 5.4MPa

Elongation at Break 330%

Youngs Modulus 1.88MPa

Hardness 40o Shore A

The magntic particle filler that has been chosen is Carbonyl Iron powder. This is a typical

magnetic filler as it has high magnetic permeability, low remnant magnetisation and high

saturation.5 The CIP powder being used has the properties shown below in table 2

4 Z. Varga Magnetic Field Sensitive functional elastomers with tunable modulus 5Dr Philip Harrison - Magneto-Rheological Elastomers: Manufacture, characterisation and modelling Presentation

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Table 2 CIP properties

These values are based on the information provided by the provider BASF Ltd

*Values are based on BASF’s SQ standard

There is a third component which has been added to the MRE that is being used for this

project. It is defined by the manufacturer as ACC34 thinner. The reason that this is being

used is that the rubber on its own has a high viscosity and this leads to the agglomeration of

particles in the matrix. This in turn produces a non uniform distribution of particles. This can

makes modelling much harder. Therefore this solvent thinner has been added at 30%

weight to reduce the viscosity. This in turn allows for an even distribution of particles and

also allows the particles to align with the magnetic fields easily. However adding the thinner

will reduce the modulus of samples while no magnetic field is applied, this may lead to a

higher MR effect.

The amount of CIP that is required for testing is 10, 20 and 30 percent volume. The

equivalent mass was calculated using the Table 3 and Equation 1 shown below.

Parameter Unit Specification Test method

Iron Content g/100g Min 99.5 Calculated Carbon Content g/100g Max 0.05 IRS (RCA/Q-C-296)

Permeability (µi)* % 98-110 RCA/Q – C 302

Q-Value * a 100kHz % 95-120 RCA/Q – C 302

Particle Size Distribution

D50 µm 3.7-4.7 Microtrac X 100

Using 50g of Rubber Component A

Therefore: Mass of part B = 0.1 x 50 = 5g

Using 30 w% of Solvent therefore:

Mass of solvent = 0.3 x (50+5) = 16.5g

Table 3 Calculation of Masses

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Equation 1 Equation for Mass of CIP[6]

Where v = relative volume of CIP and x = required mass, 71.5g is the total mass of pure

rubber 1.06g/cm3 is density of rubber and 7.874 g/cm3 is density of CIP.

The next stage of the process was to mix the mixture thoroughly using a hand mixer for a

minimum time of three minutes. The mixture is then degassed in a vacuum chamber for ten

minutes in order to avoid air bubbles when the rubber is cured. The mixture is then poured

into moulds. These moulds are designed according to the standard sample size for test

method A of BS ISO 77427. The sample size required is 29mm ± 0.5mm diameter and

12.5mm ± 0.5mm height.

After the rubber has been moulded it requires time to cure, 24 hrs at 25oC or 1 hrs at 100oC

as defined by the manufacturer. In order to fast cure the rubber at 100oC the heating plates

shown in Figure 2 are used.

Figure 1 Picture of Heating Plates

6 Equations and Calculations are from Guide for rubber mixing process by Ms Gerlind Schubert 7 BS ISO 7742 Determination of Compression stress strain properties for Vulcanized Rubbers

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One of the objectives for this report is to optimize the manufacturing process therefore

samples will be fast and slow cured to find the optimal curing time.

In order to create anisotropy within the samples they will be cured while under the

influence of a magnetic field produced by an electromagnet. As shown in figures 3 and 4.

This will create chains of magnetic particles within the samples. For this project a magnetic

field density of 400mT (milli Teslas) was used during curing. This value was measured using a

gauss meter at the centre of the poles with no medium present. Unfortunately the amplifier

tends to get hot and becomes overloaded after time, this meant that the higher magnetic

field densities that were measured (max of 1 Tesla) could not be used. 400mT was found to

be a safe value in order to cure the samples for the necessary time without overloading the

amplifier. Furthermore other research projects have successfully used similar field densities

for creating anisotropy for example Varga 2006 [4].

Test Method

For this project the British Standard for Determination of compression stress-strain

properties for Rubber, vulcanized or thermoplastic (BS ISO 7743:2008) is being used. Test

method A from the standard has been selected and requires that the compression plates be

lightly coated in a film of lubricant. Furthermore the test requires four cycles at a speed of

10mm/min. From the recorded force displacement data the stresses and strains can be

calculated. The standard also requires a minimum of three samples for each sample

configuration.

