Abstract
Due to manufacturers desire to make lighter and more comfortable personal armour
systems, combined with the availability of higher energy ballistic impacts, nonpenetrating injuries such as BABT and BFS are likely to rise. This project, titled ‘The
Development of a Ballistic Trauma Pack’, investigates the concept whether foam can
be used in trauma attenuation protection equipment that can be either: 1) flexible
without a great deterioration in certain mechanical properties, and 2) improve the
energy absorption characteristics of the foam by preventing fracture without
increasing the plateau stress of the foam.
Results confirmed that the method of modelling the investigation was wrong. Too
many variables entered experimentation, altering the results desired. Flexible trauma
packs were successful in allowing bending to occur within one direction and not the
other, although there were slight deteriorations with the energy absorption properties
with the trauma packs.
These were caused by the damaged cell faces, when the
foam was organized into a layer format. These damaged cell faces can also explain
the significant deterioration in strength and energy absorption qualities of the trauma
packs designed to improve them, although a reduction in fracture was also evident
Page 1
List of Objectives
•
Investigate on the advantages of expanded polystyrene foam and how foam
would work within a trauma pack
•
Analysis on expanded polystyrene foam.
This would include standard
mechanical testing and includes analysis on a cellular level.
•
Quasi-static testing with the EPS foamed material.
•
Exploration on how to change mechanical properties of a material without
altering other specific characteristics. Specifically, the improving the fracture
properties of the expanded polystyrene foam, without making a dramatic
fluctuation in the samples density.
•
To create a flexible trauma pack without drastic deterioration in strength and
energy absorption properties compared to a monolith sample.
•
To create a sample which can absorb as much energy, if not more, than a
monolith sample, and also demonstrate an improvement in shear
characteristics.
•
To understand the concept of deformation that occurs within an indentation
test and a ballistic impact test
Acknowledgements
I would like to acknowledge several people for their help, support, resources and
patience, throughout the first semester and helping me complete this report.
My project advisor: Dr Phil Harrison
Technical supervisors: Mr John Davidson, Mr Kaz Piechowiak, Mr Brian Robb and Mr
Alan Campbell
Phd supervisor: Mr Qusai Jebur
Page 2
Table of Contents
Introduction
6
Foams
9
Classification
9
Expanded Polystyrene Foam
10
Manufacture of EPS Foam
11
Characteristics of EPS Foam
12
Further Investigation into Energy Absorption
14
Microstructure of Cellular Materials under Compression
16
Concepts of the Project
17
Objective 1
17
Objective 2
18
Execution
20
Fabric Backing Material
21
Adhesive
21
Foam Characterisation
22
Cell Size
22
Density Variation
25
Inhomogeneous Structure
28
Standard Compression Test
29
Monolith vs. Layered
32
Fast Rate vs. Slow Rate
34
Young’s Modulus
38
Three-point Bend Test
41
Plane-Strain Deformation Impact Tests
44
Test Results & Analysis
53
Fracture
66
Adhesion Failure
68
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Improved Samples
70
Limitations on Experiments
74
Further Analysis
76
Conclusion
77
References
79
List of Figures
Figure 1
Differences between Closed and Opened Cell Structures
9
Figure 2
EPS Foams Beaded Nature
10
Figure 3
Other Applications of EPS Foam
13
Figure 4
Common Response of Cellular Plastics in Uniaxial Deformation
14
Figure 5
Side View of Tiled Trauma Pack Specimen
17
Figure 6
Example on Sample Sides Unable to Deform Compressively
19
Figure 7
Individual Cells that make up the EPS Foam
22
Figure 8
Image Manipulation with image analysis equipment
23
Figure 9
Bead Boundaries of the EPS Foam
24
Figure 10
Preparation for Density Variation Experiment No 1
25
Figure 11
Test Results of Density Variation Experiment No 1
26
Figure 12
Preparation for Density Variation Experiment No 2
26
Figure 13
Test Results of Density Variation Experiment No 2
27
Figure 14
Differences Between Initial Starting Positions
28
Figure 15
Test Results of Inhomogeneous Structure Experiment
28
Figure 16
Force-Displacement Response Curves of EPS Foam
29
Figure 17
Stress-Strain Response Curves of EPS Foam
31
Figure 18
Stress-Strain Response Curves of EPS Foam
32
Figure 19
Typical Behaviour of Foams with Increased Strain Rates
34
Figure 20
Stress-Strain Response Curves of EPS Foam
35
Figure 21
Average % Difference of Slow & Fast Rates of Loading
35
Page 4
Figure 22
Stress-Strain Response Curves in the Linear Elastic Regime
38
Figure 23
Young’s Modulus Automated Calculations
39
Figure 24
Results of the 3-Point Bending Tests with Tiled Specimens
42
Figure 25
Illustrations of Different Specimen Types
50
Figure 26
Results of Compressive Plane Strain Deformation Tests
53
Figure 27
Results of Small Indenter Plane Strain Deformation Tests
53
Figure 28
Results of Small Indenter Plane Strain Deformation Tests continued 54
Figure 29
Results of Large Indenter Plane Strain Deformation Tests
54
Figure 30
Foam only Deformation vs. Specimen Deformation
58
Figure 31
Monolith vs. Layered Compressive Plane Strain Deformation Tests 59
Figure 32
Monolith vs. Layered Uniaxial Deformation Tests
59
Figure 33
Results of Small Indenter Plane Strain Deformation Tests
61
Figure 34
Adhesion Failure
62
Figure 35
Monolith under Small Indenter Plane Strain Deformation Tests
66
Figure 36
Fractures Experienced by Double Bonded Sample
67
Figure 37
Results of Peel Testing with Wood Resin Adhesive
68
Figure 38
Results of Peel Testing with other Adhesives
69
Figure 39
Small Indenter Plane Strain Deformation Results
71
Figure 40
Small Indenter Plane Strain Deformation Results
72
Figure 41
Failures of the Double Bonded by Tape Specimen
73
Figure 42
Highlights of Tensile and Shear Deformation
76
List of Tables
Table 1
List of Cell Dimensions
23
Table 2
Standard Compression Test Specifications
29
Table 3
Accuracy between Methods for Calculating Young’s Modulus
40
Table 4
Variations of Loading in Plane Strain Deformation Experiments
44
Table 5
Guidelines for Specimen Parameters
45
Table 6
Sample Dimensions used in Uniaxial Compression Tests
46
Table 7
Sample Dimensions used in Small Indenter Tests
47
Table 8
Sample Dimensions used in Large Indenter Tests
48
Page 5
Introduction
Although ballistic armour is able to stop projectiles from penetrating through the
armour, injuries from the process of capturing the projectile can still occur. The rapid
jolting force of an impacting bullet is contrasted with the usually encountered
mechanisms producing blunt trauma injury.
Vital organs and areas such as the
heart, lungs, spleen and spinal chord, are all vulnerable to injury, despite the
projectile not perforating the armour, and in extreme circumstances, these injuries
have recorded cases that have resulted in death [1].
These non-penetrating injuries can be caused by two distinct mechanisms; the
deformation of the surface of armour in contact with the body wall and the energy
transfer from the projectile. The depth of depression in the backing material that
results from a non-penetrating projectile is known as the ‘Backface Signature’ or
BFS. The deformation is part of the retardation and energy absorbing process that
captures the projectile. It is also referred to as ‘Backface Deformation’ or ‘Trauma
Signature’. The backface signature is measured from the plane defined by the front
edge of the backing material fixture and can be formally classed as “the greatest
extent of indentation in the backing material caused by a non perforating impact on
the armour” [2].
The energy deposited in the armour by the retarded projectile may be transferred
through the armour backing and body wall. The protective vest may impede the
projectile, but some of the kinetic energy is transferred to the body. It may produce
serious injury to the thoracic and abdominal contents behind the plate. Pressure
waves propagate through the body which can also affect the brain [3], even though
the head is not hit. With very high energy bullet impacts, the internal thoracic injuries
may result in death.
Page 6
Currently, there are two types of non penetrating injuries categorized: Behind armour
blunt Trauma and Backface signature.
Behind Armour Blunt Trauma (BABT) is
defined as the spectrum of non-penetrating injuries to the torso resulting from the
rapid deformation of projectiles on personal armours, covering the body. The classic
behind armour blunt trauma injuries, historically have consisted of moderate to
severe bruising and rib fractures. These blunt trauma injuries occur when the vest
distributes the impact energy over a large area, causing a global deformation of the
chest without localized deformation. Usually, such injuries are not life-threatening to
the wearers, although lung contusions can also occur.
The backface signature injuries can be described as a more localized injury, when it
is in comparison to behind armour blunt trauma injuries.
Although the vest is
successful in containing the round, it is not effectively dissipating the energy enough
to prevent large amounts of vest deformation at the area of impact. Therefore, the
increased deformation of the vest is causing a penetrating injury, as well as a blunt
trauma injury due to the localized nature of the impact.
As a practical, real-life
interpretation, the backface signature can be defined as open, penetrating wounds
that occur even though the projectile did not penetrate the vest. The deformation of
the tissue exceeds the threshold of skin and penetrating wound results.
Cellular materials such as polymeric foams are often employed in shock mitigating
applications. Polymeric foam materials are widely used for impact protection and
energy absorption applications, such as the automotive crash safety systems. In the
automotive field compressive strain rates will reach up to 500-800/s [4]. Cellular
plastics may also be considered for higher rate applications. However, due to the
insufficient knowledge of compressive response of polymeric foams at such high
rates of strain (where ballistic impacts and blast waves can achieve rates of
deformation that exceed 1000/s [4]), such materials are not used yet in the
development of improved protection equipment.
Page 7
A trauma pack can be easily confused with a ballistic vest. A ballistic vest is where
the bullet is captured and where the majority of the energy absorption processes
takes place. There are various ballistic resistant materials ranging from the more
familiar Kevlar® (DuPont), Spectra®fiber (Honeywell), Goldflex® (Honeywell), Twaron®
(Teijin Twaron), Dyneema® (DSM) and Zylon® (Toyobo) [5]. The Nation Institute of
Justice certify that in order for ballistic resistant vests to be circulated for practical
use, then a tolerance of no more than 44 mm of backface indentation depth, must
take place when shot with a certain calibre of gun [6].
Although there are solutions to reduce the backface signature, which includes
inserting ceramics, metals or reinforced fabric behind the armour, even though the
indentation depth may be reduced, the energy transferral from the projectile to the
armour then to the body is unaffected. These solutions describe the aim of a passive
trauma pack where the aim is to keep the backface signature away from the wear.
However, with an escalation of the available energy of bullets and the desire of
armour designers to minimise the weight and bulk of the personal armour systems,
this will in all likelihood, increase the number of BABT and BFS or force the body
armour to become heavier and less flexible. This is where an active trauma pack can
play a pivotal role, where not only these trauma packs keep the backface signature
away from the wear, but also provide some reduction in depth of the backface
signature and to provide some energy absorption.
Page 8
Foams
Techniques which cause tiny bubbles to form within a plastic material such that when
the plastic solidifies, the bubbles, or at least the holes formed by the bubbles remain
within the material, are called foaming.
This unique internal structure, with the
solidified bubble-containing material, are generally though of as a cellular structure.
Cellular solids are made up of interconnected networks of solid struts or plates that
form the edges and faces of cells. Products made by these processes are referred to
as cellular plastics or more commonly, foams.
Advancements in technology also
mean that this foaming process can also occur in metals and natural materials. This
project will only refer to foams that are created with a plastic material base.
Classification
In the field of cellular plastics, there are two possible ways to categorize the types of
plastic foams: cell structure and wall rigidity [7].
Cellular structure is the most
common method to classify plastic plastics and there are two types: closed and open
cell structure. In a closed cell structure, each individual cell is impermeable, meaning
no fluid can pass between each cell. Each cell is a separate and discrete entity,
which means each cell can hold an individual gas. In an open cell structure, cells are
linked to each other due to the holes found in the cell walls. As a result, fluids easily
move within and throughout the entire plastic foam and the open cell foam is filled
with whatever fluid it is surrounded with (figure 1).
(a)
(b)
Figure 1 (a) Microscopic close up of open celled Polyurethane foam. Figure 1(b) is a microscopic close
up of a closed cell Low Density Polyethylene foam (LDPE) [1].
Page 9
Wall rigidity describes the reaction of the cell walls when they are under
compression. In rigid foams, cell walls remain stiff, whereas in flexible foams, cell
walls collapse when they pressed. Both open and closed cell foams can have either
flexible or rigid walls.
