testing and analysis of composite protective panels for...

1

1 Department of Mechanical and Aerospace Engineering, University of Strathclyde, Glasgow

2 Department of Mechanical Engineering, Technical University of Denmark, Copenhagen

3 TenCate ABDS, Denmark

Testing and Analysis of Composite Protective Panels for Military Vehicles:

Characterisation, Simulation and Blast Testing of Fibre Reinforced Polymer Panels

Calum John Sharp1 (s131770, 200912866)

Karen Anne Swindell1

(s131771, 200812430)

Supervisors:

Christian Berggreen2 Rasmus Eriksen2

Søren Giversen2

Benjamin Riisgaard3

September 2013 – January 2014

2

Acknowledgements

Firstly, we would like to thank our project supervisors, Professor Christian Berggreen and Benjamin

Riisgaard. We greatly appreciate the opportunity to work as part of this Advanced Research Group.

We would also like to acknowledge Søren Giversen and Rasmus Normann Wilken Eriksen, PhD students

from the Mechanical Engineering Department, who oversaw the day to day running of the project. Their

time and knowledge has been invaluable during this academic year. In addition to this, the project would

have been virtually impossible had it not been for the work they had previously carried out to create both

Matlab scripts and LabVIEW programs.

Additionally, we take this opportunity to thank TenCate Advanced Armor for providing us with the blast

panels to carry out this project. We would also like to give thanks to all the technicians who have helped us

throughout our project making specimens, pulse shapers and cutting our tested blast panels.

3

Abstract

This report provides a study into the behaviour of an S-glass/Phenolic composite material subjected to high

strain rates. This was studied using two methods: firstly, blast testing on Fibre Reinforced Polymer Panels

was undertaken; secondly, a Split Hopkinson Pressure Bar (SHPB) was used to examine the performance of

the material as it was exposed to high strain rates. Both of these cases were simulated using LS-DYNA

Software.

The blast testing was carried out using Digital Image Correlation to obtain the strain data as the panels

were subjected to explosive forces. The panels of the S-glass material were tested with 250g of explosive at

100mm and 50mm standoff distances. In both cases the panel did not fail completely but showed some

deformation. An E-glass/epoxy panel was also tested with 250g at 50mm. This test resulted in a hole being

created through the panel. In an attempt to replicate this with the S-glass material, 375g of explosives was

used at 50mm but this was still not enough to create a hole. This shows that the S-glass material was much

stronger than the E-glass material.

The SHPB tests were intended to provide a comparison between, square cross section in plane and out of

plane specimens, and round out of plane specimens. However, the results of static compression tests

completed prior to the SHPB testing, suggested that it would not be possible to cause failure in the out of

plane specimens. As a result of this only stress-strain data for the in plane specimens was recorded and the

out of plane specimens were used for practice tests. After the in plane tests were completed an out of plane

specimen was tested three times in an attempt to achieve failure in the specimen. However, as the material

is far stronger in the out of plane direction this was not possible.

4

Table of Contents Acknowledgements ........................................................................................................................................... 2

Abstract ............................................................................................................................................................. 3

Nomenclature .................................................................................................................................................... 6

List of Figures ..................................................................................................................................................... 7

List of Tables ...................................................................................................................................................... 9

1 Introduction ............................................................................................................................................. 10

2 LS-DYNA ................................................................................................................................................... 11

3 Composites .............................................................................................................................................. 12

3.1 Background ...................................................................................................................................... 12

3.2 SheildStrand S / Phenolic ................................................................................................................. 13

4 Blast Testing ............................................................................................................................................. 14

4.1 Theory .............................................................................................................................................. 14

4.2 Pentaerythritol tetranitrate ............................................................................................................. 15

4.3 Digital Image Correlation ................................................................................................................. 15

4.3.1 Aramis Software for Digital Image Correlation ....................................................................... 17

5 Material Study ......................................................................................................................................... 18

5.1 MAT_161 and MAT_162 .................................................................................................................. 18

5.2 Single Element Analysis ................................................................................................................... 18

6 Simulation ................................................................................................................................................ 26

6.1 Blast Modelling in LS-DYNA ............................................................................................................. 26

6.1.1 CONWEP Model ....................................................................................................................... 26

6.1.2 *LOAD_BLAST .......................................................................................................................... 26

Table 4: Description of variables in *LOAD_BLAST Card ......................................................................... 26

6.1.3 *LOAD_BLAST_ENHANCED ...................................................................................................... 27

6.2 Simulation ........................................................................................................................................ 28

6.2.1 Modelling Delamination .......................................................................................................... 28

6.2.2 Initial Simulations .................................................................................................................... 29

6.2.3 Initial Simulation 1 ................................................................................................................... 29




6.3 Initial Simulations Discussion .......................................................................................................... 31

7 Experimental ............................................................................................................................................ 32

7.1 Location ........................................................................................................................................... 32

5

7.2 Procedure ........................................................................................................................................ 32

7.2.1 Preparation of Blast Panels ..................................................................................................... 32

7.2.2 Blast Testing Procedure ........................................................................................................... 33

7.3 Experimental Results ....................................................................................................................... 35

7.4 Comparison Simulations .................................................................................................................. 38

7.5 Simulation Results ........................................................................................................................... 38

7.5.1 20 Layer Model ........................................................................................................................ 40

7.6 Discussion ........................................................................................................................................ 41

7.7 Comparison between S-Glass and E-Glass ...................................................................................... 48

7.8 Post-test Material Examination ....................................................................................................... 49

7.9 Blast Conclusions ............................................................................................................................. 50

8 Split Hopkinson Pressure Bar................................................................................................................... 51

8.1 Background ...................................................................................................................................... 51

8.2 Theory .............................................................................................................................................. 51

8.2.1 One Dimensional Wave Propagation Theory .......................................................................... 52

9 SHPB Simulation ...................................................................................................................................... 54

9.1 Determining Size/Shape of Specimens ............................................................................................ 54

9.2 Dispersion ........................................................................................................................................ 58

9.3 Pulse Shaping ................................................................................................................................... 58

9.4 Manufacturing of Test Specimens ................................................................................................... 59

10 SHPB Experimental .............................................................................................................................. 60

10.1 Procedure of SHPB Experiments ..................................................................................................... 60

10.1.1 Set up of Test Rig ..................................................................................................................... 60

10.1.2 Test Procedure ......................................................................................................................... 63

10.1.3 Safety ....................................................................................................................................... 67

10.2 Static Compression Tests ................................................................................................................. 67