Figure 3 Picture of Electromagnet

Figure 2 Picture of Electromagnet with mould in between poles

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Test Setup

In order to test these materials with an applied magnetic field it is necessary to create a

device or alternative setup to allow the magnetic field to pass through the samples while

they are compressed. A paper by Varga [4] indicated that a solenoid coil was used to

implement a uniform magnetic field during testing. The aim of this project was to use quite

a high field density of 400mT, and after some calculations (see appendix A) it was decided

that the required coil would be expensive and impractical for use. Another paper by Farshad

[3] indicated that a pair of permanent magnets could be used to generate a uniform field

through the sample. The test setup used by Farshad [3] indicated that the plates be wedged

between two aluminium plates while the compression took place, thereby the magnets

would move up and down with the compression. It was decided that this method was

inaccurate due to the fact that the attractive force between the magnets would increase as

the magnets were brought closer together. This would add false readings to the load cell

and would mean that additional steps would have to be taken to interpret the results

correctly. Therefore a new test setup was designed and assembled using neodymium

permanent magnets. The technical drawing is shown in figure 4. Unfortunately when this

setup was used there were some problems with the test results (see appendix B). Therefore

the setup was reworked again the revised setup is shown in figure 5. The magnetic field

density can be altered simply by making the distance between the magnets larger or

smaller. During testing a magnetic field density of 400mT was measured between the poles

at a separation of 36mm and this decreased to around 270mT at a distance of 47mm.

From the drawings provide you will see that the magnets are held in place as the

compression plates are free to move.

11

Figure 4 Original Magnetic Setup

Figure 5 Revised Magnetic Setup

12

Figure 7 Picture of Test Setup

Figure 6 Rendered Drawing of Test Setup

Wooden Blocks

Magnets

Clamps

13

Test Results

The tests that have been completed are:

Compression of Pure rubber, 10%, 20%, 30% volume CIP cured for 24 hours at 25oC. Purely Isotropic samples.

Compression of Pure Rubber cured for 1 hour and 1.5 hours at 100 oC.

Compression of 10% volume cured for 1 hour and 1.5 hours at 100 oC. Purely Isotropic samples.

Compression of 10%, 20% and 30% Anisotropic samples cured for 1 hour at 100 oC

under a magnetic field of 400mT.

Compression with applied magnetic fields using samples of 10%, 20%, 30% volume CIP cured for 1 hour at 100 oC. Purely Isotropic samples.

Compression with applied magnetic field using samples of 10%, 20%, 30% volume CIP cured for 1 hour at 100 oC under field of 400mT magnetic field. Purely Anisotropic Samples

During the testing it was noticed that the first cycle of loading showed larger force than the subsequent three cycles. This is effect is known as the Mullins effect and is typical for rubbers. This effect is defined as:

“The Mullins Effect can be idealized for many purposes as an instantaneous and irreversible

softening of the stress-strain curve that occurs whenever the load increases beyond its prior

all-time maximum value. At times when the load is less than a prior maximum, nonlinear

elastic behaviour prevails.”[8]

The main theory for why this occurs says that it is caused by the breaking of cross links in

the matrix materials, thereby reducing the overall cross-linking density and therefore the

stiffness of the material. This effect is illustrated by the full compression cycle test shown in

figure 8. As you can see the first cycle is higher than the others and all the others are equal.

8 Reference from (http://en.wikipedia.org/wiki/Mullins_effect)

http://en.wikipedia.org/wiki/Elastic_(solid_mechanics)

http://en.wikipedia.org/wiki/Mullins_effect

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Figure 8

Due to this effect for the comparisons of all tests the upload part of the third cycle will be

used. A mean curve will then be calculated from the third cycles of the four samples tested.

This ensures that there will be no softening after this loading cycle and therefore provides

more accurate data for creating a constitutive model.

This of course means that if these materials are ever used in a practical application there

will need to be a degree of conditioning before entering service. This would require the

material to be loaded to a higher stress than that which would be expected to encounter

during service.

Pure Rubber, 10%, 20%, 30% Isotropic samples cured for 24 Hours at 25oC

The samples mixed for this testing regime were cured for 24 hours at 25oC as prescribed by

the manufacturer. The samples produced the stress-strain data shown in figures 11 and

table 4. Figure 8 below shows the structure of an isotropic sample loaded with 10% volume

CIP at a magnification factor of x20 using a microscope, the white flecks are CIP clusters.

This photograph shows that there is no order to the distribution of particles. Figure 9 shows

a 20% volume isotropic sample of the same magnification. From figure 9 it can be seen that

there is a higher density of white flecks and therefore CIP.

Cycle 1 Upload

Cycle 2-4 Upload

All Unload Parts

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Figure 9 Microscopic Picture of 10% Isotropic Sample

Figure 10 Microscopic Picture of 20% Isotropic Sample

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Figure 11 Graph of all Isotropic Sample Configurations

Table 4 Youngs Moduli for all Isotropic Sample Configurations

Sample

Composition

Cure Time

(hrs)

Mean Youngs

Modulus (Mpa)for

0-10% strain

Percentage

Increase compared

to pure rubber

Pure 24 0.4856

10% 24 0.9505 95.737

20% 24 1.6845 246.890

30% 24 2.4553 405.622

Note that for comparing Young’s moduli we are considering only the 0-10% strain region

due to the fact that this region has very linear stress-strain behaviour and therefore a

relatively constant gradient, i.e. young’s modulus, unlike the higher strain regions where the

behaviour is very much non-linear.