Even though this project is interested in investigating using foam as an active trauma
pack, a certain type of foam must be chosen in order to represent the material.
Although there may be certain types of cellular plastics that are more suited to
become a part of an armoured system, expanded polystyrene foam has been
favoured for this project. Being cheap and commercially available, the main reason
why expanded polystyrene foam has been chosen is because of the cell size the
EPS foam has (see chapter ‘Cell Size’).
Expanded Polystyrene Foam
Pure solid polystyrene is a colourless, hard plastic with limited flexibility. It can then
be cast into moulds with fine detail, which the final product can be transparent or be
made to take on various colours. It is economical and can be found in uses such as
plastic modelling assembly kits, plastic cutlery or CD ‘jewel’ cases.
However,
polystyrene’s most common use is as expanded polystyrene foam.
Expanded Polystyrene foam (EPS) are made up of expanded polystyrene beads and
usually white. Polystyrene is a polymer made from the monomer styrene, a liquid
hydrocarbon which is commercially made from petroleum by the chemical industry.
Close examination of the EPS foam will permit identification of the individual beads
that have been fused to form a continuous part, as in figure 2.
Figure 2 is taken from cushioning equipment from Wikipedia page
http://en.wikipedia.org/wiki/File:Polistirolo.JPG
Page 10
Polystyrene foams are closed cell foams, which mean that they are generally denser
than their open cell counterparts but more expensive to produce, since they require
more material. Their advantage over open cell foams are that in general, closed cell
foams acquire more compressive strength due to their wall structure.
Manufacture of EPS Foam
The most common method for making EPS foam involves the use of pre-foamed
polystyrene beads. The resin manufacturer makes these beads by adding an inert
gas, such as pentane or carbon dioxide, during polymerization. Polymerization is a
process of reacting monomer molecules together in a chemical reaction to form a
polymer chain or three-dimensional networks.
Under proper conditions, which
usually involve a water suspension environment, polymerization occurs with the
formation of small, internally foamed polystyrene beads with the inert gas trapped
inside. These beads are then shipped to the part moulders. The part moulders
convey the beads from the shipping container to the mould by air pressure or
vacuum. During this conveying step, the beads are often heated and will expand up
to 20 times their original volume, however this is only a partial expansion. This
heating causes the beads to further expand, often doubling their size over the
partially expanded size and to fuse together. The moulds are then cooled and the
parts are removed. It is because of this manufacturing process, that variations in
density can be seen throughout the foam, which will be further discussed in the
‘Foam Characteristics’ chapter.
The EPS foam that would be used throughout this project would be the ‘Jablite
Flooring Insulation Polyboard White’. The material was bought at a local home store,
which was originally intended for home insulation purposes. The EPS foam came in
packs of 4 and in dimensions of (L) 1200mm x (W) 50mm x (T) 2400mm.
Page 11
Characteristics of EPS foam
Plastic foams have some physical characteristics that are valuable for several
important applications. The advantages of EPS foam over competitive materials
include the following:
·
Low heat flow, making good insulation.
·
Good energy absorption for packaging delicate instruments and other impact
applications.
·
High buoyancy
·
High stiffness to weight so that parts can be self-supporting and lightweight
·
Low cost per volume
An advantage that is relevant to this project, of plastic foams, is the low weight it has
which can be traced back to its cellular structure. Due to the open structure of the
plastic foam, this means that the material is inherently lightweight. Weight can have
a very significant factor with ballistic protection wearers. Obviously, the lighter the
trauma pack, the ease of mobility for the wearer and therefore foam would be an
excellent choice. Other applications that take advantage of this light weight would
include flotation devices used in boats and planes such as life jackets, buoys and
pontoons.
Not only are plastic foams lightweight, they can also have excellent specific
properties. This high stiffness/load-bearing strength to weight ratio are not found in
all plastic foams and are somewhat a surprising attribute. The reason for this is
because of the cell walls within the foam, acting like many tiny columns, which
support the heavy loads. As a result, rigid foams can be found as structural parts or
cores for structural parts in areas such as aerospace, automobile and retail. In other
words, foams can be found in industries were weight is especially important and
applications can capitalize on the load-bearing capability of rigid foams. Examples
include airplane wings, space structures and furniture frames. By having this high
load bearing strength to weight ratio will also allow trauma packs to be not only
lightweight, but convenient, thus allowing sufficient protection without having a bulk of
clothing restricting the movements of the wearer. Many other applications require
that the foam material occupy space to give a desired shape and resist moderate
impacts, such as would occur in automobile dashboards.
Page 12
However, the characteristic of EPS foam that this project is most interested in, would
be the foams ability to absorb the high energy associated with impacts on the foam.
This energy absorption can be accounted by due to the internal structure of the foam
being able to collapse, when the material is crushed. The micro-mechanics of foam
energy absorption and their crushability properties will be further discussed in
another chapter. EPS foam can be found in many applications where they are used
to provide protection against high energy impacts such as furniture cushioning,
delicate instrument packaging and even in the transport industry with examples such
as seating, carpet padding, shock absorbers, crash pads and helmets. Combined
with their light weight and cheap production costs, these reasons further enhance
and reinforce the use of EPS foam within the advanced trauma attenuation protective
equipment area.
(a)
(b)
Figure3 (a) bicycle helmet with EPS foam liner (b) EPS foam furniture cushioning
Page 13
Further Investigation into Foam Energy Absorption
As discussed in the previous chapter, due to their internal cellular structure, this
endows foams with several favourable properties such as low density, relatively high
strength-to-weight ratio, low heat flow and a significant degree of crushability.
Crushability is defined as compressing a material with a force, until it is deformed or
even destroyed. The Polymer handbook [9] states that ‘the term crushable implies
permanent plastic deformation or fracture of a compressed foam’. With the cellular
structure being collapsible, this high crushability is due to the presence of the large
void ratios within the foam. When the foam is impacted, the cell walls are able to
collapse, which enables the cell walls to flex, via buckling and bending, and therefore
absorb some energy of the impact.
With the foam under uni-axial deformation through compression, a common stressstrain response would include three phases: (1) linear elastic region, (2) plateau
regime and (3) the final densification phase, as shown in figure 4.
Figure 4: Stress-strain response curve of an open-celled polyurethane foam under uniaxial compression
[static impact crushing layered], with the three common response regimes highlighted.
Linear elastic - occurs at low strain (a few percent, usually <5%) due to the uniform
cellular wall elastic bending and stretching throughout the whole foam structure. The
stress increases linearly with deformation and the phase deformation is recoverable.
This region defines the foam’s elastic modulus of the material.
Page 14
Plateau - corresponds to plastic yielding for rigid PS foams.
By continuing the
permanent deformation at a relatively constant stress, this stage provides the
majority of the energy absorption capabilities of the material. This regime is the
dominant characteristic response of cellular materials when they are crushed. The
cellular buckling under compression commences a long stress plateau and happens
via the plastic buckling, yielding and rupture of cell walls and edges. With open
celled foams, the plateau region is generally responds as a level, constant force
(figure 4). The closed cell EPS foam, however, will exhibit a rising stress plateau
because of the compression of air within the closed cells (figure 6). The enclosed
gas pressure and membrane stretching will increase the level and slope of the
plateau.
Densification - where the cellular structure within the material has completely
collapsed and further deformation requires compressing the solid foam material. In
other words, the foam will have to behave as a compacted, homogeneous solid,
since the voids within the structure have been completely eliminated. The cell walls
are crushed together and there is a tight compaction of cell material. As a result, a
steeply rising hardening regime (a sharp increase in force) due to the consolidation of
the foam will be experienced.
Energy dissipation via further deformation is
accompanied by a steep rise in force.
The ideal energy absorber is quoted as ‘one that minimizes force while dissipating a
given energy within a given energy within a specified stroke length’ [10]. This implies
that during the compressive deformation of the foam, the ideal energy absorber will
have a stress-strain response of a constant force.
In practice, this is only achieved
in the middle stage, the plateau phase, when crushing the cellular material, although
this is also the predominant phase when a cellular plastic is being compressed.
It is only this plateau region and linear elastic area that is of interest to this project. If
any further deformation is experienced by the foam and the densification stage is
entered, then the steep rise in force that accompanies the deformation will also be
transmitted to the wearer. That is why through this project, emphasis in the analysis
will be on the linear elastic and plateau regimes.
Page 15
Microstructure of Cellular Materials under Compression
Crushing of cellular materials is characterized by the occurrence of localized
deformation, as described before. When a cellular plastic is being crushed, yielding
and collapse of the cell walls, originate where cells are the weakest. Weak cells are
determined from the structural imperfections, examples being randomly occurring
larger voids generated by coalesced gas bubbles and broken cells at surfaces
created by incisions. In turn, the collapse of these initial sites of failure reduces the
structural integrity of neighbouring cells, thus encouraging localisation of deformation
within the region. The collapsing nature from these locations are then transmitted
throughout the rest of the structure. This progression of deformation results in a
force response which is relatively constant and can account for the long post-yield
plateau in the stress-strain curve.
Page 16
Concepts of the Project
There are two main objectives for this project in order to create a successful active
trauma pack with foam:
1. to create a flexible trauma pack that can bend in one direction and not the
other (asymmetric flexing properties) without a great deterioration in strength
and energy absorbing characteristics.
2. to create a trauma pack that shows an improvement in fracture properties and
maintain, if not improve upon, the strength and energy absorbing
characteristics
Objective 1
In terms of comfort, flexible trauma packs are required in order to provide adequate
protection without restricting or hindering the movements of the user. To make an
active trauma pack more flexible, blocks of foam will have to be sliced into thin layers
of foam. How thin these layers can be, depend on how small the cell sizes the foam
possesses and are further investigated in the chapter, ‘Cell Size’.
However,
enabling the trauma pack to flex in one direction and not the other will require further
manipulation of the EPS foam. Further incisions to enable these layers to turn into
tiles will allow these asymmetric bending qualities, and by making further incisions
will require a fabric backing layer, in order to maintain these tiles not becoming
individual small monolithic blocks and fall apart (figure 5).
Figure 5: Side view of the one sided bond with polypropylene, tiled structure.
By trying to create the sample shown in figure 5 not only includes the problem of
deciding which fabric backing layer to use, but also what bond will maintain a firm
hold between the EPS foam and fabric backing layer.
Page 17
Objective 2
To show an improvement in shear properties means that there has to be a reduction
in crack depth. By bonding these layers of EPS foam to a denser textile material on
one side, this will allow the specimen’s deformation in the tensile direction to
improve, and hence an improvement in shear characteristics of the overall specimen.
Rather than deforming further by fracturing, the deformation will be distributed in the
other directions, more specifically in the tensile direction. Hence, if a material which
is denser than the EPS foam is chosen to become the fabric backing layer, then both
flexible trauma packs and fracture reduction trauma packs can both be made with the
same material.
Once again, the bonding situation is brought up between the two materials. A firm
bond must be established between the two materials in order the sample to achieve
an improvement on energy absorption results compared a monolith sample.
By
having a firm bond between the foam and fabric backing material will allow more
backing material to be drawn into the compact zone, thus when the foam is being
impacted, more foam can be involved in the deformation and allow more energy to
be absorbed. This will be further discussed in the ‘Adhesives’ chapter.
In order to take a step closer in modelling a ballistic environment, then a point load
must be applied to the samples.
By introducing this point load, samples will
encounter three types of deformation: compression, tensile and shear.
Mills &
Gilchrist modelled the behaviour of impact response of foam under various forms of
indentations (figure 6) and discovered that it was difficult to model certain
deformation fields, especially if the foam unloaded, or stressed in shear, or tension
[11]. From their report, it can be concluded that certain areas of the foam are being
left relatively unstrained, due to the presence of fractures that occur.
The compressive behaviour will be thoroughly investigated through uniaxial
compression testing; where only compressive deformation can happen. Out of the
two remaining deformations, it is failure in tensile direction that interest this project,
since it is this behaviour that influence the fracture behaviour within the specimens.
Page 18
Figure 6: A plane-strain deformation impact testing showing an extruded polystyrene foam block under
loading by a falling, large cylindrical indenter striker mass [11]. Figure shows pieces of the foam being
ejected laterally after 7ms under impact.