10.3 Results of SHPB Tests ...................................................................................................................... 69

10.4 Discussion ........................................................................................................................................ 69

10.5 Post-Test Material Evaluation ......................................................................................................... 71

10.6 SHPB Conclusion .............................................................................................................................. 72

11 Conclusion ........................................................................................................................................... 73

12 Ideas for Further Work ........................................................................................................................ 74

13 Appendix 1 ........................................................................................................................................... 76

14 References ........................................................................................................................................... 78

6

Nomenclature

Stress of incident wave

Stress of reflected wave

Stress of transmitted wave

Strain of incident wave

Strain of reflected wave

Strain of transmitted wave

Wave velocity

Stress at interface between specimen and incident bar

Stress at interface between specimen and transmitter bar

Coefficient for strain rate dependent strength properties

Density

Particle velocity

True strain rate

Young’s Modulus

7

List of Figures

Figure 1: Composite Structure ......................................................................................................................... 12

Figure 2: Stress-Strain Curve for composite material [5] ................................................................................ 13

Figure 3: Pressure-time evolution ................................................................................................................... 14

Figure 4: Free air burst .................................................................................................................................... 15

Figure 5: Speckle pattern for DIC ..................................................................................................................... 16

Figure 6: Cross used for calibrating blast test ................................................................................................. 16

Figure 7: SEA model before and after deformation ........................................................................................ 18

Figure 8: Stress-strain graph for tensile strength in x-direction...................................................................... 20

Figure 9: Stress-strain graph for compressive strength in x-direction ............................................................ 21

Figure 10: Stress-strain graph for shear strength in xy-direction.................................................................... 21

Figure 11: Stress-strain graph for tensile strength in x-direction comparing strain rates of 1 and 1000 with

damage and rate parameters set to zero ........................................................................................................ 22

Figure 12: Stress-strain graph for tensile strength in x-direction for numerous strain rates where damage

and rate parameters were set to required values........................................................................................... 22

Figure 13: Stress-strain graph for tensile strength in x-direction for CERATE parameters ............................. 23

Figure 14: Stress-strain graph for tensile strength in the x-direction when the OMGMX parameter is

modified .......................................................................................................................................................... 24

Figure 15: Stress-strain graph of OMGMX and SFFC comparison ................................................................... 24

Figure 16: Investigation by Gama into SFFC and OMGMX parameters .......................................................... 25

Figure 17: Composite plate with defined layers for subsequent comparison simulations ............................. 28

Figure 18: Initial Simulation 2 .......................................................................................................................... 30

Figure 19: Nodal displacement around plate bend ......................................................................................... 31

Figure 20: Location of blast lab ....................................................................................................................... 32

Figure 21: Mounted blast plate with DIC speckle pattern .............................................................................. 34

Figure 22: Rope system used to secure box .................................................................................................... 35

Figure 23: Maximum displacement of blast panel .......................................................................................... 36

Figure 24: Displacement along section for blast tests carried out with 250g of explosives at 100mm .......... 37

Figure 25: Displacement along section for blast tests carried out with 250g of explosives at 50mm ............ 37

Figure 26: Displacement-time graphs for simulations 1, 5 and 6 in Table 11 ................................................. 39

Figure 27: 20 layer model with eroded elements ........................................................................................... 40

Figure 28: Comparing scale factors with 50g blast .......................................................................................... 43

Figure 29: Displacement-time graph for listed simulations comparing with 50g blast .................................. 44

Figure 30: Displacement-time graph for listed simulations comparing with 250g blast ................................ 45

Figure 31: Displacement-time graph for listed simulations ............................................................................ 46

Figure 32: Strain-time graph for listed simulations ......................................................................................... 46

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Figure 33: Displacement-time graph for listed simulations ............................................................................ 47

Figure 34: Strain-time graph for listed simulations ......................................................................................... 47

Figure 35: Left, shows the internal damage of panel SP5 and right, shows no visible internal damage in

panel SP6 ......................................................................................................................................................... 49

Figure 36: Delamination of Simulation 19 ....................................................................................................... 50

Figure 37: SHPB rig set up................................................................................................................................ 51

Figure 38: Simplified Split Hopkinson Bar Diagram with stresses shown [17] ................................................ 52

Figure 39: Part view of Split Hopkinson model in LS Prepost .......................................................................... 54

Figure 40: Elements on specimen that were used to plot z-stresses .............................................................. 55

Figure 41: Comparison of stresses on the front surface of specimen for all simulations ............................... 56

Figure 42: Stress difference between front and back of specimen ................................................................. 57

Figure 43: SHPB rig explaining distance ‘x’ ...................................................................................................... 57

Figure 44: Mean strainrate against range of strainrate for pulse shaper and striker bar combinations ........ 59

Figure 45: SHPB rig at DTU .............................................................................................................................. 60

Figure 46: Diagram of Wheatstone Bridge, amplifier, data acquisition and computer set up ....................... 62

Figure 47: Strain gauge set up for each bar ..................................................................................................... 62

Figure 48: Internal set up of amplifier for each strain gauge .......................................................................... 63

Figure 49: LabVIEW software .......................................................................................................................... 65

Figure 50: SHPB high speed camera and spotlight set up ............................................................................... 66

Figure 51: Main user interface for obtaining readings from strain gauges ..................................................... 66

Figure 52: Static compression test rig and high speed camera ....................................................................... 67

Figure 53: Stress-strain graph of static compression tests .............................................................................. 68

Figure 54: Incident, reflected and transmitted wave from In Plane specimen 7 ............................................ 70

Figure 55: Stress-strain graph using non-equilibrium calculation ................................................................... 70

Figure 56: Strainrate-strain graph ................................................................................................................... 71

Figure 57: Tested specimen compared to untested specimen ....................................................................... 72

9

List of Tables

Table 1: Deformation directions ...................................................................................................................... 19

Table 2: MAT162 Material Card ...................................................................................................................... 19

Table 3: *LOAD_BLAST Card ............................................................................................................................ 26

Table 4: Description of variables in *LOAD_BLAST Card ................................................................................. 26

Table 5: 'LOAD_BLAST_ENHANCED Card’ ........................................................................................................ 27

Table 6: Variables defined in ‘LOAD_BLAST_ENHANCED Card’ ...................................................................... 27

Table 7 Initial Simulations ............................................................................................................................... 29

Table 8: Maximum displacement of nodes around bend ............................................................................... 31

Table 9: Details of all S-Glass blast panels ....................................................................................................... 33