As expected the higher volume percentage of CIP produces higher stiffness’s. The choice of

material for a specific application will depend on the required stiffness but also the limit of

weight.

17

Compression of Pure Rubber with different curing conditions

The samples for this set of tests were cured at 100oC for 1 hour, 100oC for 1.5 hours and

25oC for 24 hours. This is to check to see if there is a significant difference in stiffness for

different curing times in order to optimize the manufacturing process.

Figure 12 Graph of Pure Rubber with different Curing Conditions

Table 5 Youngs Moduli of Pure Rubber with different Curing Times

Sample

Composition

Cure Time

(hrs)

Mean Youngs Modulus

(Mpa)for 10% strain

% increase compared

to 24 hrs

Increase

Factor

Pure 24 0.4856

Pure 1 0.67 37.974 1.3797

Pure 1.5 0.7073 45.655 1.4565

From these results the fast curing process produces higher stiffness’s. This may be due to

additional energy being provided by the heating process, creating more intermolecular

bonding and therefore producing higher stiffness. Furthermore the 1.5 hours cured samples

have slightly higher stiffness than the 1 hour cured since the additional heat energy is

provided for a longer period.

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Compression of 10% volume Isotropic samples with different curing conditions

This set of test has been done to see if the stiffness of filled samples is altered by the

additional heat energy provided as shown in the pure rubber samples shown before. The

samples as before have been cured for 1.5 hours, 1 hour and 24 hours. These results are

very important to optimize the manufacturing process.

Figure 13 Graph of 10%v CIP samples with different curing conditions

Table 6 Youngs Moduli of 10%v CIP samples with different curing times

Sample

Composition

Cure Time

(hrs)

Mean Youngs Modulus

(Mpa)for 10% strain

Percentage increase

compared to 24 hrs

Increase

Factor

10% 24 0.9505

10% 1 0.9996 5.166 1.051657

10% 1.5 1.0052 5.755 1.057548

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From these results it can be seen that the addition of heat has very little affect on the

stiffness of the samples, there is only a 5% increase in stiffness. Therefore unlike the pure

rubber there is only a small amount of additional bonding caused by the additional energy

provided. This means that the interaction between the filler and the matrix does not allow

for strengthening of the matrix, it can therefore be assumed that most of the heat energy is

absorbed by the CIP particles. This may be due to a higher thermal conductivity. From these

results all future samples will be cured for 1 hour at 100oC.

Compression of 10%, 20% and 30% Anisotropic samples

These samples have been cured for 1 hour at 100oC under a magnetic field of 400mT. This

field strength was used mainly because the amplifier being used overloads after time while

high currents are used. The value of 400mT was a safe magnetic field density that could be

achieved for the full curing time needed. Furthermore other studies (VARGA [4]) have

shown that 400mT is adequate to create anisotropy. Figure 14 shows the structure created

by applying the magnetic field during curing. As you can see there are distinct chains of

particles as opposed to random orientation shown in figure 8 and 9.

Figure 14 Microscopic Picture of 10% Anisotropic Sample

Direction

of

Alignment

20

There have been some problems with the compression tests for this anisotropic structure.

The rubber samples when compressed actually buckled which is not supposed to happen

the rubber should remain at a constant volume and therefore the diameter of the sample

should increase with decreasing height. Figure 15and 16 shows one of the samples as it

buckles.

The result from this buckling is a very steep upload at the beginning of the cycle then it

flattens out. Interestingly this behaviour is very consisitent for all the samples. At first it was

suspected that because the moulds between the poles of the electromagnet were not

completely covered by the pole and it was thought that the flux density would be weaker at

the edge of the poles.

To stop this only one mould at a time was cured between the magnetic poles. Unfortunately

this did not solve the problem. It was then discovered that the moulds that were being used

had deformed due to the heat and pressure of the curing process. New top plates were

manufactured with additional screw holes for extra security. Unfortunately this still did not

stop the buckling. It may be that the shear modulus is much less than the compressive

modulus. In order to stop the buckling occurring, the film of oil on the sample during testing

was removed. This did stop the buckling but unfortunately this causes additional friction on

the sample during testing which means that the force displacement will not be comparable

with the other tests. The test results are shown in figure 14 and table 7, but it must be

stated that these results will not be an accurate representation of the anisotropic samples.