This type of deformation will reduce energy absorption
capabilities of the foam (with less material to compress with) and one of the objectives is to reduce this
fracture behaviour
Considering the deformation processes that the foam will undergo when the material
encounters a ballistic environment. For illustration purposes, image a 22’’ calibre
solid rifle round impacting the foam. With speeds of at least 330s encountered, the
response of the foam is limited to a localised area within the region of impact. The
foam simply does not have enough time to transmit the responding information to the
rest of the material in order for it to react, as shear deformation would.
As a
compromise, further tensile stretching is more likely to occur, since there are a limited
number of ways the foam can deform. Hence, it is most likely that a majority of
deformation through tensile stretching occurs, and not shear, along with compression
during a ballistic impact.
Page 19
Execution
First and foremost, to discover how thinly EPS foam slices can be made, cell size
investigation must first be completed. Due to the EPS foams beaded nature, an
investigation into density variation and inhomogeneous structure will also have to be
completed to confirm that all foam sections cut from the initial slab of EPS foam will
have consistent properties and that direction of loading does not influence response
results, respectively.
To be enable comparison between the different types of specimens, a standard
uniaxial compression test with a cube of monolith block of foam, will then be tested.
This will enable a set of results which can be referred upon as a reference, and
possibly obtain values the EPS foam three phases, if the EPS foam follows the
typical response of cellular plastics.
Exploration will then be focused in finding if by cutting the cube of monolith block of
foam into equal layers, will change the results. The reference monolith block of foam
can also be used to compare results tested with changes in strain rate. Young’s
Modulus calculations will also be attempted to find the elastic modulus of the EPS
foam between the two different loading rates.
To confirm the trauma pack can achieve asymmetric flexure qualities, three-point
bending tests will have to be employed, along with the quasi-static plane strain
deformation experiments.
The quasi-static plane-strain impact experiments are employed to view the
specimens in deformation through compression, tensile and shear.
These
experiments will model closely to the experiments Mills & Gilchrist done to explore
foam impact responses [11]. These experiments will differ from uniaxial compression
tests, since uniaxial tests will only deform in a compressive manner, but the
deformation field experience on the samples surface is the same as that as the
interior.
By testing with an indenter loading head, this will allow quasi-static testing
to take a step closer towards a point load produced by a bullet during ballistic impact.
Quasi-static testing is also easier to control and analyze than ballistic testing.
Page 20
Fabric Backing Material
The material chosen to be the fabric backing material of the specimens was
polypropylene. Polypropylene is a stronger, stiffer and denser material than the EPS
foam, thus by using the polyefin as a fabric backing material, this should reduce the
fracture behaviour of the specimen reducing crack length. Due to the woven nature
of the polyefin, polypropylene is also a difficult material to handle as well as a difficult
material to bond with, as discussed in the next chapter ‘Adhesives’.
Adhesives
Adhesion between the polypropylene and EPS foam layers provide a pivotal role
within this project.
However, selecting the correct adhesion for this project may
prove to be difficult, which will be explained below.
Polypropylene is a very difficult surface to bond with and is best bonded using an
acrylic adhesive rather than an epoxy adhesive.
As with all polyolefins,
polypropylene is very difficult to bond on account of their non-polar, non-porous and
chemically inert surfaces. The low surface energy polypropylene may need a coating
of primer, one such example being RS 108-722.
Expanded polystyrene foam is another material which is not straight forward to bond.
Any adhesives containing solvents will tend to melt polystyrene.
Expanded
polystyrene also has low cohesive strength; therefore it is most likely that if a
successful bond with the expanded polystyrene is achieved, the adhesive will only
hold the polystyrene surface to the polypropylene.
One successful approach to adhesive bonding of these materials involve proper
surface pre-treatment prior to bonding, along with the proper adhesive used. The
options of different adhesives include:
•
Araldite 2011- which will bond polystyrene
•
Araldite 2018 - a highly flexible Polyurethane adhesive
•
Wood Resin Adhesive – this will enable to seal the EPS to give a smooth flat
finish that can be bonded
•
Double-sided adhesive tape – examples being 555-033 or 512-884
Page 21
Foam Characterisation
Cell Size
It is important that to have a rough estimate of the average of the sizes of the
individual cells, that make up the EPS foam. For polymer foams, cell sizes dictate
how small, or in this case how thin, the EPS foam can be made without size effects
occurring.
Size effect can be defined as the material‘s dimensions having an
influence on its mechanical properties. In the case of polymer foams, size effect will
only be factor, if they do not go beyond the cell size by 20 times [9].
The cell shapes inside a moulded bead can vary.
Cells which are close to the
surface of the bead skin tend to have brick-like shapes, with two of their faces
parallel to the bead boundary. Cells which are found closer to the core of the bead
have equiaxed polygonal shapes [9]. A skin-core morphology variation can influence
the mechanical properties of the moulded foam, as the denser skins are of higher
modulus (this is discussed further in the ‘Density Variation’ chapter).
To examine how small the specimen sizes could be without encountering the
phenomenon of size effect, microscopic testing was performed on the EPS foam. An
Optical Microscope Bressier Biolux AL 20X-1280X was used to provide figure 7 with
a magnification setting of x10.
Figure 7: Expanded Polystyrenes foams cells with the Optical Microscope Bressier Biolux AL 20X1280X at a setting x10 magnification
With an image analysis software Image-J, a more accurate approach in determining
the boundaries of the individual cells could be accomplished, as shown in the figures
below. Measurements from a rule could then be achieved, which a list of the cell
sizes could then be complied and are presented in figure 8 and table 1, shown below.
Page 22
1 mm
1 mm
y
x
Figure 8: Image manipulation with image analysis software Image-J
Cell No
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Average
x/y
0.80597
0.929577
1.454545
0.586207
1.414634
0.903226
0.783333
1.102941
1.196078
1.24
1.107692
0.983871
1.068182
0.734375
1.098361
0.756757
1.090909
0.939394
0.766667
1.130435
1.004658
(x+y)/2
60.5
68.5
67.5
46
49.5
59
53.5
71.5
56
56
68.5
61.5
45.5
55.5
64
32.5
57.5
32
53
49
55.35
x true (mm)
0.17614
0.2216
0.2614
0.108
0.19318
0.1818
0.1591
0.25
0.19886
0.2045
0.2386
0.2045
0.1534
0.1591
0.22159
0.0909
0.19886
0.10227
0.1534
0.17045
0.1823825
y true (mm)
0.2273
0.2386
0.1818
0.19318
0.13068
0.2045
0.19886
0.227
0.17045
0.16477
0.2159
0.2045
0.1477
0.2045
0.2045
0.125
0.1818
0.1136
0.2045
0.1534
0.184627
Table 1: Cell Sizes. The cell number refers to figure 14
From table 1, it is clear that the average cell size is 0.182mm in the horizontal (x)
direction, and 0.185mm in the vertical (y) direction, with a standard deviation of 0.047
and 0.036 respectively. In relation to calculating the smallest possible EPS foam
specimen without encountering size effect, the largest cell size dimension
encountered was 0.26mm. With this guideline, this meant that the EPS foam was
limited to being cut at minimum of 5mm, in order to dispose of size dependence.
Page 23
The sizes of the individual beads could also play an important part in the EPS foams
response. Again with the Optical Microscope Bressier Biolux AL 20X-1280X and a
magnification setting of x4, evident beads can be observed in figure 9. Nevertheless,
with the lack of information with bead sizes, bead size influence will not known or
taken into account during these experiments.
2.5m
y
x
Figure 9: Microscopic image with the same microscope taken at a x4 magnification. Bead boundaries
can be viewed as darkened regions of the picture
Rao and Hofer stated that the yield stress of a cellular material can be enhanced by a
decrease in the cell size [12]. Be that as it may, the importance of the investigating
the EPS foams cell size, is to find out how small specimens of the EPS foam can be
made, without the phenomenon size effect occurring.
Page 24
Density Variation
With bead foam mouldings, the Young‘s modulus and strength of a specimen can
vary with the position cut from the moulding. This is a result of the EPS foams
inhomogeneous microstructure. Bead foam mouldings usually vary in density, shape
and size from the skin to the core.
Most beads are distorted spheres, with flat
patches in contact with neighbouring beads. The near spherical shapes are due to
the bead having a solid skin. Beads near the surface of the moulded product have
not deformed sufficiently to eliminate the inter-bead channels. If a polystyrene bead
is at a higher pressure than its neighbour, the pressure differential causes the interbead boundary to be curved.
Hence curved boundaries indicate either that the
beads contain differing amounts of blowing agent or that they have expanded by
different amounts. There is likely to be a density variation from moulded bead to
moulded bead, since the space for expansion is variable and the beads cannot move
relative to their neighbours once they begin to fuse at the boundaries.
A simple analysis in exploring the structural variation within the foam was completed
by measuring the weight throughout the foam, in different sections. In theory, by
increasing the material density, the effect of an increase crushing stress plateau and
a decreasing strain to densification, with an increasing strain rate, should be seen
[13].
Two different variations of these tests were done: one where the density variation
was tested throughout the whole slab of the EPS foam and the other where the
density variation was tested throughout an individual layer.
By taking a whole slab of Jablite EPS foam material, 20 identical pieces (dimensions
of (l) 0.45 x (w) 0.06 x (t) 0.05 m) were made as shown in figure 10. The individual
segments were then weighed and the density could be calculated from these values
(figure 11). The density variation in this test was measured along the thickness of
the foam.
Thickness
Reference
Surface
=
Length
Width
Figure 10: EPS foam preparation for density variation analysis within the whole structure (slab) of
material.
Page 25
Density Variation (Slab)
20
18
16
Density (Kg/m³)
14
12
10
8
6
4
2
0
0
0.2
0.4
0.6
0.8
1
1.2
Distance away from Reference Surface (m)
Figure 11: Test Results of density variation experiment no 1. The reference surface is highlighted in
previous figure 10
The other density variation test would be measured along the length of the foam.
Using an individual layer cut from the EPS foam, this segment of foam would also be
made into several identical pieces (dimensions (l) 20 x (w) 50 x (T) 6 mm, shown in
figure12.
Again, variations in density were measured by weighing the individual
segments (figure 13).
Thickness
Reference
Surface
Width
Length
Figure 12 EPS foam preparation for density variation analysis within a single layer of material
Page 26
Density Variation (Single Layer)
18
16
Density (Kg/m³)
14
12
10
8
6
4
2
0
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Distance away from Reference Surface (m)
Figure 13: Test Results of density variation experiment no 1. The reference surface is highlighted in
previous figure 12
Results confirmed that there was indeed a density variation throughout the EPS
foam.
However, due to the magnitudes of the variation, around 2 Kg/m3, the
properties of the EPS foam is treated as a constant with calculations of the individual
specimens not requiring to specifically refer back to which area they were cut from,
calculating the exact mechanical properties they should hav
Page 27
Inhomogeneous Structure
Further testing was done to explore EPS foams inhomogeneous structure. Even
though the beaded nature of the EPS foam was found not to have a uniform structure
throughout the material, confirmation was required that test data was not influenced
by the direction of compression of the foam.
Further slow rate compression testing was continued, with differences on how the
cube samples were positioned, were attempted. Specimens 1 and 2 were placed on
the machine as in figure 20(a), while specimens 3 and 4 were mounted on the
machine as in figure 20(b)
Width
Thickness
Thickness
Width
Length
Length
(a)
(b)
Figure 14: Figures depicting the method of testing a sample through different directions of loading.
Even though the machine was constricted to vertical testing, specimen samples could be altered in their
boundary conditions to achieve this.
Results showed that the direction of loading did not matter, with all four samples
achieving identical results (figure 15).
900000
800000
700000
Stress (MPa)
600000
500000
1
2
400000
3
4
300000
200000
100000
0
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-100000
Strain
Figure 15: Stress-Strain response curve of foams tested in a uniaxial compressive manner. Variations
between results were in the initial starting position of the samples as shown in figure 20.
Page 28
Standard Compression Tests
A standard cyclic compression test was applied to cubed (50mm x 50mm x 50mm)
EPS foam specimen, in order to investigate the EPS foams properties going through
compressive deformation only.
Specimens are cubed, to avoid buckling and to
ensure a uniform stress distribution.
Testing was achieved by a vertical testing
machine, the Zwick Roell Z2.0 Uni-axial Tension Compression Machine.
The
following parameters used for the analysis can be given in the table 2 and the results
are shown in figure 16.