Table 10: Blast tests carried out ...................................................................................................................... 35

Table 11: Comparison simulations for blast testing ........................................................................................ 38

Table 12: Displacement of experiments and comparison simulations ........................................................... 39

Table 13: Simulations run where a number of parameters were modified .................................................... 42

Table 14: Comparison between E-Glass and S-Glass ....................................................................................... 48

Table 15: Split Hopkinson Pressure Bar Simulations ....................................................................................... 55

Table 16: Component of SHPB ........................................................................................................................ 60

Table 17: Characteristics of the incident, transmitter and striker bars .......................................................... 61

Table 18: Calibration of elastic wave speed and Young’s Modulus ................................................................ 64

Table 19: Static compression tests .................................................................................................................. 68

Table 20: SHPB tests carried out ..................................................................................................................... 69

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1 Introduction

Many engineering components are subjected to high strain rates. Examples include, vehicle collisions and

ballistic impacts. The behaviour of materials at high strain rates can be very different to how they would

behave when subjected to quasi-static testing. For most materials, an increase in strain rate corresponds to

an increase in yield strength and ultimate tensile strength. Because there are many applications which see

components subjected to high strain rates, it is important to gain a complete understanding of the exact

difference an increased strain rate will have on the mechanical properties of the materials. In particular,

composite materials show a dramatic change in properties as the strain rate is altered.

In recent years, there has been an increasing trend in the use of composite materials for components

subjected to these conditions. There are many reasons for this increase in popularity. Some examples of

the advantages that composites have over traditional materials are they typically have; a high strength to

weight ratio, an increased fatigue life, and good corrosion resistance. In addition to these, they also have

the ability to be designed to have special properties such as temperature dependence and low electrical

conductivity. As a result of these properties they can be used in a range of applications. In particular, they

are favoured by many high performance car manufacturers and also the defence industry to provide

protection from ballistic impacts. One example of this is the use of composite panels on armoured fighting

vehicles. For this reason it is important to gain a good understanding of the material behaviour when

subjected to similar conditions.

The aim of this project is to give a deeper understanding of the behaviour of a particular composite

material when subjected to blast loading. The project provides a study into the behaviour of composite

materials subjected to high strain rates. This will be studied using two methods: firstly, blast testing on

Fibre Reinforced Polymer Panels will be undertaken; secondly, a Split Hopkinson Pressure Bar will be used

to examine the performance of the material when exposed to high strain rates. Both of these cases will also

be simulated using LS-DYNA Finite Element Software, thereafter, the simulation results will be compared

with the experimental results. A material study was carried out to determine whether the Material Model

162 could be validated for the specific material data provided for the blast panels.

Before the Split Hopkinson Pressure Bar testing was carried out, appropriate bars, in terms of geometry and

material, needed to be chosen. Also, an appropriate loading pulse had to be obtained through the use of a

pulse shaper material. Once the specimen shape had been determined, static compression tests were

carried out and thereafter, dynamic tests in the Split Hopkinson Pressure Bar rig.

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2 LS-DYNA

LS-DYNA is the latest evolution of the DYNA3D finite element analysis software developed by the Lawrence

Livermore National Laboratory in the 1970s [1]. The original software was used to analyse the stresses in

structures subjected to impacts. The current version of LS-DYNA can now be used to simulate many real

world situations. LS-DYNA is particularly popular for modelling non-linear and transient dynamic problems.

A non-linear problem which involves at least one of the following; changing boundary conditions, large

deformations, and non-linear materials that do not exhibit perfect elastic behaviour. A transient dynamic

problem is defined as a high speed, short duration problem. Common examples include modelling;

automotive crash tests and explosions. As this project investigates the behaviour of a non-linear composite

material when subjected to high strain rates, LS-DYNA is perfect for simulating the physical tests.

LS-DYNA is controlled by a keyword input file. In this file different keywords are used to specify the various

properties of the model such as; the model geometry, boundary conditions, material(s), and the loading

that is applied to the model. To create the model geometry a pre-processor is required. For the purposes of

this project LS-PrePost was used to create the geometry and also to create sets of nodes and elements

which loads and boundary conditions could be applied to. Once the geometry keyword file had been

created a separate master file was written. This file included the material card(s), boundary conditions,

loading conditions, control options and part identifications. The master file could then be run using the LS-

DYNA solver. Once the termination time has been reached the results can be viewed using LS-PrePost. In

this post-processor the results can be analysed using a number of different methods including; contour

plots, XY-plots and movies of the simulation.

In the case of this project, to save time, both when creating the geometry and computational time when

running the simulations, the models were created using quarter symmetry.

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3 Composites

3.1 Background

There is evidence of composite materials being used in ancient Egyptian times where mud was combined

with straw to create a material used in the construction of buildings [2]. Up until the 1900s, natural

materials were used as glues and resins, which limited the performance of the composite materials during

this time. In the early 1900s, plastics including vinyl, polystyrene and phenolic were developed. These new

plastic materials gave greater performance than the natural resins. In the 1930s, the first glass fibre was

developed by Owens Corning [3]. By combining fibreglass with a plastic polymer, an incredibly strong and

lightweight material can be created. This type of composite is known as a fibre reinforced polymer (FRP).

Currently, composite materials are commonly used in aerospace, automotive, marine and construction

industries where specific properties can be created to suit a particular design.

Figure 1 [4] illustrates the different fibre and matrix layers that make up a composite material. Fibres tend

to be extremely strong whereas matrix layers are comparatively weaker. Properties of a composite material

tend to be different in each direction resulting in difficulties when using composites in numerical

simulations.

Fibres

Matrix

Figure 1: Composite Structure

13

3.2 SheildStrand S / Phenolic The material of interest to this project is ShieldStrand S, a composite used to withstand high impact loads in

military technologies. It was first developed in 1963 and has since been developed in line with

advancements in technology [3]. It is a durable, protective material which is corrosion, fire and smoke

resistant, therefore very suitable to this application.

From Figure 2, it can be seen that S-Glass, present in the material, has the highest tensile and compressive

strengths when compared with the other fibre materials shown in the graph.

Figure 2: Stress-Strain Curve for composite material [5]

S-Glass is stronger than both E-Glass and Aramid fibres but its Young’s Modulus is not as high as Aramid or

Carbon fibres. The phenolic resin is used to support the fibres and keep them in the relative position. The

use of ShieldStrand S gives substantial weight reduction, when compared with steel it is up to 50% lighter.