Figure 15 Buckling Samples

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Table 7 Youngs Moduli for Anisotropic Samples

Sample

Composition

Particle

Orientation

Mean Youngs Modulus

(Mpa)for 10% strain

% increase compared to

equivalent isotropic

30% Anisotropic 4.625 88.368

20% Anisotropic 2.5068 48.816

10% Anisotropic 1.2233 28.701

30% Isotropic 2.4553



Figure 16 Graph of all volume percentages of CIP for Anisotropic and Isotropic structures

22

Interestingly it can be seen that the higher percentages of CIP produce larger increases in

the Young’s modulus. This will be due to denser particle chains created by the magnetic

field. The higher concentration of ferromagnetic elements will create a higher magnetic flux

density within the samples when curing, meaning that the individual particles will be

magnetically attracted towards each other creating thicker and longer chains.

Due to the fact that buckling is a factor in the testing of Anisotropic samples, it may be more

poignant to perform tensile tests instead of compression to discover the mechanical

properties that Anisotropy creates.

Compression of 10%, 20% and 30%, Anisotropic and Isotropic Samples with applied

magnetic fields

This set of tests will deal with the effect of applying a magnetic field through the samples

while being compressed. The magnetic field should increase the stiffness of the samples and

the higher volume percentages should produce a bigger MR effect. Furthermore the

Anisotropic samples should produce a bigger increase compared to the Isotropic samples.

The increase in stiffness is caused by the interaction of the magnetic particles in the matrix.

The magnetic flux causes a magnetic dipole interaction between every particle in the matrix.

In the Anisotropic samples the magnetic particles will be closer together, thereby increasing

the attractive force between them as attractive force is a function of distance.

23

10% Isotropic Samples

Table 8 Table of Youngs Moduli for 10% Isotropic Samples

Sample Composition Flux Density

0-10% Youngs Modulus

10% 400 1.2453

10% 270 1.2697

10% 0 1.4567

As we can see the results are not as expected. The applied magnetic field should increase

stiffness not decrease it. The reason for this is currently unknown. It is a completely

unexpected result. The curves indicate that the samples with the 400mT applied field have

higher stress values than the 270mT but the gradient of these lines i.e. Young’s Modulus

indicate that the stiffness is lower for the higher Flux Density. This is contrary to work that

has been carried out previously. Furthermore the zero field samples, especially at higher

strains, have much higher stresses than those samples with an applied field. The only thing

that changed between the magnetically tested samples and the no field samples was that

for the no field samples a standard compression setup for the Zwick Z250 test machine was

used. That particular setup involved less pinned joints and fittings. These fittings may have

been slightly loose at certain points and may have resulted in a slightly decrease in the

measured force.

Figure 17 Graph of 10% Isotropic CIP Samples with different applied magnetic fields

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Sample Composition

Flux Density (mT)

0-10% Youngs Modulus (MPa)

20% 400 1.6624

20% 270 1.6478

20% 0 1.806

From figure 18 and table 9, we can see a similar result from the 10% isotropic samples in

that the samples with the applied magnetic fields have lower stiffness’s than the no field

samples. This would support the theory that the magnetic test setup is slightly flawed in

some way. This sample however shows that the Youngs modulus did increase slightly for a

higher magnetic field. From these results I would assume that the 10% samples have

become magnetically saturated and this may have had a detrimental effect on the

mechanical properties. The 20% samples, having a higher Ferro-Magnetic content can have

higher flux densities applied to them without saturating and therefore maintain an increase

in stiffness.

Figure 18 Graph of 20% Isotropic CIP Samples with different applied magnetic fields

25



From the curves and values shown in figure 19 and table 10 respectively, we can see that

the problem of the zero field samples having a higher stiffness than those with the applied

magnetic field is still partly true as the 270mT field samples still have lower stiffness.

However we are starting to see a larger MR effect as the stiffness of the 400mT sample is

higher than the other two configurations. This shows that for higher magnetic particle

loading we are getting a larger MR effect. If the problem with the magnetic test setup had

not been present, we would have seen that the 270mT field samples curve would fall

inbetween the other two configurations.

Sample Composition

Flux Density

(mT)

0-10% Youngs

Modulus (MPa)

30% 400 2.7491

30% 270 2.519

30% 0 2.5882

Figure 19 Graph of 30% Isotropic Samples with different applied magnetic fields

26

10% Anisotrpic Samples

Table 11 Table of Youngs Moduli for 10% Anisotropic samples

Sample Composition Flux Density (mT) Youngs Mod for 0-10% Strain MR Effect

10% 400 2.763363 0.123328795

10% 270 2.627874 0.068251451

10% 0 2.459977

From the results in figure 20 and table 11 we can see that compared to the Isotropic

samples we are seeing a larger MR effect, this is due, as stated previously, to the magnetic

particles being closer together. Still present is the fact that the zero field samples are

producing higher stresses than the 270mT applied field samples. From the curves we can

also see that there is a steep gradient in the 0.05 to 0.1 strain region followed by a levelling

off of the curve after this region. This may have been caused by buckling but it is unclear at

this point.