Strain Rate
Number of Cycles
Displacement
5mm/min
1 cycle
45mm deformation (90% compression)
Table 2: Standard compression testing specifications
Figure 16: Force-displacement response curve of the EPS foam tested within a standard compression
-5
test of strain rate 8.33 x 10 m/s and 90% deformation.
The response of the EPS foam matches the common description of polymeric foams,
which include three phases. The first and second phase, which is the linear elastic
response and stress/collapse plateau respectively, are almost identical within all
specimens. Even though the three regimes can be observed, there is difficulty in
determining at what exact values these regimes start and end.
By eye, all 3
specimens enter the stress/collapse plateau under 200N force and remain almost
identical, including a rising plateau due to the trapped air associated with closed cell
Page 29
foams, until they enter the final phase, which is around 400N. It is this final phase
(‘densification’ or ‘hardening’) of the compression response where, apart from first
specimen, all other specimens retrieved almost identical results with 0.1mm
difference between them. Although the first specimen was able to compress and
unload under a force of under 2000N (1780N), the other three required a
compression force of over 2kN to reach the 45mm deformation target. Hence a
machine which could exert and measure a force of over 2kN was required.
Subsequently of the incomplete analysis obtained with the Zwick Roell Z2.0, the
Zwick Roell Z250 was employed. With an upper force limit of 250kN, in comparison
to 2kN the Z2 could achieve, complete full cycle data could be retrieved. Using the
same criteria as Table 2, the results of the compression tests with the Zwick Roell
Z250 are given in figure 17.
Again, a significant difference is seen between the fifth specimen tested and the
others at the final stages of compression response. Mirroring the first machine, the
fifth specimen was only 20N under the 2kN force to load and unload, whereas the
other two specimens passed the 2000N mark by a sizeable amount. Again, all 3
specimens went through the first two stages just like the previous four specimens
(i.e. a linear elastic response until reaching a mark under 70kPa and a
stress/collapse plateau of around 200kPa). Similarities are also spotted between
specimens 2 and 3 within the final stage, just like the above; however, they were not
nearly as identical. Unlike the above, comparisons on the unloading phase could
now be made, with all three following a similar trend.
All three test specimens
recorded no reaction force after a strain of 30mm, which incidentally, is also true for
the very first specimen tested in the first machine. This signifies that the EPS foam
had permanently deformed under a height of 30mm.
Results that were directly recorded from the testing were the data of ‘Standard Force’
in Newtons and ‘Deformation’ in mm. To analyze data that is independent from the
size and shape of the specimen measurements of stress and strain are preferable.
Equations on how the two were obtained are given below. The work energy can also
be calculated with the recorded data by determining the area under the graph. Units
of work energy would therefore be in N/mm.
Page 30
Force
Area
Engineering Stress =
Engineering Strain=
Change in length − Original length
Original length
Where Area = length x width = 0.05 x 0.05 = 0.0025m2 & Original length = 0.05m
1200000
1000000
Stress (Pa)
800000
600000
400000
200000
0
0
0.2
0.4
0.6
0.8
1
Strain
Figure 17: Standard compression tests results, in terms of stress and strain, completed on the Zwick
Roell Z250 machine.
Pink lines indicate a cyclic compression testing was done, whereas green lines
represent the data obtained in the compression only testing.
Compression only evaluations were then completed with the Zwick Roell Z250, to
ensure data repeatability (figure 17). Another aim of these tests was also to provide
information to allow Poisson’s Ratio calculations, although this will be discussed in
another chapter. Maintaining the same strain rate of 5mm per minute and displacing
the EPS foam 45mm (90% deformation),
Once again, repeatable results were produced within the first two stages of
compression response with results show identical similarities with the cyclic test
results. However, this time the EPS foam for both specimens peaked at a value of
below 2kN (1920N and 1960N respectively).
Page 31
Monolith vs. Layered
As mentioned within the ‘Concepts of the Project’ section, compression results
between a monolith block of foam compared to a block of foam that contains layers
of the same material, should obtain the same strength and energy absorption results.
To confirm this, more static crushing tests would be employed on both kinds of
samples. Monolith samples would be represented by a 50mm x 50mm x 50mm block
of foam whereas layered samples would correspond to five 50mm x 50mm x 10mm
pieces of foam stacked on top of one another. All cutting was performed by using a
band saw.
Together with the Zwick Roell Z250 Uni-axial Tension Compression
Machine and with the same criteria in Table 2, the results produced can be viewed in
figure 18.
3000000
2500000
Stress (Pa)
2000000
1500000
1000000
500000
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Strain
Figure 18: Stress-Strain compressive response of monolith (black) vs. layered samples (red)
The uniform layered width system has a similar force-deformation response to a
monolithic block. The three characteristic phases, initial linear elasticity, a post-yield
plateau and densification, are evident.
However, there were obvious differences
between the monolith and layered samples. These differences were evident in the
first and third stage of results i.e. linear elastic response and densification regime of
response.
Page 32
During the first characteristic phase, linear elastic, the layered foam showed less
resistance, although similarities can be seen between the layered and monolithic
foam when the response begins to enter the plateau phase around the 50 kPa mark.
For the monolith, the strain recorded when the linear elastic region ends is roughly
0.04, whereas for the 1cm layered foam, the strain was measured around the 0.09
mark.
During the densification stage, it was clear that the layered specimens needed over
twice the force to compress the specimen 45mm, compared to the monolith
specimens.
However, despite these differences, this project is only interested in the first and
second stage of the characteristic phases, especially the plateau stage, since this is
where most of the energy absorption occurs. Taken these factors into consideration,
then it can be concluded that the results are similar to a monolith block of EPS foam.
Unloading also shows signs of slight discrepancies, although once again, this is an
area of little interest to this project.
Differences are thought to be due to be to the difference of boundary conditions of
the layers and monolith. Due to the specimen now made up of layers, there is a
slight increase in shear stress when the specimen is compressed. A phenomenon
called barrelling is also more likely to occur, due to the lack of lubrication between the
plate and specimen. To achieve more similar results, concluding that there is no
difference in compressive properties between a monolith and a layered block of
foam, the test can be repeated with lubrication, such as Teflon powder or oil with low
viscosity (WD-40 or hydraulic oil being such examples of low viscosity oil).
Page 33
Fast Rate vs. Slow Rate
Polymer foams are renowned for their strain rate dependence. By increasing the
strain rate, many polymeric foams have exhibited the same behaviour through an
increased elastic modulus, increased plateau stress level and a decreased
densification strain (figure 19). Yield stress increases with strain rate. The general
trend of cellular plastic seems to be the faster the strain rate, the stiffer the material
responds with a higher likelihood of fracturing.
Figure 19: A stress-strain response curve of a polymer foam under uniaxial compressive loading with
the variation in results expected by increasing the strain rate [4]
The examination of the effects of different strain rates would require the Zwick Roell
Z2.0 Uniaxial Tension Compression Machine, due to its faster loading rate compare
to that of the Z250 machine. With previous knowledge and experience gained by
using the machine in previous testing, it was clear that certain alterations, and not
only the strain rate, would have to be made. By operating the machine at the fastest
strain rate, 15000mm/min, or 0.25m/s, a displacement of 36.5mm was decided, in
order to keep within safe operating limits of the machine. The 73% deformation
‘calibration’ was agreed upon, through trial and error runs (see Limitations chapter).
Monolithic specimens were employed during this procedure and compression only
testing, not cyclic, was completed.
Page 34
1200000
1000000
Stress (Pa)
800000
600000
400000
200000
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Strain
-5
Figure 20: Results of loading a monolith EPS foam with a slow rate (8x10 m/s) which is shown in light
blue and a fast loading rate (0.25m/s), shown in pink
The results, given in figure 20, confirm that EPS foam, like all other polymers, is
strain rate dependent. Even through the initial stages of the foam response, there
are discrepancies between the fast and slower loading rates. Not only does the
faster loading rate require a great deal more strength in deforming the foam at the
same displacement (signifying that the faster the strain rate, the higher the stiffness
response of the EPS foam will become), the displacement where the response
regime changes as well. For the 5mm/min strain rates, the linear elastic region ends
at around a strain of 0.025. Contrasting this with the 15000mm/min strain rates, the
plateau regime seems to start at a strain value around 0.002, taking a tenth of the
distance of the slower strain rate.
To summarise, the EPS material exhibited
increasing crush stress plateaus, and decreasing strain to densification, with
increasing strain rate.
Average Percentage Difference
25
20
15
10
5
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Strain
Figure 21: Average percentage difference between the slow and fast loading rates within the plateau
region
Page 35
From figure 21, it can be distinguished that there is a maximum of 23% difference of
results, between the faster and slower rates of loading within the plateau region of
foam response. By loading the EPS foam at a higher rate, it can be seen that more
energy can be absorbed, and more force is required to reach the densification stage.
The material is overall, in other words ‘stiffer’ and stronger, as is true with all other
polymer foams. The stiffness is quite an important parameter since this will affect
how the shock waves propagate through the material. Although unrelated to the area
of interest, by being restricted to use the quicker, smaller machine, the peak rates of
fast loading of the specimen were immeasurable.
For many materials, a significant increase in the loading rate often results to higher
rates of deformation.
Foam mechanical properties are extremely rate sensitive.
Generally the higher the loading rate, the stiffer the cellular material reacts, with the
consequence that it is more likely to fracture. The cause of this is fundamentally due
to the base polymer material from which the foam is made from, which is also strain
rate sensitive.
dependence
This is also true in regards to cellular materials temperature
properties,
polymers
are
very
temperature-sensitive
materials.
Nevertheless, fluid within the voids of the cellular structure can also play a role in the
foams strain rate sensitivity.
In cellular materials, the fluid or gas contained within the voids is compressed and
expelled by flowing through the cells, as the material is compressed or crushed. As a
result, viscous forces generated when the fluid is pushed out of the foam cells during
the deformation increases when the deformation rate increases, leading to an
increased rate sensitivity. If the cells are relatively large and the deformation rate is
reasonable small, then the contained fluid usually has no effect on the material and is
generally ignored, especially in the analysis of quasi-static tests to determine the
mechanical properties of foams at low compression rates. This is especially true in
open-celled structures, which allows fluid to flow to one cell to the next with little
internal resistance.
Since the entrapped fluid is compressed locally within the cell for closed cell foams,
the effect of rate sensitivity is even more evident within these types of cellular
plastics. Combining closed-cell materials together with high loading rates, resistance
against the dynamic compression of fluid within cells becomes significant and will
affect characteristics such as the yield strength of the material to be strain rate
Page 36
sensitive.
Not much knowledge or research has been completed with polymeric foams
responding under high rates and significant deformation, although there are a few to
note. Altering the strain rate will also lower the densification strain [14]. This can be
attributed to the reduced ability of the foam cells and minimize the volume of the
compressed material. Stress wave effects, stress which now include inertia forces
and accelerations, will also become more evident within cellular materials when the
loading speed is increased [15]. Explosive responses have been reported by Green
et al [16], when the foam is impacted at sufficiently high velocity.
Page 37
Young’s Modulus
The Young’s modulus, or also known as the modulus of elasticity, is the mechanical
description of a subject’s tendency to deform along an axis when opposing forces are
applied along that axis, or ‘stiffness’. The elastic modulus of a material is defined as
the uniaxial stress over the uniaxial strain of a material, from the numerical evaluation
of Hooke’s Law.
To find the Young’s modulus of the EPS foam, data from the Fast vs. Slow Rate
chapter is adopted. The Young’s modulus can be found by the gradient of the slope
within the initial linear elastic regime.
There are two approaches that can be
employed to find the gradient of this area. The first is by drawing a gradient by eye.
However, this technique is slightly subjective being based upon an individual’s
judgement (figure 22). Young’s Modulus values are given as, for the slow strain rate,
2.01 – 2.532MPa and for the faster strain rate, values range massively around 22.31
– 89.43MPa, although data repeatability suggests the value to be nearer the 27MPa
mark.
70000
60000
Stress (Pa)
50000
40000
30000
20000
10000
0
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
Strain
Figure 22: Stress-Strain response curve of EPS foam within the linear elastic region. Strain rate of
-5 -1
loading is 8.33x10 s . Blue line represents test data and the Pink line the arbitrary Young’s modulus
gradient by eye
Page 38
To avoid this subjectivity a second method is used.