This reduction in weight leads to an increase in potential payload and increased manoeuvrability.

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4 Blast Testing

4.1 Theory

When an explosive detonates a pressure front propagates from the source. This pressure front is known as

the blast wave. The blast wave is seen as an instantaneous increase from ambient pressure to the peak

incident pressure. Once this maximum pressure is reached, the pressure drops gradually to below ambient

pressure before rising to once again be at the ambient pressure. This is shown in Figure 3 [6].

Figure 3: Pressure-time evolution

Explosions are split into three categories: free air burst, surface air burst and explosions with ground

reflection effects. Each of these types of explosion needs to be studied differently because of the way that

the blast front interacts with the surrounding environment. In this report, it is free air bursts that are

investigated. This type of burst occurs when the incident wave reaches the structure before being

reinforced. In this form of burst, the main type of reinforcement takes place during impact with the ground.

A typical free air burst is shown in Figure 4 [6].

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Figure 4: Free air burst

4.2 Pentaerythritol tetranitrate

This project used a plastic bonded explosive, PBX. A PBX is a mixture of Pentaerythritol tetranitrate, PETN

and a non-explosive plastic binder such as polyester or polystyrene. PETN is one of the most powerful high

explosives and has a high brisance or shattering capability [7]. However, the explosive is also relatively safe

when compared to many other explosives. This is because it is harder to detonate than most explosives. For

example, dropping or igniting PETN will not usually cause an explosion. PETN is usually detonated using an

electric spark. The PBX used in this project was PETN (85/15) which is made up of 85% PETN and 15% oil

based binder [8].

4.3 Digital Image Correlation

Digital Image Correlation (DIC) is a method used to track the motion of a surface or volume of an object

under loading conditions using a camera system which produces grey scale digital images. The method uses

a non-contact approach in order to determine the deformation and strain of a material for a number of

different static and dynamic tests [9]. The method also allows more than one camera to be used to enable

the displacement and strain of objects in 3D space to be determined.

For the purposes of the blast testing during this project, two synchronized high speed video cameras are

used to track the motion of a patterned test surface. Pattern recognition software, in this project ARAMIS,

is used to analyse the displacement of each area of the pattern. The particular pattern which is used in

Digital Image Correlation is called a speckle pattern. The speckle pattern that is applied to the surface will

still work accurately even if large deformations occur in the object as the speckle pattern deforms with the

surface of the object. An example of this type of patterned test surface is shown in Figure 5.

16

Figure 5: Speckle pattern for DIC

The image of the patterned surface is divided into several small areas called facets. The pattern distribution

within each facet is tracked from frame to frame. This results in a displacement vector for the centre of the

pattern within each facet. The position of all points on the surface can be tracked from the range of

displacement vectors resulting from the image correlation process.

Before each test the DIC equipment has to be calibrated. This is done by focussing each camera on the

centre of a calibration cross for the purposes of the blast testing and a calibration block for the purposes of

the static compression tests. The calibration cross, shown in Figure 6, consists of a black cross which is able

to be rotated. On the black cross are white shapes of known size and spacing which both cameras are able

to track. The calibration process involves rotating the cross to various positions and allowing the cameras to

determine the location of each of the white shapes in space.

Figure 6: Cross used for calibrating blast test

17

DIC can be used to measure displacements ranging from microns to tens of centimetres. The error of DIC

systems is typically in the region of 0.04 pixels depending on the accuracy of the calibration procedure. The

surface strain can be calculated from the displacements given by the DIC and these strains can then be used

to compare experimental results with results from numerical modelling.

4.3.1 Aramis Software for Digital Image Correlation

The software used to analyse the results produced with Digital Image Correlation is Aramis, developed by

Gesellschaft für Optische Messtechnik, commonly known as GOM [10]. It is a measuring system used for

the post-processing of results, which is most commonly used to determine material properties for static or

dynamically loaded tests, as well as strain rates, surface coordinates, displacements, velocities and the

strain values of surfaces.

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5 Material Study

5.1 MAT_161 and MAT_162

In LS-DYNA, the keyword *MAT_COMPOSITE_MSC_ (OPTION), can be used to model the progressive failure

of unidirectional and woven fabric composites subjected to high strain rates and high pressure conditions

[11]. The two options available are <BLANK> (material 161) and DMG (material 162). Both of these material

models can be used to model fibre failure, matrix damage, and delamination in each of the three failure

modes; opening, closure, and sliding of failure surfaces. When the DMG option is activated, the damage

mechanics approach is adopted to characterise the softening behaviour of the material after damage

initiation. In this project, it is Material 162 that was of interest. In order to use Material 162 an additional

license needed to be purchased. For this reason, it was important to get a good understanding of how the

material model behaved, and whether it would be suitable for the purposes of the project during the thirty

day free trial period.

5.2 Single Element Analysis

In order to understand the behaviour of Material 162, a Single Element Analysis (SEA) was performed. This

involved creating an LS-DYNA model comprising of nine, four node, cube elements. Each of the cubes had a

different set of constraints and a velocity applied to it so that each cube was deformed in one of the

following directions; x-compression, x- tensile, y-compression, y-tensile, z-compression, z-tensile, xy-shear,

xz-shear, and yz-shear. Figure 7 shows the LS-DYNA model used to perform the SEA. The deformation

directions for each element are shown in Table 1.

Figure 7: SEA model before and after deformation

19

Table 1: Deformation directions

Element Number Deformation Direction

1 x-tensile 2 x-compression 3 y-tensile 4 y-compression 5 xy-shear 6 xz-shear 7 yz-shear 8 z-tensile 9 z-compression

The LS-DYNA user manual defines the input deck required to use Material 161/162 as shown in Table 2

[11]. As it was Material 162 that was used for the SEA, all 8 cards were specified. A description of all of the

variables can be seen in Appendix 1. In order to fully understand the effect of each variable the SEA was run

several times. Each time the simulation was run with different variables activated to investigate the effect

that they had on the stress-strain behaviour in each deformation direction.