Figure 20 Graph of 30% Anisotropic Samples with different applied magnetic fields

27

20% Anisotropic Samples

Table 12 Table of Young’s Moduli for 20% Anisotropic Samples

Sample Composition Flux Density (mT) Youngs Mod for 0-10% Strain (MPa) MR Effect

20% 400 4.009061 0.042071333

20% 270 3.873636 0.006870444

20% 0 3.847204

As with 10% Anisotropic Samples we are seeing that the zero field samples have a similair

than the 270mT field samples. Again it is suspected that a loose fitting in the magnetic test

setup is to blame. We are also seeing that at higher strains for the zero field samples have a

slightly higher stresses than the 400mT samples. The upload curves however show that all

samples have very similar upload behaviour up to around 30% strain. This is unexpected as

we would have expected larger differences in all curves for this sample configuration.

Figure 21Graph of 20% Anisotropic samples with different applied magnetic fields

28

30% Anisotropic Samples

Table 13 Table of Youngs Moduli for 30% Anisotropic samples

Sample Composition Flux Density (mT) Youngs Mod for 0-10% Strain (MPa) MR Effect

30% 400 5.947736 0.588323435

30% 270 5.146382 0.374324472

30% 0 3.744663

The curves shown in figure 22 are like what was expected, we can see that the lowest curve

is the zero field samples, with the red line representing the 270mT field samples and just

above that the 400mT field samples. There is very little difference in the stresses off the two

magnetic samples. This graph is a good indicator of the sort of MR effect we would hope to

achieve in practice with these materials. The Young’s moduli figures shown in table indicate

a larger MR effect than previous samples configurations.

Figure 22 Graph of 30% Anisotropic samples with different applied magnetic fields

29

Modelling of MREs

In this report the modelling of the Isotropic samples will be concentrated on. The main

reason is the experimental problems with the anisotropic samples which need to be solved

first. I am using for analysis the Abaqus 6.8 Student Edition. Already implemented models

for rubber-like materials are the Neo-Hookean, the Mooney-Rivlin and the Ogden Model

which are all models for isotropic materials. Modelling an anisotropic material would

require a user defined constitutive equation using UMAT. This would go beyond the scope

of this report. A further assumption of the said implemented models is that the materials

are fully incompressible i.e. the volume does not change during deformation and the

poisson ratio is 0.5. Furthermore G the shear modulus is related to the Elastic modulus E by

the equation, , but this is only valid on the linear theory ,i.e. in the small strain

region.

The standard hyper elastic models which will be used are the, Neo-Hookean and Mooney

Rivlin. All these models are derived from the standard Ogden model shown in Equation 2.

This model is based on the relationship between the Strain Energy Function9 and the

principal stretch ratios.

Equation 2 Standard Ogden Model

Where is the strain energy and , are the principal stretch ratios for each

direction. is defined as the shear modulus, and is a material constant.

The Mooney Rivlin model is obtained by setting N=2, = 2, = -2. This produces Equation

3 shown below.

Equation 3 Standard Mooney Rivlin Model

Where c10

, c01

, and the shear modulus is µ =

The Neo-Hookean model is derived from the standard Ogden model by setting N=1, = 2,

this results in Equation 4.

Equation 4 Standard Neo Hookean Model

9 Equations from Non-Linear Solid Mechanics by Gerhard A Holzapfel

30

Where c1

and the shear modulus is

The Young’s modulus can be calculated from the coefficients calculated by Abaqus shown by

these equations:

These constitutive model need to be fitted to experimental data to calculate the model

parameters. This fitting will be done by Abaqus using a least square method. To get an idea

of the suitability of the fit a coefficient of determination R2 will be calculated. This

coefficient is often used in statistics. It approaches 1 the better the fit, a value of 0 would

mean the fit is useless.

exp fitres

22

2

2

1 ... nresresresnorm

i

itotS 2exp

_

exp, )(

tot

tot

S

normSR

2

2

Where res are the residuals, norm is the 2-Norm also known as the Euclidian length of the residuals, Stot is the sum of squares and finally R2 is the coefficient of determination.