The second method is an
automated process and is not influenced by an individual’s preferences. By plotting a
graph of the foams gradient vs. the strain, as shown in figure 23, the variations in
gradients, along with the maximum gradient, can be observed. By isolating certain
amounts (an example of 30%) of data neighbouring and including the maximum
value, by averaging these figures, a straight line equation can be formulated. This
straight line is the elastic modulus of the foam, which passes through the point of
maximum gradient of the measured results.
3
Youngs Modulus (MPa)
2.5
2
1.5
1
0.5
0
0
0.01
0.02
0.03
0.04
0.05
Strain
Figure 23: The elastic modulus within the linear elastic region with a step increment of three individual
-1
samples tested with a strain rate of 0.25s . By averaging a certain region within the maximum value, an
accurate automated value of the Young’s Modulus of the foam can be obtained
Although the second approach can be considered a more reliable method, it is a
method which can only be applied to specimens tested in the slow, 5mm/min strain
rate. This is due to the number of data points that is obtained from the slow strain
rates (thousands), compared to the 100 or so data points gathered from testing with
the quicker strain rates. Attempts to gather more data points with the faster rate of
loading experiments, however none were successful. Table 3 shows the accuracy of
the automated system compared to the first approach by eye, with specimens loaded
at the slower, 8.33 x 10-5s-1 rate of strain.
Page 39
Method
Cut-off
Young’s Modulus (MPa)
% Difference of Eye
Eye
Na
2.01 - 2.532
Automated
30%
1.9 - 2.378
1.933 - 6.07
Automated
20%
2.00 – 2.49
0.148 – 1.6
Table 3 Accuracy between Naked Eye Observations and Automated Calculations
As stated in the previous chapter, the EPS foam is confirmed to be strain rate
dependent. Results clearly indicate that the EPS foam is rate dependent as the
plateau stress level is increased and the densification decreasing with an increasing
rate. Comparing the foam response of a monolithic block of EPS foam from a slow
loading rate of 8.33 x10-5s-1, to faster loading rate of 0.25s-1, will see a massive
difference from 2MPa and 27MPa in elastic modulus respectively. However, the
number of data points collected by the faster loading rate causes concern on the
reliability of the data, as well as determining the elastic modulus by readers
perception. This behaviour is confirmed through Young’s Modulus calculations.
Page 40
Three-Point Bend Tests
Three-point bend tests can only be performed on rigid foams. Given the low Young’s
modulus of polymer foams compression tests can easily generate stress-strain data.
With the foams brittle behaviour in the tensile direction, three point tests are usually
used to determine the tensile strength of EPS bead foams, since bead foam products
often fail in bending. Failure in a three-point bend test initiates a small, high stress
region, so the results are usually less affected by the random location of large flaws.
The three-point bending tests are employed to confirm that the tiled specimen
samples are flexible in one direction and not the other. To recap, tiled specimens
were constructed in order to investigate whether comfortable trauma packs could be
created with the EPS foam. To achieve this comfort, the rigid EPS foam would have
to be flexible and bend easily in one direction and not the other. It was assumed that
by tiling the one sided bond samples with polypropylene with the minimum adhesive
technique, that the tiled samples would have a slight reduction in performance than
the un-tiled samples. This assumption will be confirmed or rejected through the main
quasi-static strain deformation experiments.
If these tiled samples are used within the trauma pack, then the tiles must be placed
in manner so that they can flex in the direction away from the body armour easily and
do not flex towards the body armour.
To test these tiled samples, three-point
bending tests were carried out as close to the British Standard Methods for Test for
Rigid Cellular Materials - Determination of flexural properties [17].
There are several notable differences from the method 14 of BS 4370-4:1991
compared to the three-point testing that was executed for this project. Firstly, BS
4370 recommends using a beam of span 300mm, depth 25mm and a loading point of
radii of 15mm. Hence, layers were made 300mm x 50mm x 5mm, and samples were
organized with 4 layers stacking on top of one another, giving a totally depth of
25mm in both samples. A total of 10 Incisions made were, 30mm apart. Skin and
moulded surfaces were removed from the samples. Cylinder supporting edges also
differed from BS4370, measuring a diameter of 19.6mm
The loading point also had to be altered. An initial attempt was given with the Zwick
Roell Z2.0 to complete the three-point bending tests. However, with the 20mm
loading head, it was found that the forces measured were miniscule and heavily
Page 41
influenced by background noise, in order to give clear results to formulate from. A
more successful approach was with the Zwick Roell Z250 machine, equipped with a
more sensitive 5N load cell. With the 5N load cell, the loading head became only a
single point. To distribute the load more evenly, a rectangular metal plate with a
length of 13mm and width of 5mm was placed between the specimen and 5N load
cell.
The metal plate measured a weight of 3.4989g, which would have to be
acknowledged when calculations on elasticity of flexure and flexural strength are
applied.
1.6
1.4
1.2
Force (N)
1
Polypropylene Top
(Flexible)
Polypropylene Bottom
(Stiff)
0.8
0.6
0.4
0.2
0
-50
0
50
100
150
-0.2
Displacement (mm)
Figure 24: Results from three-point bending of tiled samples.
Even without calculations, examination with figure 24 can clearly see there is a
significant difference in rigidness between the two directions.
The phenomenon
sagging was encountered when the flexible direction of the tiled samples were being
tests, which is why there is a delay in recording displacement. No fracture was found
with any of the samples tested, however this was expected due to no end
constrictions were employed on the samples to could contribute to the fracture. No
crushing was found throughout the foam, enabling flexural calculations to be
attempted.
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Equations for elasticity in flexure (E) and flexural strength (R) can be found from
BS4370 and is given below:
E=
where
L3 FT × 10 6
4bd 3 xT
FT is the force
R=
1.5 FR L × 10 6
bd 2
xT
is
the
corresponding
deformation
FR is the maximum force applied
L is the span
b is specimen width
d is specimen thickness
With values given by drawing a tangent against the steepest gradient of the curve,
values of force = 1.00084N, displacement = 30.3913mm and maximum force = 1.35N
are found for the tiled specimen in the stiff direction. Considering the force generated
by improvised loading head = 3.4989 x 10-3N, this will enable values of elasticity in
flexure and flexural strength to be calculated.
E=
350 3 × (0.00100084 − 0.0000035) × 10 6
= 450.24kPa
4 × 50 × 25 3 × 30.3913
R=
1.5 × (0.00135 − 0.0000035) × 350 × 10 6
= 22.6212kPa
50 × 25 2
The identical procedure was done for the flexible direction of the tiled samples.
Using values of force = 0.0308021N, displacement = 26.5346mm and a maximum
force of 0.0321675, values of elasticity in flexure and flexural strength are given
below.
350 3 × (0.000030802 − 0.0000035) × 10 6
E=
= 14.117kPa
4 × 50 × 25 3 × 26.5346
R=
1.5 × (0.000321675 − 0.0000035) × 350 × 10 6
= 5.345kPa
50 × 25 2
Values confirm the conclusions that were made in the observations from figure 37, in
that flexibility has been achieved in one direction, while remaining stiff in the other.
Combining this data with the quasi-static plane strain deformation tests, where tiled
samples showed no dramatic deterioration from monolith samples, it can be
confirmed that indeed flexible active trauma packs can be made and are successfully
through testing. Future investigations on in testing even higher strain rates, and
maybe even ballistic experiments, can be continued with tiled samples.
Page 43
Plane-Strain Deformation Impact Tests
The main focus of this project is exploring the concept of foam being used in a
trauma pack with specific properties and the analysis of the behaviour of the trauma
pack when it is under impact.
Although ballistic testing would seem the most
appropriate for this project, there are reasons why quasi-static tests was chosen
ahead of ballistic testing to investigate the material. One key reason was that quasistatic testing would be easier to set up, control and analyze than the ballistic
experiments. Quasi-static simple geometry experiments with plane strain deformation
in the foam would allow the deformation field on the foam surface to be the same as
that in the interior.
A venture to recreate the Mills & Gilchrist’s plane-strain deformation impact
experiments [11] was attempted. In their experiments, simple geometry experiments
were tested on extruded polystyrene foam. The source of impact was created by
dropping a striker mass between 1.0 and 2.0 m to achieve their desired impact force
on the foam and their analysis heavily emphasised on the fracture behaviour of the
foam.
In this experiment, variations of the foam block would be subjected to three different
types of compression tests with the machine Zwick Roell Z2.0. All experiment strain
rates will be travelling at 15000mm/min (0.25m/s) and with simple geometry
variations of the loading head, given in table 4.
1
Uni-Axial Compression
Several Final Compression Strains
2
Small Cylindrical Indenter (18mm diameter)
70% compression
3
Large Cylindrical Indenter (100 mm diameter)
70% compression
Table 4: Variations of loading heads along with final compression strain
By using cylindrical indenters, instead of having only compression deformation, as
the uniaxial experiments, indenter testing will allow other forms of deformation to be
introduced. The indenter testing will allow quasi-static testing to take a step closer
towards a point load produced by a bullet during ballistic impact. The logic behind
the two different types of indenters is due to the fact that impacts with indenters can
be divided into two cases. Assuming that a flat topped block of foam is being tested,
indenter geometries are classified according to strain field symmetry, where:
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1. The cylinder diameter is smaller than the original foam block thickness, so the
principle compressive stress field tends to radiate from the cylinder axis.
2. The cylinder diameter is larger than the original foam block thickness, and the
stress field in the foam tends to be vertical.
Despite recognizing the limitations on the strain rate and allowable force on the
machine, as previously with the foam characterisation tests, it needs to be noted that
there is another key difference between the these experiments and the Mills &
Gilchrist’s plane-strain deformation impact experiments.
With Mills & Gilchrist’s
experiments, a variation of impact velocities were recorded due to the method they
deployed to achieve their impact force; by using a striker to fall between 1.0 and 2.0
meters with twin wire guidance.
However, due to the method the strain rates are applied in these experiments, the
same problems do not arise, since there is no variation in the striker mass.
Experiments are simply compression experiments with a different loading shaped
head.
A high speed camera - Optimas UK Kodak MotionCorder Analyzer model 1000 - was
also employed during the testing. Settings on the high speed camera included a
frame rate of 240 frames per second and a shutter speed of 1/500 sec. This allowed
analysis of the failure as specimens were tested.
The purpose of having variations in foam specimens is to change some the foam
properties without deteriorating others. The cross-sectional areas of the foam layers,
polypropylene and adhesion inserts in all foam plate systems are kept constant.
Guidelines of specimen sizes and dimensions are given in tables 5, 6 , 7 & 8. At
least two of each specimen was constructed so that experiments could be tested for
data repeatability.
Experiment
Specimen Length
Specimen Width
Specimen Height
Small Indenter
100mm
50mm
50mm
Large Indenter
200mm
50mm
50mm
Table 5: Guidelines for specimen parameters
Page 45
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Page 47
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Specimens for Plane-Strain Impact Experiments
The range of the specimens that were made and tested is given below, along with a
description on how they were made. The purpose and ideas of every manipulation
with the specimens can be seen in the ‘Concepts of the Project’ chapter.
Monolith
The monolith samples should obtain if not the best, then one of the best results in
terms of strength and energy absorption under deformation through compression
only. External interactions with these samples will only be on the top and bottom
surfaces of the monolith samples (figure 25(a)).
With no other influences, the
monolith samples should be able to put up more resistance against the compression.
The data from the monolith will be used as a reference in comparison to other
specimen types.
In terms of fracture, on the other hand, the monolith samples should obtain the most
evident cracks. Foams break due to their brittle behaviour in tension and it is this
weakness in the tensile direction that must be altered, in order for foams to absorb
more energy. However restrictions into changing the foam property includes that
altering foam density is to be kept as minimum as possible.
Layered Specimens
There are three types of specimens that use this layered structure:
•
Layered – where the samples only contain EPS foam.
•
Single bonded – where samples are bonded with polypropylene on one side
of the EPS foam only. Further distinctions can be made through the amount
of adhesive used to bond the two materials together: minimum and generous.
Tiled specimens are samples which are made from single bonded with
minimum adhesive samples with a further step induced (figure 6).
•
Double bonded – where samples are bonded with polypropylene on both
sides of EPS foam.
Again, further distinctions can be made through the
amount of adhesive used to bond the two materials together: minimum and
generous.