Table 2: MAT162 Material Card

Card 1 1 2 3 4 5 6 7 8

Variable MID RO EA EB EC PRBA PRCA PRCB Type 1 2E-06 29.7 24.8 12.0 0.1 0.2 0.2

Card 2 1 2 3 4 5 6 7 8

Variable GAB GBC GCA AOPT MACF Type 4.5 2.9 3.1 2 1

Card 3 1 2 3 4 5 6 7 8

Variable XP YP ZP A1 A2 A3 Type 0 0 0 1 0 0

Card 4 1 2 3 4 5 6 7 8

Variable V1 V2 V3 D1 D2 D3 BETA Type 0 0 0 0 1 0 0

Card 5 1 2 3 4 5 6 7 8

Variable SAT SAC SBT SBC SCT SFC SFS S_AB Type 0.549 0.204 0.457 0.138 0.052 1.54 0.165 0.073

Card 6 1 2 3 4 5 6 7 8

Variable S_BC S_CA SFFC AMODEL PHIC E_LIMT S_DELM Type 0.049 0.049 0.3 2 10 5.0 1.2

Card 7 1 2 3 4 5 6 7 8

Variable OMGMX ECRSH EEXPN CERATE1 AM1 Type 0.988 0.001 5.0 0.03 2

Card 8 1 2 3 4 5 6 7 8

Variable AM2 AM3 AM4 CERATE2 CERATE3 CERATE4 Type 2 0.5 -0.2 0 0.03 0.03

20

The first stage of the SEA was to compare Mat162 with two more simple composite material models,

Mat22 and Mat59. To investigate the differences, the SEA was run three times, once with each material

model. The first graph, shown in Figure 8, displays the behaviour of each material in the tensile x-direction.

It can be seen that both Mat22 and Mat59 both act in the same way, they rise to a maximum stress of

approximately 550MPa, relatively close to the x tensile strength given in the data sheet, and then fall

instantaneously to zero. Mat162, however, rises at the same rate to the same maximum stress but after

this point drops to just above zero. The stress then begins to increase with less of an incline which is due to

the component of tensile strength in the matrix material.

The graph shown in Figure 9 illustrates the behaviour of the materials in the compressive x-direction. In this

case, Mat59 and Mat162 act in a similar manner where both model damage. Both of these materials reach

a maximum compressive stress before returning to zero. However, the compressive stress in Mat22

continues to rise linearly indicating no failure has occurred. Graphs of the tensile and compressive stresses

in the y and z directions were also plotted and showed similar behaviour to those already discussed.

Figure 8: Stress-strain graph for tensile strength in x-direction

21

The behaviour of each material in the xy shear direction is shown in Figure 10. It can be seen that all

materials reach a common point before they begin to act differently. The stress in Mat22 continues linearly

until failure at an extremely large stress level. Mat59 fails at this common point of approximately 70MPa

and the stress falls to zero. However, the stress of Mat162 rises gradually until approximately 70 MPa, the

value stated on the data sheet, and then continues to rise at a lower rate indicating no failure has occurred.

Figure 9: Stress-strain graph for compressive strength in x-direction

Figure 10: Stress-strain graph for shear strength in xy-direction

22

Secondly, it was important to understand how altering the strain rate would affect the maximum stresses.

Initially, a simulation was carried out where the damage (AM) and rate (CERATE) parameters were all set to

zero, where the result is displayed in Figure 11. There is very little difference in the maximum stress at

strain rates of 1 and 1000.

The simulation was run again to include the damage and rate parameters. Numerous simulations were run

at varying strain rates and the result of these simulations can be seen in Figure 12.

Figure 11: Stress-strain graph for tensile strength in x-direction comparing strain rates of 1 and 1000 with damage and rate parameters set to zero

Figure 12: Stress-strain graph for tensile strength in x-direction for numerous strain rates where damage and rate parameters were set to required values

23

It is evident that when the damage and rate parameters are included in the simulations, the maximum

stress rises as the strain rate is increased. Further to this, figure 12 does not show instantaneous failure

within the element. Strain rates of 0.01 and 1 produce the same maximum stress which is equal to the

tensile strength specified in the material card.

The Single Element Analysis was also used to explain how various parameters in the material card affected

the results of the simulations. Simulations were run with the AM parameters being activated in turn. It was

found that the AM 1 parameter had the greatest impact on the results of the simulation for the tensile and

compressive x-directions. This was as expected as AM 1 is the strain softening property for fibre damage in

the x direction. The AM 4 parameter affected the shear results in all directions as its definition states it is

the coefficient for strain softening property for matrix and delamination damage.

Similarly, the effects of the CERATE parameters were investigated by activating them in the same manner

as was done for the AM parameters. It was found that all the CERATE parameters had the same effect on

the model as shown in Figure 13.

Furthermore, from Figure 13 when only the CERATE parameters were activated the graph shows an

instantaneous drop at the point of failure. However, when AM parameters are activated no instantaneous

drop can be seen as shown in Figure 12.

The Single Element Analysis also found the reason for the increasing stress after failure within the element.

It was discovered that the OMGMX variable altered the gradient of this slope.

Figure 13: Stress-strain graph for tensile strength in x-direction for CERATE parameters

24

It can be seen from Figure 14 as the OMGMX tends to 1 the gradient of the line tends to zero. Also evident

from Figure 14 is that the SFFC parameter does not affect the tensile stress in the x-direction. Conversely,

Figure 15 shows that the SFFC variable does have an effect on the compressive behaviour of the material.

Figure 15: Stress-strain graph of OMGMX and SFFC comparison

Figure 14: Stress-strain graph for tensile strength in the x-direction when the OMGMX parameter is modified

25

It is interesting to mention information taken from Gama [12], who investigated the effects of both the

SFFC and OMGMX parameters shown in Figure 16.

The SFFC value is defined as the scale factor for residual compressive strength. As the SFFC value becomes

closer to 1, it increases the residual compressive strength at which it levels out.

Figure 16: Investigation by Gama into SFFC and OMGMX parameters

26

6 Simulation

6.1 Blast Modelling in LS-DYNA

6.1.1 CONWEP Model

The CONWEP code is a collection of conventional weapons effect calculations. These calculations are based

on the empirical data obtained from a number of real explosions carried out by Kingery and Bulmash

between 1959 and 1964.

6.1.2 *LOAD_BLAST

In LS-DYNA the *LOAD_BLAST keyword is based on an implementation of the loading functions from the

CONWEP code. The *LOAD_BLAST keyword can be used to simulate the effects of either; the free air

detonation of a spherical charge or the surface detonation of a hemispherical charge. This project examines

the first of these two options. Table 3 shows the card that is required when using the *LOAD_BLAST

keyword and Table 4 gives a description of the variables referred to in the input deck [13].