Modelling of 10% Isotropic Samples

Figure 23 10% Isotropic Samples with 400mT applied magnetic field

31

Coefficients for 10% Isotropic samples with 400mT applied magnetic field

HYPERELASTICITY - MOONEY-RIVLIN STRAIN ENERGY

D1 C10 C01

0.000000 84061.8510 34812.0823

HYPERELASTICITY - NEO-HOOKEAN STRAIN ENERGY

D1 C10 C01

0.00000 83567.7120 0.00000000

Coefficients for 10% Isotropic Samples with 270mT applied magnetic field


D1 C10 C01

0.00000000 120041.678 18855.2399


D1 C10 C01

0.00000000 145569.612 0.00000000


32

Coefficients for 10% Isotropic Samples with no applied magnetic field


D1 C10 C01

0.00000000 62757.9238 78950.0356


D1 C10 C01

0.00000000 172278.547 0.00000000

Figure 25 10% Isotropic samples no applied magnetic field

33

From Figure 23 we can see that the best model fit is the Mooney-Rivlin. This was confirmed

by the R2 coefficient which was calculated as 0.9988 for the Mooney-Rivlin and 0.5558 for

the Neo-Hookean.

From Figure 24 we can see that both models are quite good for most strain levels. The R2

coefficient for the Mooney Rivlin model the R2 value was 0.9987 and for the Neo-Hookean

model R2 is 0.9902. this shows that the Mooney-Rivlin is still the better fit for this material

configuration with and without magnetic fields.

From Figure 25 we can also see that the Mooney Rivlin model is still the best fit, and the R2

values confirm this as they are 0.9917 for the Mooney-Rivlin and 0.9231 for the Neo-

Hookean. Finally the Mooney-Rivlin Model is the best fit for this material tested with and

without magnetic field. Using the coefficients shown previously Table 14 and Table 15 were

constructed to show the differences in the Young’s moduli from test data and coefficients.

Table 14 Table of Coefficients for Mooney-Rivlin Model

Samples Composition

Applied Field (mT)

C10 Coefficient

C01 Coefficient

Shear Modulus (MPa)

Youngs Modulus (MPa)

Youngs Modulus form test data (MPa)

10% 400 84061.851 34812.0823 0.2377 0.7132 1.2453

10% 270 120041.67 18855.2399 0.2778 0.8334 1.2697

10% 0 62757.923 78950.0356 0.2834 0.8502 1.4567

Table 15 Table of Coefficients for Neo-Hookean Model

Samples Composition

Applied Field (mT)

C10 Coefficient

Shear Modulus (MPa)



10% 400 83567.7120 0.1671 0.5014 1.2453

10% 270 145569.6120 0.2911 0.8734 1.2697

10% 0 172278.5470 0.3446 1.0337 1.4567

34


Figure 26 20% Isotropic Sample with 400mT applied magnetic field



D1 C10 C01

0.00000000 95259.1322 61905.0798


D1 C10 C01

0.00000000 89553.1134 0.00000

35



D1 C10 C01

0.00000000 128736.268 48048.7121


D1 C10 C01

0.00000000 192142.047 0.00000000


36

Figure 28 20% Isotropic Samples with no applied magnetic field

Coefficients for 20% Isotropic Sample with no applied magnetic field


D1 C10 C01

0.00000000 -20993.9161 162880.115

UNIAXIAL TENSION: UNSTABLE AT A NOMINAL STRAIN LARGER THAN 2.9800

UNIAXIAL COMPRESSION: UNSTABLE AT A NOMINAL STRAIN LESS THAN -0.6414

BIAXIAL TENSION: UNSTABLE AT A NOMINAL STRAIN LARGER THAN 0.6700

BIAXIAL COMPRESSION: UNSTABLE AT A NOMINAL STRAIN LESS THAN -0.4987

PLANAR TENSION: UNSTABLE AT A NOMINAL STRAIN LARGER THAN 1.6700

PLANAR COMPRESSION: UNSTABLE AT A NOMINAL STRAIN LESS THAN -0.6255

VOLUMETRIC TENSION: STABLE FOR ALL VOLUME RATIOS

VOLUMETRIC COMPRESSION: STABLE FOR ALL VOLUME RATIOS

37


D1 C10 C01

0.00000000 174917.522 0.00000000

From Figure 26 we can see that again the Mooney-Rivlin Model is the best fit for this sample

configuration. This is confirmed with the R2 coefficient being 0.9987 for the Mooney-Rivlin

and 0.2354 for the Neo-Hookean.

Figure 27 shows that for lower strains both models are quite accurate but as strain increases

the Neo-Hookean curve starts to move away from the test data. The Mooney-Rivlin is still

the best model for this material. Furthermore this is confirmed with the R2 coefficient, it is

0.9970 for the Mooney-Rivlin and 0.9671 for the Neo-Hookean.

In Figure 28 we are starting to see a few discrepancies between the Mooney-Rivlin model

and the test data especially at higher strains. Even so the Mooney-Rivlin is still the best

fitting model for this data as shown again by the R2 coefficient. For the Mooney-Rivlin R2 is

0.9827 and for the Neo-Hookean R2 is 0.7041. Unusually the Abaqus has stated the

Mooney-Rivlin Model as unstable.