Page 49
(a)
(b)
(c)
(d)
Figure 25: Illustrations of the different specimen types. Figure 25(a) represents a monolithic foam block,
where Figure 25(b) shows how 3 foam layers where organized in the layered specimens. Figure 25(c)
illustrates the singled sided bonded with polypropylene (represented by the grey layers) with the yellow
surfaces indicating where adhesion was positioned in the samples. Graphical representation of the tiled
samples can be seen in Figure 25(d)
Layering Foam Only
By layering the foam, this will allow a flexibility of the trauma pack to increase, yet
see the compressive properties of the foam to maintain. By having the foam in this
layered structure will also require constraints to be put on the ends of the specimens.
This is to enable no bending to occur with any of the foam layers during testing. With
the string attachment, this will enable the whole specimen system to respond to the
impact loading. However by having this string attachment, a small flexion during the
test will also be recorded.
This small flexion is considered insignificant and is
ignored.
Organizing the foam into layers meant that the foam slices had to be cut from the
original EPS foam slab. This was done through a ‘band saw’ cutting tool, which as a
consequence, exact layers of 5mm thickness were not able to be obtained. On
average, the thickness of foam was 5.38325mm, with a standard deviation of
0.00361.
One Sided Bonded with Minimum Wood Resin Adhesive between Polypropylene and
EPS Foam
Although layering the EPS foam will allow some flexibility, by adding polypropylene to
the foam, as shown in figure 25 (c), this should further reduce fracture depth yet
allow the compressive components of the layered foam to remain still remain the
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same. By introducing the polypropylene, this denser material will alter the whole
specimens shear properties, making the material stiffer and show less signs of
fracture, compared to the monolith samples.
Through the advice from adhesive specialists and cases of trial and error, Evo-stik
Wood Resin adhesive was judged to provide a decent bond between the two
materials with no pre-treatment necessary. Specimens of this type were also made
using the adhesion through double sided adhesive tape.
One of the objectives of this project was ideally, to change the fracture properties of
the EPS foam, without changing the yield plateau of the cellular plastic. With the
polypropylene being predetermined, the only option left to keep the density from
differing away from its original value as possible, was to use the minimal amount of
adhesive possible. This was achieved by applying a small and controllable amount
of adhesive to the EPS foam layer, spreading it across the foams cross sectional
area and scrapping the excess adhesive away before the polypropylene was applied.
No weights were used to ensure the adhesion of both materials, since it would be
likely that the weights would alter the performance of the foam by damaging the
unique cellular structure of the foam and hence achieve poorer results when tested.
One Sided Bonded with Generous Wood Resin Adhesive between Polypropylene
and EPS Foam
With the minimum adhesion technique, although this ensures that the specimen
density is kept as low as possible, the technique did not ensure that the firmest bond
possible with the two materials was applied. To establish the polypropylene and EPS
foams firm bond with one another, samples were made where a generous amount of
adhesive was applied.
To enable measurability, the same amount of volume of
adhesive was applied through a syringe. For the specimens that were to be tested
with the small indenter, 2.5ml of wood resin adhesive was applied between the foam
and the polypropylene. For the specimens to be tested for the large indenter, the
amount was altered to 4ml.
One Sided Bond with Minimum Wood Resin Adhesive between Polypropylene and
EPS foam, Tiled
Tiling the trauma pack will enable flexibility to be achieved in one direction, and
Page 51
inflexibility in the other. In terms of this project, comfort is defined as the foams
flexibility.
To judge, whether these tiled samples are more flexible or not, and
therefore more comfortable, tiled samples will have to be made to be subjected to
three-point bend testing.
The tiled samples were made in the identical manner as the one sided bond with
polypropylene with the minimum adhesion technique, only a further step was
introduced once the adhesive had fully dried. Once given enough time to dry within
the manufacturers’ specifications, incisions were made into the EPS foam, cutting it
into effectively ten sections of EPS foam bonded to the polypropylene (figure 25 (d)).
Incisions were made by a pen-knife, 10 and 20 mm apart for the small and large
indenter tests respectively.
Both Sided Bond with Minimum Wood Resin Adhesive between Polypropylene and
EPS foam
With uni-axial compression, there is no shear behaviour occurring within the foam
and the whole foam is reacting to the compressive force, indiscriminately. However,
with the indenter tests, only a certain region of foam will be compressed. By bonding
the foam on both sides, although there may be a loss in flexibility, the energy
absorption results should improve considerably with the indenter experiments. This
is a result of enabling to introduce more foam material into the indenter compression
region of the foam.
Both Sided Bonded with Generous Wood Resin Adhesive between Polypropylene
and EPS Foam
These samples were built in order to achieve the same purpose as the single sided
bond with generous amount of adhesion. The exact same measuring method of
using a syringe was adopted, with samples created for the small indenter having
2.5ml of wood resin adhesive in between layers of polypropylene and EPS foam, and
4ml for specimens to be tested with the large indenter.
However, the purpose of these specimens, were not only to see the effects of a firm
bond, but to also try and introduce more foam into the indenter compression region.
In turn, by allowing more material to be deformed by the indenter, these samples
should record more energy absorbing properties and higher strength.
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Test Results and Analysis
2500
Force (N)
2000
1500
1000
Monolith
Layered
One Sided Bond Min
Two Sided Bond Min
500
0
0
10
20
30
40
Displacement (mm)
Figure 26: Stress-strain response curves of different specimens under uni-axial compression.
Specimens all had approximately uniform dimensions of 100(l) x 50 (w) x 50 (t).
700
600
500
Force (N)
400
300
200
One Sided Bond Min
Layered
Tiled
100
0
-10
0
10
20
30
40
-100
Displacement (mm)
Figure 27: Force-displacement compressive response curves under the small indenter testing
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900
800
700
Force (N)
600
500
400
Monolith
300
Double Bonded
Min
200
100
Double Bonded
2.5ml
0
0
10
20
30
40
Displacement (mm)
Figure 28: Force-displacement compressive response curves under the small indenter testing
(continued)
1600
1400
1200
Force (N)
1000
800
600
Monolith
Layered
1 Sided Bond
1 Sided Bond
Double Sided
Double Sided
400
200
Min
Tiled
Bond Min
Bond 4ml
0
0
10
20
30
40
Displacement (mm)
Figure 29: Force-displacement compressive response curves under the large indenter testing
Page 54
With mechanical and quasi-static tests, it is preferred that the results are expressed
in terms of stress and strain, since the results will, and should be, independent of the
size and shape of the test specimen. However, with the indenter tests, it is unclear
whether the whole test specimen is involved with the experiment and results. Due to
the shape of the indenter, it is obvious that the loading head does not interact directly
with the whole foam block, unlike the uniaxial compression tests. As a result, when
referring to the data for the indenter tests, force and displacement units are given.
Another notable difference between the compression and indenter tests is that unlike
the compression tests, all tests with the indenters were able to record results within
the 70% compression without recording an error within the Zwick testing machine i.e.
none of the samples recorded a force over the 2000N limit. Again, this can be
explained by uni-axial compression, implying that the whole foam is involved in the
crushing deformation and the results. Contrasting this with the indenter tests, regions
on both sides of the samples can be considered uninvolved with the test, at least not
in terms with the strength and energy absorption. This may also explain the difficulty
in determining the different stages of the foam response and why a typical polymer
compressive response curve is hard to determine, like the ones discussed in the
‘Energy Absorption’ and ‘Standard Compression Test’ chapters (figures 4 & 26).
As mentioned previously, not only are there difficulties in determining at what exact
values the samples enter or leave a certain regime, there are difficulties in
distinguishing the three phases of deformation within the indenter tests. Analysis will
emphasize only on the interested regions, which are the first two regimes of foam
response, linear elastic and plateau stage, and results will not refer to densification or
the maximum force obtained by the samples.
Mechanical strain is a measurement in deformation. If a material is considered to be
incompressible, then when it is under a uniaxial compressible test, where the only
deformation is compression, then it cannot suffer deformation.
Hence no strain
differences will be measured. With an assumption that the fibre backing material
(polypropylene) and adhesive (wood resin) are incompressible, then it is possible that
the strain measured during the plane-strain impact tests, is not the actual value of
foam deformation but the foam deformation plus incompressible layers.
With a
second assumption that the adhesive thickness is half of the polypropylene
thickness, values of only foam deformation can be seen in figure 30.
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Figure 30 showing overlapping, identical results of strain, despite the pink line only showing foam
deformation and the blue line showing deformation of the whole sample. This figure represents the
thickness of incompressible textile and adhesive layer makes little difference to strain calculations
As seen in figure 30, the difference between both values is miniscule and it can be
stated that the inclusion of polypropylene and adhesive substance layers are
insignificant, in terms of the strain measurements.
Page 56
Monolith
Uniaxial tests
With uniform uniaxial loading up to 70% compression, even though the specimens
have doubled in their length, the monolith samples show the same type of
compressive stress-strain response as typical polymeric foam and with the high
strain rate compressive tests done previously with the cubed EPS foam (figures 18 &
26 respectively). This is an expected result, since no other variables have changed
from the high strain rate experiments, other than specimen dimensions, specifically
length.
The three phases of deformation can be clearly observed and the results of all three
monolith specimens are almost identical to one another, showing data repeatability,
at least within the areas of interest (linear elastic and plateau regime). The plateau
regime starts and ends at strains 0.03 and 0.6, respectively or in terms of
displacement, 2mm and 27mm respectively. In all three tests, results showed that
within the linear elastic and plateau regime, the monolith samples required the most
strength, in order to deform, although there was an exception.
Indenter tests
Unlike the uniaxial tests, however, with both of the indenter experiments, the typical
polymer foam response under compression could not easily, if at all, be recognized
(figures 27 & 29).
The energy absorption properties of the foam were calculated by using Microsoft
Excel and fitting a polynomial trend line against the interested curve. By gaining the
equation of the trend line, integration could then be performed and a value of the
work energy was calculated. Since it is unclear where the plateau region ends,
where most of the energy absorbing properties is concerned with, estimation on the
strain was done in order to calculate the work energy.
The most noticeable fractures that came from the indentation tests were from the
monolith specimens. Fractures were more evident with the small indentation tests,
than the large indentation tests. Fracture analysis will be discussed in the ‘Fractures’
chapter.
Page 57
Layered Foam Only
Uniaxial test
Samples that showed the least strength and least energy absorption in all three
different experiments were the layered EPS foam structures (figures 26, 27 & 29).
Uniaxial compression tests were performed up to 70% compression and even though
both samples showed signs of data repeatability, both did not show typical foam
behaviour under uniform loading. Results showed signs that there was no linear
elastic regime within layered samples and the densification stage began at a strain
value of 0.6 or displacement value of 30mm.
These results highly differed from the results obtained in the ‘Monolith vs Layered’
chapter.
In that chapter, the linear elastic and plateau regime of both samples
(monolith and 10mm layered samples) showed nearly identical results and no
significant differences. However, with the clear figures below, it can be clearly shown
that there are differences between the 5mm layered samples with the monolith
and/or 10mm layered samples, even though both the rate of loading and deformation
is kept the same, 0.25m/s and 90% compression respectively.
2500
Force (N)
2000
1500
1000
Monolith
Layered
500
0
0
10
20
30
40
Displacement (mm)
Figure 31:Force-displacement response curves with samples under uniaxial compression testing. The
Page 58
layered samples were 5mm thick. Specimen dimensions were 100 (l) x 50 (w) x 50(t) mm and strain
rate was at 0.25s
-1
2500
Standard Force (N)
2000
1500
1000
1cm Layered
Monolith
500
0
0
10
20
30
40
50
Displacement (mm)
Figure 32: Force-displacement response curves with samples under uniaxial compression testing
completed in the initial stages of the project.
The layered samples are 10mm with sample dimensions
-5 -1
50 x 50 x50 mm, straining at a rate of 8.33x10 s
The significant deterioration between the layered samples and the rest of the
samples can be explained by the introduction of more damaged cell faces within the
layered specimens. In the monolith samples, damaged cell faces caused by the
knife incision would only appear on the top and bottoms surfaces specimens.
Theoretical analysis states that “an exterior of weak, cut surface cells on the sample,
of thickness approximately half the mean cell diameter, combined with the
neighbouring cells affected, and the contribution of weaker cells on the total stress
should be less than 5% of the total” [9].
Layered samples, on the other hand, contained 7 times more damaged cell faces
than the monolithic samples. With damaged cell faces located roughly 5mm apart,
failure is more easily initiated within the sample and hence the weaker response.
The overall density of the specimen must also be considered, with the layered
samples weighing slightly less than the monolith counterparts.
Again surface
roughness plays an important part, as discussed before in the Specimens chapter,
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where even though both types of samples measuring roughly the same height, the
layered samples do not contain the same amount of material as the monolith, due to
debris contamination.