Table 3: *LOAD_BLAST Card

Table 4: Description of variables in *LOAD_BLAST Card

Card 1 1 2 3 4 5 6 7 8

Variable WGT XBO YBO ZBO TBO IUNIT ISURF Card 2

1 2 3 4 5 6 7 8 Variable CFM CFL CFT CFP DEATH

Variable Description

WGT Equivalent mass of TNT XBO x-coordinate of point of explosion YBO y-coordinate of point of explosion ZBO z-coordinate of point of explosion TBO Time-zero of explosion

IUNIT Unit conversion flag EQ. 1: feet, pounds-mass, seconds, psi EQ. 2: meters, kilograms, seconds, Pascals (default) EQ. 3: inch, dozens of slugs, seconds, psi EQ. 4: centimetres, grams, microseconds, Megabars EQ. 5: user conversions will be supplied (see Card 2)

ISURF Type of burst. EQ. 1: Surface burst – is located on or very near the ground surface EQ. 2: air burst – spherical charge (default)

CFM Conversion factor – pounds per LS-DYNA mass unit CFL Conversion factor – feet per LS-DYNA length units

CFT Conversion factor – milliseconds per LS-DYNA time unit CFP Conversion factor – psi per LS-DYNA pressure unit

DEATH Death time. Blast pressures are deactivated at this time

27

6.1.3 *LOAD_BLAST_ENHANCED

A recent improvement of the *LOAD_BLAST keyword is the *LOAD_BLAST_ENHANCED keyword. This

keyword is very similar to the original keyword but features improvements in the way it deals with

reflected waves, moving warheads and multiple blast sources. The card required when using

*LOAD_BLAST_ENHANCED is shown in Table 5. It is very similar to the card shown in Table 3, but there are

some different variables to allow users to model different types of explosions. The variables in Table 5 are

described in Table 6. In order to model some types of explosions, extra cards need to be defined. However,

as this was not the case for this project, they have been omitted from this section [13].

Table 5: 'LOAD_BLAST_ENHANCED Card’

Table 6: Variables defined in ‘LOAD_BLAST_ENHANCED Card’

Card 1 1 2 3 4 5 6 7 8

Variable BID M XBO YBO ZBO TBO UNIT BLAST Card 2

1 2 3 4 5 6 7 8 Variable CFM CFL CFT CFP NIDBO DEATH NEGPHS


BID Blast ID. A unique number must be defined for each blast source. Multiple charges may be defined, however, interaction of the waves in air is not considered.

M Equivalent mass of TNT XBO x-coordinate of point of explosion YBO y-coordinate of point of explosion ZBO z-coordinate of point of explosion TBO Time-zero of explosion UNIT Unit conversion flag

EQ. 1: feet, pounds-mass, seconds, psi EQ. 2: meters, kilograms, seconds, Pascals (default) EQ. 3: inch, dozens of slugs, seconds, psi EQ. 4: centimetres, grams, microseconds, Megabars EQ. 5: user conversions will be supplied (see Card 2) EQ.6: kilogram, millimetre, millisecond, GPa EQ.7: metric ton, millimetre, second, MPa EQ.8: gram, millimetre, millisecond, MPa

BLAST Type of burst. EQ. 1: Surface burst – is located on or very near the ground surface EQ. 2: air burst – spherical charge (default) – no amplification of the initial shock wave due to interaction with the ground surface EQ.3: air burst – moving non-spherical warhead EQ.4: air burst with ground reflection – initial shock wave impinges on the ground surface and is reinforced by the reflected wave to produce a Mach front

CFM Conversion factor – pounds per LS-DYNA mass unit CFL Conversion factor – feet per LS-DYNA length units CFT Conversion factor – milliseconds per LS-DYNA time unit CFP Conversion factor – psi per LS-DYNA pressure unit

NIDBO Optional node ID representing the charge centre. If a non-zero value is entered XBO, YBO and ZBO are ignored

28

When using either *LOAD_BLAST or *LOAD_BLAST_ENHANCED the equivalent mass of TNT must be

specified, rather than simply the mass of the explosives used.

6.2 Simulation

6.2.1 Modelling Delamination

Delamination is a failure mode of laminated composite materials. It occurs when the layers of the material

separate due to cyclic stresses or high impact forces. Mat162 allows for delamination to be simulated only

if each layer of the material is defined as a separate part. In order to do this, a 4 node mesh of the desired

size was created and the ELGEN command was used to create a solid part. The ELGEN command was then

used again to create a second solid part (layer) using the mesh on the top surface of the first layer. This

resulted in the 2 layers sharing common nodes at the point where their surfaces meet. This process was

repeated until the desired number of layers was obtained. Figure 17 shows a plate with 8 layers created as

previously described.

In order for the delamination to be modelled correctly, each layer had to be assigned a different

orientation. In this case, as the material being investigated was a plain weave composite, it was necessary

to define two material cards, material card 1 with BETA equal to 0o and material card 2 with BETA equal to

360o. The two material cards were assigned to alternating layers so that no adjoining layers had the same

orientation.

DEATH Death time. Blast pressures are deactivated at this time NEGPHS EQ.0: negative phase dictated by the Friedlander equation.

EQ.1: negative phase ignored as in ConWep.

Figure 17: Composite plate with defined layers for subsequent comparison simulations

29

6.2.2 Initial Simulations

Before simulating the exact physical conditions of the experimental blast test, a series of simulations were

carried out in order to investigate how the boundary conditions affected the results of the simulation. Each

of these simulations modelled a blast on one quarter of an 8 layer plate, with each layer being 2.5mm thick.

All of these simulations used the *LOAD_BLAST_ENHANCED keyword with the mass of explosives set to

250g of TNT. The four initial simulations are described in Table 7. In each case the displacement of the

centre node in the z-direction was plotted and the maximum value recorded.

Table 7 Initial Simulations

Simulation

Number Description

1 Symmetry BC on inside edges, nodes on outside edges constrained in all DOF

2 Symmetry BC on inside edges, with blast box frame, nodes on outside edge of plate

constrained in all DOF

3 Symmetry BC on inside edges, with blast box frame, only constrained on the frame,

friction defined between frame and plate

4 Symmetry BC on inside edges, with blast box frame, only constrained on the frame

6.2.3 Initial Simulation 1

Simulation 1 was run with the model shown in Figure 17. The plate had symmetry boundary conditions

applied to the inside two edges and all the nodes on the outside two edges were locked in all degrees of

freedom. When the simulation was run, it was found that the maximum z-displacement of the centre node

was 37.5mm.


The second simulation introduced the blast box frame. This frame, shown in Figure 18, was fully

constrained. In addition to this frame, the same edge boundary conditions as used in Simulation 1 were

used in this simulation.