Table 16 Table of Coefficients for Neo-Hookean Model

Samples Composition

Applied Field (mT)

C10 Coefficient

Shear Modulus (MPa)



20% 400 89553.1134 0.1791 0.5373 1.6624

20% 270 192142.0470 0.3843 1.1529 1.6478

20% 0 174917.5220 0.3498 1.0495 1.806

Table 17 Table of Coefficients for Mooney-Rivlin Model

Samples Composition

Applied Field (mT)

C10 Coefficient

C01 Coefficient

Shear Modulus (MPa)



20% 400 95259.

1322 61905.07

98 0.3143 0.9430 1.6624

20% 270 128736

.2680 48048.71

21 0.3536 1.0607 1.6478

20% 0 1.806

38




D1 C10 C01

0.00000000 265354.405 59029.5065


D1 C10 C01

0.00000000 352369.597 0.00000000


39

Coefficients for 30% Isotropic Samples with 270mT Magnetic Field


D1 C10 C01

0.00000000 162187.941 94669.0067


D1 C10 C01

0.00000000 238740.306 0.00000000


40

Coefficients for 30% Isotropic Samples with no applied magnetic field


D1 C10 C01

0.00000000 -93284.8951 304559.773

***WARNING: UNSTABLE HYPERELASTIC MATERIAL

UNIAXIAL TENSION: UNSTABLE AT A NOMINAL STRAIN LARGER THAN 0.9500

UNIAXIAL COMPRESSION: UNSTABLE AT A NOMINAL STRAIN LESS THAN -0.4513

BIAXIAL TENSION: UNSTABLE AT A NOMINAL STRAIN LARGER THAN 0.3500

BIAXIAL COMPRESSION: UNSTABLE AT A NOMINAL STRAIN LESS THAN -0.2839

PLANAR TENSION: UNSTABLE AT A NOMINAL STRAIN LARGER THAN 0.7200

PLANAR COMPRESSION: UNSTABLE AT A NOMINAL STRAIN LESS THAN -0.4186

VOLUMETRIC TENSION: STABLE FOR ALL VOLUME RATIOS

VOLUMETRIC COMPRESSION: STABLE FOR ALL VOLUME RATIOS

Figure 31 30% Isotropic Samples with no applied field

41


D1 C10 C01

0.00000000 325749.014 0.00000000

From these simulations we can see that the Mooney-Rivlin Model is a good model for the

samples where a magnetic field is present. However when there is no magnetic field present

this model becomes unstable. The R2 values for all the cycles are shown in Table 18. This

means that this model will have to be altered in order to be used for simulations. Table 19

and Table 20 show a comparison of the simulated young’s moduli to the calculated Modulus

from the test data.

Table 18 Table of R2 values for 30% Isotropic Samples

Samples Composition

Applied Field Strength (mT)

R2 for Mooney Rivlin

R2 for Neo-Hookean

30% 400 0.9964 0.9854

30% 270 0.9977 0.8139

30% 0 0.9496 0.3185

Table 19 Youngs Modulus for 30% Isotropic Samples for Neo-Hookean Model

Samples Composition

Applied Field (mT)

C10 Coefficient

Shear Modulus (MPa)



30% 400 352369.5970 0.7047 2.1142 2.7491

30% 270 238740.3060 0.4775 1.4324 2.519

30% 0 325749.0140 0.6515 1.9545 2.5882

Table 20 Youngs Modulus for 30% Isotropic Samples for Mooney-Rivlin Model

Samples Composition

Applied Field (mT)

C10 Coefficient

C01 Coefficient

Shear Modulus (MPa)


Youngs Modulus from test data (MPa)

30% 400 265354.40

50 59029.506

5 0.6488 1.9463 2.7491

30% 270 162187.94

10 94669.006

7 0.5137 1.5411 2.519

30% 0 2.5882

42

Modelling of Pure Rubber

Figure 32 Pure Rubber Modelling Curves

Coefficients for Pure Rubber Testing


D1 C10 C01

0.00000000 73412.7398 23617.1556


D1 C10 C01

0.00000000 79240.8245 0.00000000

43

Table 21 Youngs Moduli for Pure Rubber for Mooney Rivlin Model

Samples Composition

Applied Field (mT)

C10 Coefficient

C01 Coefficient

Shear Modulus (MPa)



Pure 0 73412.7398 23617.155 0.1941 0.5822 0.67

Table 22 Youngs Moduli for Pure Rubber Neo-Hookean model

Samples Composition

Applied Field (mT)

C10 Coefficient

Shear Modulus (MPa)



Pure 0 79240.8245 0.1585 0.4754 0.67

The pure rubber is like all the rest of the samples that have been modelled in that the best fit is with

the Mooney-Rivlin model. The R2 values are 0.9995 for the Mooney-Rivlin model and 0.7656 for the

Neo-Hookean.