Indenter tests
The pattern with the specimens showing least strength and least energy absorption is
continued with both the indenter experiments. Instead of having no apparent linear
elastic region, both indenter experiments seem to demonstrate an initial reaction of
low resisting force for a displacement of 3-5mm. This could possibly be explained by
the surface roughness that is present between the layers of the specimen. The
presence of the debris can create space between the layers of foam and when a
compressive force interacts with the whole specimen, the primary reaction of the
specimen is to eliminate these gaps of space.
Due to an indistinguishable typical polymer response shape, that is usually observed
when the polymeric foam is under compression, the plateau region is hard to identify.
It could be possible that the plateau stage is not encountered with both indentation
tests with the layered specimens, due to the amount of force the machine is limited to
operate at. With both indentation responses being similar to the monolith response
data, this would suggest that the previous statement was true.
Compared to the monolith, the layered samples tested with the big indenter
experiments, almost halved in value of the work energy, the specimen could absorb
(figure 29).
One Sided Bond (minimum adhesive technique)
Uniaxial Tests
These samples showed slightly better results by having slightly better in the strength
and energy absorption than the layered un-bonded specimens (figures 26). Uniform
loading was both performed at 70% and 60% compression due to force limitations
within the machine. The response curve of the uniaxial compressive showed a curve
which the three regimes could barely be recognized.
Indenter Tests
Although no similar trend was followed in the uniaxial compression tests, this
remained untrue for both indenter tests. Showing similar performances in strength
Page 60
and energy absorption for identical samples, the one sided bond with polypropylene
with minimum adhesion samples also exhibited a similar pattern of results within the
layered specimens in the indenter tests. Once again the three typical responses
were difficult to identify or signify if they were even present during testing.
700
600
Force (N)
500
400
300
200
100
0
0
10
20
30
40
Displacement (mm)
Figure 33: One sided bonded with minimum wood resin adhesive between polypropylene and EPS foam
in small indentation tests.
Red shows the sample without constraint on the foam, whereas blue
indicates string was used to constrain the sides of the sample deflecting upwards.
A total of three of these samples were tested with the smaller indentation tests, with
two showing very similar results and the other fairing slightly worse (figure 33). The
latter result was due to the fact that this specimen was not constrained vertically,
allowing some of the specimen layers to deflect upwards. By not constraining the
ends of the foam and isolate the effect of bending, the ends of the top layers of foam
will deform by bending and the ends of the bottom layers of foam will not be involved
with the foam response. By bounding the layers of foam together, the string will
allow samples to act like a whole structure and involve more foam to respond, when
the sample is deforming.
As with the small indenter, the samples tested with the large indenter faired only
slightly better than the layered specimens. Energy absorption results indicated that
these samples were 22% better than the layered specimens but 34% worse off than
the monolith samples.
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Due to the discovery of the 5mm layers not responding in the identical manner as the
10mm layers, it is unfair to compare any samples that use 5mm thick EPS foam with
the monolith samples. However, a comparison with these samples can be made with
the layered samples. Figures 26, 27 and 29 showed that these samples had better
strength and energy absorption properties than the layered samples, and this can be
explained by the wood resin adhesive. When the adhesive is applied onto the EPS
foam layers, due to its fluid form, the wood resin adhesive is able to create infiltrate
the layer of damage cells and make them stronger.
The adhesive essentially
reinforces the damaged cells, allowing them to perform better during testing.
Two Sided Bond (minimum adhesive technique)
Uniaxial Compression
In the field of uniaxial compression testing, the two sided bond with polypropylene
with minimum wood resin samples obtained the best results, in terms of strength.
Once again, application of the wood resin adhesive can explain this by reinforcing
virtually all the damaged cells caused by cutting the foam into layers. Almost twice
the amounts of damaged cells were altered compared to the single sided bond
samples.
However, this increase in strength and energy absorption with double
bonded samples did not repeat the same kind of results in the indenter tests.
Uniform compression testing was applied up to 50% compression.
Once again,
although the sample did not express the results in the typical fashion of polymeric
foam compression response results, three distinguishable regimes are thought to be
identified (figure 26).
By eye, the linear elastic region ends at roughly 2mm of
deformation, along with the monolith samples, although slightly larger forces are
required to achieve the same displacement.
The biggest difference between
monolith samples and two sided bond samples were the displacement when
densification occurred.
Monolithic samples recorded densification occurred at
roughly a displacement of 30mm compression, whereas the two sided bond samples
are thought to record densification around an earlier displacement of 18mm.
Indenter Tests
With the small indenter tests, the same pattern that the double sided bond samples
with minimum adhesion was not followed, and instead faired worse in both strength
and energy absorption parameters within the interested region of results, than the
monolith samples. The shape of the curve made it hard to determine the three
Page 62
regimes of a typical response polymeric foam. Experiments with the large indenter
showed similar results. Evident fracture marks could be seen in both indentation
tests, although once again this will be discussed in a future chapter.
Expectations of the double sided bonded with polypropylene with minimum adhesive
specimens were that this sample would match, if not improve upon, the energy
absorption properties of the monolith samples, in the indenter tests. The explanation
on how why they did not achieve the same work energy consumption could be
justified due to the way the double sided bonded specimens fail. Although the high
speed camera was intended to analyse the fracture behaviour of the bond, the
equipment managed to unintentionally capture another kind of failure that occurred
during the indenter testing: failure to bond. By failing to manage a firm bond between
the two materials (figure 34), this revealed that the wood resin adhesive was not
doing its job by trying to introduce more foam material into the indentation region and
thus absorbing more work energy. As suggested by the low forces recorded by the
doubly-bonded samples in figures 27 and 29, failures of this nature happened within
both indentation samples. The chapter titled ‘Adhesion Failure’ further investigates
the bonding failure.
Figure 34: Two sided bonded with polypropylene specimen with minimum adhesives under large
indentation. Adhesion failure highlighted, thus not allowing as much strength and energy absorption
characteristics
One Sided Bonded with Polypropylene, Tiled
Small Indentation Tests
Tiled samples did not undergo uniaxial testing and only were experimented on using
the indentation tests. Results showed that these tiled samples performed better than
the un-tiled one sided bonded with polypropylene with minimum adhesive specimens.
Even though these samples performed the best within the one sided bond range,
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they absorbed (18% less work energy than the monolith samples and more work
energy than the one sided bond with minimum adhesive with polypropylene and
foam). Figures 27 and 29 show that the shape of the compressive response of the
tiled samples follows the same trend as the layered and one sided bonded un-tiled
samples.
The improvement of results can be traced back to the application of wood resin
adhesive onto the samples. There is an uncontrollable element on the amount of
wood resin adhesive that is applied. Even though, initially a syringe is used, the
scrapping process takes off an unknown amount of debris and wood resin adhesive.
As a result, it is possible there was more adhesion in tiled samples than the others. It
is also impossible to determine which damaged cells can become strengthened by
the adhesive.
Large Indentation Tests
The tiled samples performed the best out of the one sided bonded with polypropylene
specimens, although they still did not compare to the monolith samples within the
linear elastic and plateau region, in the large indenter experiments. The flexible
samples absorbed around 17.5% more work energy than the one sided bonded with
polypropylene with minimum adhesive (significantly more than the small indenter
tests) and 21% less work energy than the monolith samples.
Again, the better
results are explained previously, by the affect of the wood resin adhesive.
Tiled samples have shown that with added flexibility they perform just as well, if not
better, over their un-tiled counterparts in terms of strength and energy absorption
properties. The difference between these tiled samples and un-tiled samples would
be explained by the wood resin spreading.
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Both Sides Bonded with Polypropylene (Generous Amount of Adhesive)
Indenter Tests
These samples showed the greatest strength and energy absorption within the small
indenter experiments (figure 27). Both samples showed similar trends, suggesting
the plateau regime begins and ends at displacements 3-4mm and 20-23mm
respectively.
Unlike the small indenter tests, the samples bonded on both sides with more
adhesive, performed worse than both the samples bonded on both sides with
minimum adhesives and monolith samples (figure 29). This is only true during the
linear elastic and plateau region. The energy absorption however, remains better
that the both sided bonded with polypropylene with minimum adhesive, absorbing a
value around 10% more work energy.
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Fracture
For the small diameter cylinder indenter, cracking can be observed in three types of
specimens: monolith and both double sided bond with polypropylene with minimum
and generous adhesion. Other samples
For the Monolith samples, cracking could be clearly noticed from the foam surface of
the monolith specimen when observed through the high speed camera or by eye, as
shown in figure 35. With the high speed camera, it confirmed that the crack initiates
outside the contact area. The fracture is caused by the local bending of the foam
surface, which in turn provides a maximum tensile stress. Foams, as with the EPS
foam, react like a brittle material, when they are in tension. Tensile results are
affected by the random location of large flaws.
surface where the stresses are highest.
Fracture initiates on the tensile
As the bending moment increases, the
compressive stress may exceed the foam yield stress at locations on the
compressive surface, often near the central loading point. The crack stops with
lengths 15-18 mm with an angle of 22-30° to the ver tical.
Figure 35: High speed camera image of fracture with the monolith samples in the small indentation
tests.
The only other specimens that showed signs of fracture would be with the 2.5ml
adhesive. Although not that evident in the high speed camera, close inspection of
the sample after the specimen was tested confirmed that fracturing did occur within
the top layer of the EPS foam. Due to the size of the fractures and the viewing
position, the cracking is difficult to be seen with the high speed camera and is difficult
to describe with dimensions (figure 36)
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Figure 36: Fractures with double sided specimens with generous adhesion, tested with the small
indenter
Among the large diameter cylinder indenter, the only samples to encounter fracturing
failure were the monolith samples. The crack can be best described as a surface or
an edge crack, within the contact region, 1-2.5mm in length with a 52° to the vertical.
No other fractures were determined within other samples, tested with the large
indenter. In comparison to the Mills and Gilchrist experiments which this project was
aiming to build upon, the larger diameter cylinder indenter caused the largest
fracture, by able to create cracks that were long enough to separate the foam into
three isolated segments. The strain rate and different type of low-density polystyrene
foam was judged to be the cause of the difference in results, where with Mills and
Gilchrist experiments were able to achieve velocity impact rates of 4.4 to 6.3m/s,
compared to strain rates of 0.25m/s acquired in the above experiments.
Nevertheless, fracture processes tend to be less strain rate dependent than yielding
processes, therefore high-speed impact causes a more brittle-like response.
Whether or not cracks form and propagate depends solely on the strain energy
release rate associated with the crack propagation. Predictions and further analysis
on fracturing with EPS foam can be intestate further through the method of the J
integral [9].
Analysis cannot be done by some other method, due to the
inhomogeneous structure of the beads of EPS foam.
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Adhesion Failure
After the analyzing the results, it was found that samples were not responding in the
behaviour that was expected. Through the high speed camera, it was indicated that
this was due to the bonding method used. However, with the alternative bonding
method (the double sided tape method), this suggested that due to the similarity in
results, the reason for failure was not the adhesive, but the region of foam beside the
adhesive.
Further of investigation was done to find out which of the above statement was true.
By taking a used sample, a layer of polypropylene was peeled off a layer of EPS in
order to be inspected by the naked eye. Figure 38 shows the result of the peel
testing. With the lack of foam being attached to the polypropylene combined with the
ease the polypropylene was peeled off, it was determined that indeed that the failure
was due to the adhesive and not the region of foam neighbouring the adhesive.
Figure 37: Results of the wood resin adhesive bonding strength between EPS foam and polypropylene
after a peel test.
With the failure being adhesive related, an investigation began on how to achieve a
sturdier bond between the polystyrene and EPS foam. A surface pre-treatment guide
was provided by the company R.D Taylor, which provided useful surface pretreatments for Epoxy Araldite 2015 and polymer foams [18].
Pre-treatment on the polypropylene was attempted by sand-blasting the material and
by deforming it using emery paper. Both results found that this only frayed the
Page 68
polypropylene into an unusable condition. Different adhesives were also attempted,
and were also subjected to a peel test: epoxy araldite 2015 and two different types of
double sided tape.