30

This simulation gave a maximum displacement of 36.4mm. This value was lower than in the first simulation

because some of the energy from the blast was needed to overcome the friction between the plate and the

frame.


In the third simulation the edge boundary condition was removed so that the edge nodes were free to

move. This resulted in a maximum displacement of 27.8mm. This displacement is much lower than in the

first two simulations. This is as a result of the edge nodes being free to move. As a result energy from the

blast is used to move the nodes rather than to deform the elements, resulting in a lower displacement.


For the fourth simulation, there was no friction defined between the plate and the frame. This resulted in a

maximum displacement of 29.3mm. As expected, this value was higher than in the third simulation. As

there was no friction defined, more of the blast energy was used to deform the plate resulting in the

increased displacement of the centre node.

Figure 18: Initial Simulation 2

31

6.3 Initial Simulations Discussion As discussed previously, the use of the edge boundary condition increases the maximum displacement of

the centre node. To investigate this further, the behaviour of the elements near the frame was

investigated. Initially this was done by looking at how the elements had deformed and how the

corresponding nodes had displaced.

By comparing the maximum resultant displacement of the nodes where the plate appears to start to bend,

in the case shown in Figure 19, this bend occurs between nodes 22353 and 22529, it was clear that the

nodes displaced less in the simulations run without the edge boundary condition. Table 8 shows the

maximum resultant displacement of the nodes on either side of the bend for each of the simulations.

Table 8: Maximum displacement of nodes around bend

Simulation Number Maximum Displacement of Node (mm)

Outside of bend Inside of bend 1 4.86 0 2 4.27 0.75 3 3.60 0.94 4 1.51 3.00

Figure 19: Nodal displacement around plate bend

32

7 Experimental

7.1 Location

During this project all blast tests were performed at a Danish military base located south of Copenhagen at

Fælledvej 251-2791. Figure 20 shows the location of the military base and also the precise location of the

two shipping containers, which act as the blast lab, within the base. This military base provided a space

where explosives could legally and safely be detonated.

Figure 20: Location of blast lab

7.2 Procedure

7.2.1 Preparation of Blast Panels

The first stage of preparing the blast panels was to measure their dimensions and weigh them in order to

accurately model the experiments. The results of these measurements are shown in Table 9. Once this

process was completed, one side of each panel needed to have the DIC pattern applied to it. The surface to

be patterned was initially painted white. This was done in order to achieve a greater contrast when the

pattern of black dots was applied. Once the panels were painted white, black spray paint was used with a

stencil to create the black speckle pattern on the centre of each panel.

Location of blast lab

33

Table 9: Details of all S-Glass blast panels

Panel Name Mass

(kg)

Area of Panel

(mm2)

Area Weight

(kg/ mm2)

Average Thickness

(mm)

Standard

Deviation

SP1 18.74 471373.5 3.97562E-05 19.78833333 0.21447

SP2 18.74 471373.5 3.97562E-05 19.62 0.159583

SP3 18.98 471373.5 4.02653E-05 19.83333333 0.356659

SP4 18.5 471373.5 3.9247E-05 19.49583333 0.377148

SP5 18.7 471373.5 3.96713E-05 19.74833333 0.472261

SP6 18.86 471373.5 4.00107E-05 19.72 0.306621

SP7 19.18 471373.5 4.06896E-05 20.18666667 0.344706

SP8 19.04 471373.5 4.03926E-05 19.99666667 0.352664

SP9 18.28 471373.5 3.87803E-05 19.42416667 0.282414

Average 18.78 471373.5 39.84 19.76 0.319

From the information displayed in Table 9, the average thickness and mass of all the plates was calculated.

The average mass was found to be 18.78kg and the average thickness was 19.76mm. Thereafter it was

necessary to confirm whether the material values provided by the supplier of the panels were correct.

Using the average thickness, mass and area of panel the density of the material was calculated. The density

of the average plate was calculated as 2016kg/m3. This was slightly different from the quoted value of 2000

kg/m3. The new calculated density was used for all the subsequent comparison simulations.

7.2.2 Blast Testing Procedure

At the testing site, firstly, the high speed cameras and laptop were set up to allow the DIC calibration to be

carried out. Both cameras were aligned so the centre point of each camera was lined up with a wooden

post that was placed in the centre at the front of the blast box. Thereafter, Aramis was used to carry out

the calibration of the high speed camera system. The black calibration cross mentioned previously was used

in order that both cameras could locate the markers on the cross in space. The calibration cross was

rotated and moved into twenty four positions and an image was taken for each situation. To ensure an

accurate calibration, the calibration deviation couldn’t be greater than 0.04. If the value was greater than

this, the calibration procedure would need to be repeated. Errors with the calibration could be associated

with the lighting in the container, particularly areas with bright light.

After the calibration was completed the blast panel needed to be mounted between the blast box and the

blast frame. Twenty bolts were used to secure the frame and panel to the blast box. The back of the blast

panel was painted with black paint to ensure no light from outside would be visible through the plate. A

34

significant amount of duct tape was used to reduce the amount of smoke which was able to pass through

the small gaps between the blast box and container wall.

After the panel had been mounted, a noise test was carried out. This test was to find any interference that

was present and to discover the level of noise present during the test. The lowest level of strain and

displacement were determined from the noise test. The noise test was also used to evaluate the speckle

pattern applied to the panel.

To account for any movement of the blast box during the test, a number of black circular markers were

stuck on the blast frame. This allowed the DIC software to track the movement of the markers, and

therefore the frame. This then allowed a correction to be made using the Aramis software to ensure that

the overall displacement could solely be based on the movement of the panel and not the box and frame.

The set-up of the blast plate is shown in Figure 21.

During the first series of tests, it was noticed that the blast box moved a large distance into the container,

almost to the point of falling in. To limit this movement, a rope was secured to the blast box and then tied

around a tree. This would attempt to stop the blast box falling into the container due to the explosion. The

contraption which was used is shown in Figure 22.

Figure 21: Mounted blast plate with DIC speckle pattern

35

Figure 22: Rope system used to secure box

The various tests that were carried out are explained in Table 10.