In conclusion it would appear that the best model for this material is the Mooney-Rivlin model, it has

consistently close to 1 R2 value providing a good fit.

Conclusions

The main conclusions of this report are that the manufacturing process has been optimized and now

all future samples will be cured for 1hrs at 100oC. Furthermore it is now possible to successfully

create Anisotropy within the MRE’s. Another main point from these set of test is that a method

whereby a magnetic field is passed through the sample while being compressed has been achieved.

Some of the problems that have occurred unexpectedly during these tests were the buckling of

anisotropic samples. This means that in future it would be best to test the anisotropic samples in

tension rather than compression. Unfortunately applying a magnetic field through the sample will be

difficult and a new test setup will have to be created.

Future work on this material will be carried out to create a general constitutive model, and to

achieve this task many more tests will have to be undertaken to fully define the MRE’s mechanical

properties.

44

Bibliography

[1] Gerlind Schuberts 1st Year Report

[2] M. Kallio Preliminary tests on an MRE device

[3] M. Farshad Magnetoactive elastomer composites [4] Z. Varga Magnetic Field Sensitive functional elastomers with tunable modulus

[5]Dr Philip Harrison, MRE Presentation

[6] Equations and Calculations are from Guide for rubber mixing process by Ms Gerlind Schubert [7 ] BS ISO 7742 Determination of Compression stress strain properties for Vulcanized

Rubbers

[8] Reference from (http://en.wikipedia.org/wiki/Mullins_effect) [9] Equations from Non-Linear Solid Mechanics by Gerhard A Holzapfel

[10]Picture from http://en.wikipedia.org/wiki/Solenoid

[11] Referenced from http://www.powerstream.com/Wire_Size.htm (AWG 23)

http://en.wikipedia.org/wiki/Mullins_effect

http://www.powerstream.com/Wire_Size.htm

45

Appendix A : Calculation for Solenoids

First a target Magnetic Flux Density of B = 400 mTeslas was set. This is a relatively high magnetic

field but will be suitable for all experiments that need to be done. Furthermore the flux density can

be changed by altering the current supply. The max current that the power supply can safely

produce is 5A.

Figure A1[10]: A typical solenoid field. Lines represent magnetic field lines. “Dots” and “X’s” are coil

cross-section.

Figure A1 shows a wire coil in cross-section and the arrowed lines represent the magnetic field lines.

This shows that the field through a solenoid is very uniform and will be ideal for use when

compressing samples.

The basic equation for calculating the magnetic flux density at a inside the coil at a point away from

the ends is given as:

Where: B = magnetic flux density Unit is Tesla

µ = Kµ0 where k = relative permeability of core material and

µ0=magnetic constant and is the permeability of a vacuum

µ0= 4π x 10-7 unit is Tesla Metre per Ampere

N =number of turns L = length of solenoid

I = Current Unit is Amperes

10 Picture from http://en.wikipedia.org/wiki/Solenoid

46

Therefore what is required to build this solenoid is the turns density N/L. With this the appropriate

coil can be designed and manufactured.

The core material is going to be air which has K=1

B (Tesla) I (Amperes) K µ (T.m/Ampere)

0.4 5 1 1.25664e-006

Therefore:

=1.5915e+006 turns/metre

As you can see this number is completely impractical. 1.5 million turns in one metre would

require a long amount of time to wind. Furthermore the wire diameter would be required to

be 6.2832e-004mm diameter and this diameter would not support the necessary current

required as specified by the American Wire Gauge. This gauge specifies that a wire will

carry a maximum current of 4.7 Amperes with a wire diameter of 0.57404mm[11].

For all the above reasons the idea of a solenoid to apply the magnetic field was rejected.

11 Referenced from http://www.powerstream.com/Wire_Size.htm (AWG 23)

http://www.powerstream.com/Wire_Size.htm

47

Appendix B: Faulty test setup results

The results shown in figure B1 are from the original magnetic test setup which had been

intended to be used. Unfortunately there were a few problems with the test setup. The

problem was that the bottom test plates, which held a magnet between them (see figure 4

from report), had a loose connection between them and the test machine. The force of

attraction between the top and bottom magnets caused the whole bottom part of the setup

to rise up a little. Once the samples were compressed and the applied force became larger

than the force of attraction a rigid body movement took place moving the compression

plates down creating a plateau in the force displacement curve as seen in figure B1.

The problems that were caused by this were solved by decoupling the bottom magnet from

the plates and allowing the attractive force of the magnets to hold the magnets in place

while being separated by two wooden blocks as shown in figure 5.

Figure B1: Results from faulty tests

Unload Part for all cycles

Upload Part for first cycle

Upload Part for cycles 2,3,4

Plateau caused by loose

fitting

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