(a)
(b)
(c)
Figure 38: Results of peel testing. Bonds between the two materials were made by (a) Epoxy Araldite
2015, (b) Ultratape double sided tape and (c) Sellotape double sided tape
Analysis showed that the epoxy araldite 2015 maintained the same results of the
wood resin adhesive (figure 39 (a)). Although figure 39 (b) shows that there was
debris recorded with the clear double sided tape (Ultratape), which proved a slightly
better adhesion than the two previous adhesive substances, the clear double sided
tape did not perform as well as the white double sided tape. The white double sided
tape, mentioned previously as the Sellotape product) showed that it was possible for
the neighbouring foam region and not the adhesive, to fail first (figure 39 (c)).
Evident of foam failure can be observed with several beads attached to the tape,
along with fracturing of the foam from the resulting peel test.
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Improved Samples
Due to the knowledge gained by the initial plane-strain deformation experiments,
especially the way certain specimens achieved failure; newer ‘improved’ samples
were created in order to achieve the second objective. Samples which contained the
double sided tape were initially created to observe the effect of different adhesion.
Double sided tape was another adhesion method that was recommended by [22].
Two different brands of double sided tape were bought in order to be experimented
on. The first was Sellotape double sided tape, which can be described as white and
had a width of 15mm, which therefore allowed three slices of tape of length 100mm
to cover the cross-sectional area of the EPS foam. The second brand was Ultratape
double sided tape. This tape was clear and had a width of 12mm, which would allow
four slices of tape of length 100mm for the same purpose as the previous tape.
By applying adhesion with the double sided tape would provide an ease of
manufacturing with the specimens i.e. these samples would be simpler to make and
control than the wood resin adhesive.
One Sided Bond with Both Types of Double Sided Tape between Polypropylene and
EPS Foam
Samples bonded by the white double sided tape achieved slightly worse results than
the one sided bonded with polypropylene with minimum adhesive (figure 26). The
clear tape samples faired the worse out of the one sided bonded with polypropylene
samples, but again the difference between these samples were not that significantly
great with similar trends in all three samples. The similarity in results suggested that
no matter what the type of bonding was, the area that would fail first under enough
compressive strength with the small indenter, would be the weakened foam area
neighbouring the adhesive. However, investigation into the adhesion effects found in
the ‘Adhesive Failure’ chapter confirmed that failure was not with the weakened foam
area neighbouring the adhesive but the adhesive itself.
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700
600
Force (N)
500
400
300
One Sided Bond Tape
(White)
200
One Sided Bond Tape
(Clear)
100
One Sided Bond Min 2
0
0
10
20
30
40
Displacment (mm)
Figure 39: Force Displacement response curves of the one sided bonds with double sided tape between
polypropylene and EPS foam, tested with the small indenter. Similarity in curves suggested that
neighbour foam area caused failure, but was disproved in the ‘Adhesive Failure’ chapter by peel testing.
When creating these samples, it could be seen that by even adding a minimum
amount of wood resin adhesive, with weight would almost double. Thus another
advantage of testing specimens with double sided tape would be the possible
reductions in weight.
Although reductions on weight are hardly significant when
compared to the wood resin adhesive, further reductions can still be made. Currently
these tape samples have tape covering the whole cross-sectional area of the foam to
provide the adhesion. This can be considered overkill, with firm bonds between the
EPS foam and polypropylene being achieved by taping only the outer surfaces of the
foam, as shown in the figures below. By using less double sided tape, the density of
the whole specimen will lower.
Double Sided Bond with Sellotape Double Sided Tape between Polypropylene and
EPS foam
Through investigation of firm bonding between EPS foams and polypropylene, the
second objective of this project was then able to continue. By bonding EPS foam
and polypropylene on both sides, even though there was a loss in flexibility, it was
hoped that these specimens were able to make an active trauma pack absorb as
Page 71
much, or even more energy, than the monolithic samples, with a reduction in fracture
length, during the indenture tests. These samples were essentially a combination of
the double bonded with polypropylene samples but bonded with the white, Sellotape
double sided tape. Once again, the whole cross-sectional area of the EPS foam was
covered in tape, to ensure a maximum, firm bond.
900
800
700
Force (N)
600
500
400
300
200
100
0
0
5
10
15
20
25
30
35
40
Displacement (mm)
Figure 40: Force-displacement response curves between monolith and the double side bonded
specimens in the small indentation tests. Key: Monolith, Double bonded with minimum adhesive, Double
bonded with 2.5ml adhesive and Double bonded with tape.
As figure 41 shows, in expectations of these samples performing the best, in truth
they performed the worse. No clear typical polymeric foam compression response
shape can be seen with the double bond tape specimens. Regards to creating an
EPS specimen that has improved shear properties than a monolith sample, yet able
to absorb as much, if not more, work energy has failed.
Figure 41 shows the fracture behaviour the foam responded to. Out of all of the
samples which had signs of fracture, the double sided bond with polypropylene with
Sellotape double sided tape had the smallest cracks which could be viewed by the
naked eye.
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(a)
(b)
Figure 41: Failure analysis of the double side bonded with Sellotape double sided tape between
polypropylene and EPS foam. Figure 45 (a) shows the smallest fractures with the double sided bond
samples.
Figure 45 (b) confirms that unlike specimens bonded with the wood resin adhesive,
specimens bonded with the double sided tape did not fail due to unable to maintain a firm bond between
polypropylene and EPS foam.
The energy absorption results, or lack of, are believed to be accounted for in tensile
direction compromised by damaged cell faces. Although successful in improving the
shear properties of the specimen, by reorganizing the EPS foam in this layered
manner affects too much foam cells by damaging them and not able to contribute
effective to the overall performance of the foam.
The different types of bonding also have affect on the plane-strain deformation tests.
Taped samples are unable to perform better than samples bonded with the wood
resin due to the reinforced damaged cells the wood resin samples received when the
adhesive is applied to the foam. Because the tape is not in a fluid substance, this will
not allow the adhesive to seep into the foam and ‘mend’ the damaged cells caused
by cutting the foam into layers.
A closer look at the incision method could be employed. Cutting the method using
the band saw clearly creates too many damaged cell faces and debris, affecting the
results. Future investigations into achieving a smoother surface finish and maybe
less damaged cell faces, may be found through the incision method with the lathe,
along with the blade and attachment.
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Limitations on Experiment
As mentioned before in this report, there are several limitations and restrictions with
the quasi-static plane-strain deformation impact experiments, which do not truly
reflect the foams performance within a ballistic environment. Therefore, the results
and conclusions that are derived from this report cannot be considered as great
models for dynamic experimentations. Further investigation and experiments will
have to be done in order for foam to advance, if foam is considered to be a worthy
material for protection. Once again, it is stressed that the project of ‘developing a
ballistic trauma pack’ is to investigate the basic idea whether or not foam can be
used as an active trauma pack.
There are three main limitations on the quasi-static plane-strain deformation impact
experiments, all of which are related to the machine that is used to obtain these
results, the Zwick Roell Z2.0. These restrictions include: speed, sampling rates and
force limitations.
Speed
All quasi-static plane strain deformation experiments are operated at the Zwick
Roells fastest strain rate, which is 15000mm/min. Conversion puts this strain rate at
0.25m/s. Comparing this to the speed of a .22’’ solid long rifle round which travels at
roughly 330m/s, the quasi-static experiments done in this project are estimated to
travel 1320% slower than the slowest .22’’ long rifle ammunition range. Recalling
back on the introduction, strain rates of up to m/s may even be encountered due to
blast and shock waves. As a result, only an observation can be made on how higher
strain rate affects the strain dependent foam and only assumptions can be made
from the trends or patterns about how the foam will respond to ballistic conditions.
Further analysis and investigation will have to involve ballistic testing.
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Sampling
A specimen which is going through a standard compression test with the Zwick Roell
Z2.0, at a strain rate of 5mm/min can obtain several thousand points of data. This
allows a very accurate stress-strain response curve to be drawn and precise
calculations, such as the automated method for calculate the foams Young’s
Modulus. Comparing this to the strain rate of 15000mm/min, only a limited number of
around a hundred data points were retrieved. The outcome of this lack of data points
were that even though a stress-strain response could be acquired from the test data,
the results were not as detailed as the results done with the slower strain rate. It also
signified that due to the lack of amount of sampling data, the automated Young’s
Modulus calculations could not be determined. Attempts to solve this restriction have
all failed, and are an impediment that has to be abided by.
Force
With the Zwick Roell Z2.0, an upper force limit of 2000N or 2kN cannot be exceeded
without causing an error with the machine. Already mentioned and encountered
before during the standard compression tests, the upper force limit restriction
hindered analysis of the EPS foam response and sometimes even impeded on
retrieving the data obtained during testing. Initial attempts to solve the problem of
data retrieval was done by asking the software recognize breach of lower force limits
proved to be unsuccessful when strain rates of 1000mm/min and above where
applied. The cause of this unsuccessful attempt is believed to be related to switching
relay delays within the machine. The feedback from the apparatus to the software of
the Zwick Roell Z2.0 is not quick enough when travelling at such high strain rates and
encountering such erratic signals from the force.
The restriction however, was
eventually resolved manually, through trial and error methods. By using dummy
specimens, the specimen was deformed at the desired strain rate by a certain
displacement and a force reading was given. Judging from the force readout, it was
decided whether the deformation should increase, decrease or remain.
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Further Analysis
There is evidence of all three deformations that happen with the specimens when
they are being tested in the plane strain deformation experiments (figure 46). The
compressive response is evident with the data and graphs that were able to be
collected in the experiments. Tensile deformation is apparent due to the presence of
fractures that lie within the samples, especially the monolith and double bonded
samples. Not only the tensile deformation is evident through observations with the
high speed camera, but shear deformation is also noticeable. A possible method of
obtaining the data of both tensile and shear deformation would be manipulation with
image analysis software, of the images taken from the high speed camera.
(a)
Figure 46:
(b)
Deformation analysis with a high speed camera on a monolith EPS foam under small
indenter testing at a strain rate of 0.25m/s. Figure 46(a) has imprecise green line, showing elongation
and extension within the top surface of specimen foam cells, whereas Figure (b) gives a clear
It can be concluded that in terms of achieving the two objectives set out has neither
been achieved nor failed. Due to unexpected interferences, such as the layer of
damaged cells and wood resin reinforcement effects, these undesired variables alter
the results of the foam response and a conclusion is unable to be made in terms of
the objectives.
Further investigation in order to achieve both objectives will have to
either done by ‘Analytical Analysis’ methods or testing with an ‘Aero-gel’ foam, where
cell sizes of this material are in nanometres.
Page 76
Conclusion
The Jablite EPS foam was able to demonstrate the common response of
polymeric foam under uniaxial compression with the three regimes: linear plastic,
plateau and densification stages.
By reorganizing the foam in a layered manner, compared to a monolithic block,
initially it was confirmed that these were able to achieve almost identical strength
and energy absorption results with a variation in elastic modulus only. However,
but cutting the foam layers even thinner, but not surpassing limits which dictate
when ‘size effect’ occurs, changed the identical response, to a deteriorating one.
This is due to the layer of damaged cell faces introduced when cutting the foam
into thin layers. It is this layer of damaged cells.
Polymeric foams are indeed strain sensitive materials. By altering the uniform
loading during compression testing from 8.33e-5m/s to 0.25m/s changes in the
mechanical properties of the EPS foam can be witnessed. Dramatic differences
in the foams Young’s modulus can be observed, when changes of values from
2.01-2.532MPa to 22.31-89.43MPa for respective strain rates prove the strain
rate dependence. Response of when the foam enters the plateau stage can also
be observed by changing the strain rate.
Flexible specimens were made by tiling the samples (cutting them into segments)
after they were fixed onto a fabric backing layer. The compressive data showed
that the results did not suffer any deterioration in strength or energy absorption
properties when compared to identical un-tiled samples, although there was still a
discrepancy between monolith samples due to the layer of damaged cells
explained above.
Three-point bend tests confirmed that these samples were
indeed flexible in one direction and not the other, validating the creation of a more
comfortable trauma pack.
Fracture propagation was indeed restrained by putting a denser material behind
the foam. However, samples were not able to obtain the same amount of energy
absorption properties, as shown by monolith samples, due to the interference of
damaged cell layers and adhesive reinforcement of these damaged cells.
With the unforeseen impedance of unexpected variables, such as the layer of
damaged cells and adhesive reinforcement affects, it can be concluded that in
order to investigate the two objectives properly, ‘Analytical Analysis’ will have to
be employed. It may also be possible to investigate these objectives with the an
‘aero-gel’ foam, where the cell sizes of this material are in nanometres.
Page 77
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