Table 10: Blast tests carried out

Test

Number

Panel

Name

Weight of

Explosive

(g)

Distance of Explosive

from Panel Surface

(mm)

Material

1 SP5 250 100 S-glass

2 SP6 250 100 S-glass

3 SP1 250 100 S-glass

4 SP2 50 100 S-glass



7 E1 250 50? E-glass

7.3 Experimental Results

Aramis was used to analyse the data which had been obtained from the high speed cameras during the

test. Text files for various sets of data were written in order that they could be read in MATLAB and their

data plotted and compared. For SP9, it was assumed that the blast box would move too much to be able to

obtain any valid results. The point where the highest deflection in the plate occurred was found and the

36

displacement, strain and strain rate could all be plotted for this point. The graph shown in Figure 23

illustrates the results of the first five tests that were carried out.

Figure 23: Maximum displacement of blast panel

From the graph, it can be seen that the results of the three tests carried out with a charge mass of 250g and

a standoff distance of 100mm are very similar. Although, there are slight variations with the maximum and

minimum displacements, the overall trend is virtually the same. As expected, the displacement of the test

with a standoff distance of 50mm but the same charge mass had a larger magnitude of displacement. Also

as expected, there was very little displacement when the plate was tested with a charge mass of 50g.

Also evident from the graph, the frequency of oscillations is highest with a charge mass of 50g. This is

possibly due to the fact that there is very little, or no permanent damage during this test. The results of the

tests using 250g of explosives show a much lower frequency which reinforces this notion that the

frequency is inversely proportional to the internal material damage.

Thereafter, sections were created using Aramis which cut through the centre point, one horizontally and

one vertically and the same information was obtained. A graph of the displacements across the length of

the section for tests 1 to 3 is displayed in Figure 24. Using MATLAB, the time when the maximum

displacement occurred was found, represented by the green line on the graph. The other coloured lines

represent the displacement across the plate at times 0.2, 0.5 and 0.7ms before the time of the maximum

displacement.

37

From the graph, as expected, it is evident that the highest displacement at all times occurs at the centre of

the plate. The distribution of displacement is largely symmetrical.

A similar graph was plotted for test number 5 and is shown in Figure 25.

Figure 24: Displacement along section for blast tests carried out with 250g of explosives at 100mm

Figure 25: Displacement along section for blast tests carried out with 250g of explosives at 50mm

38

Similar results were achieved for this test; however, there are some differences. As there is zero

displacement across the plate at 0.7ms before the highest displacement, it can be stated that the maximum

displacement occurs quicker than was seen in experiments 1 to 3. This was as expected as the standoff

distance was decreased resulting in an increased plate velocity.

7.4 Comparison Simulations After the testing was completed, comparison simulations were ran in order to compare numerical

simulations to the completed blast tests. Table 11 describes the various simulations that were carried out.

All simulations that were carried out used a blast stand-off distance of 100mm. The CONWEP code and

therefore the *LOAD_BLAST_ENHANCED keyword doesn’t apply when the blast is any closer to the object.

Table 11: Comparison simulations for blast testing

Simulation

Number

Charge Mass

(g)

Equivalent

Mass of TNT Model Type Material Card

Material

Angles

(if applicable)

1 250 270 8 Layers MAT_162 0, 360

2 50 54 8 Layers MAT_162 0, 360

3 250 270 8 Layers MAT_002 0, 360

4 50 54 8 Layers MAT_002 0, 360

5 250 270 8 Layers MAT_162 0, 180

6 250 270 1 Part MAT_162 N/A

7 50 54 1 Part MAT_162 N/A

8 250 270 1 Part MAT_002 N/A

9 50 54 1 Part MAT_002 N/A

7.5 Simulation Results The simulations that were run were compared to the blast experiments carried out in order to determine

the accuracy of the material model. Initially, tests one to three were compared with the MAT_162

simulations for 250g. Figure 26 shows the differences between the results that were achieved and Table 12

highlights the maximum displacement that was achieved from the three simulations and an average

displacement of the experiments that were carried out.

39

Figure 26: Displacement-time graphs for simulations 1, 5 and 6 in Table 11

Table 12: Displacement of experiments and comparison simulations

Experiment/Simulation Displacement

(mm)

Average Displacement of Experiments (250g at 100mm) 39.62

8 Layer Model (Beta = 0, 360) 41.01

8 Layer Model (Beta = 0, 180) 40.83

Single Part Model 38.97

It is evident from the graph that the initial paths of the three simulations follow those of the experiments.

After the simulations reach their maximum displacements they exhibit a steeper downward slope than the

experiments. It was therefore necessary to identify the reason for this differing behaviour. The 8 layer

simulations also have greater displacements than the average of the experiments. The simulation

represents an ideal situation where all of the energy from the blast is applied to the surface of the plate.

However, in the physical experiments, some of the blast energy could have dispersed around the sides of

the blast box. It was therefore necessary to identify the reason for this differing behaviour.

40

7.5.1 20 Layer Model

A brief comparison was carried out to determine whether the layers in the model affected the response.

The panels were made up of forty layers, however, due to the restrictions in both time and capabilities of

the computers it was decided that twenty layers would still provide a reasonable comparison.

The blast panel can be seen in Figure 27, where it is evident that the elements have eroded near the centre

of the panel. This was not seen to occur in any previous simulations which used the same parameters,

suggesting that the number of layers has an effect on the stability of the elements.

Figure 27: 20 layer model with eroded elements

Figure 27 shows large strains around the centre of the plate. These strains are not representative of what

was seen during the experiments showing that they are only caused by the eroded elements.

41

7.6 Discussion After running the simulations with the data provided by the supplier, it was decided that since the results

did not match the experimental results accurately, further simulations should be run, altering some of the

material parameters each time. In this case, due to limited time, the material parameters that were chosen

to be modified were the x, y and z moduli, in addition to a few others.

Table 13 describes the various simulations that were carried out and the parameters that were changed

have been highlighted.

42

Simulation No.

Material Card

X modulus

Y modulus

Z Modulus

G23 G31 X3T AM1/AM2 AM4 Charge Mass

TNT scale factor

Notes (Model Type)

1 Mat162 29.7 24.8 12 2.9 3.1 52 2 -0.2 250g 1.08 1 part

2 Mat162 29.7 24.8 12 2.9 3.1 52 2 -0.2 250g 1.08 8 layers

3 Mat02 29.7 24.8 12 2.9 3.1 52 2 -0.2 250g 1.08 1 part

4 Mat162 29.7 24.8 12 2.9 3.1 52 2 -0.2 250g 1.08 8 layer - Beta Angle 0,

180

5 Mat02 29.7 24.8 12 2.9 3.1 52 2 -0.2 250g 1.08 8 layer

6 Mat162 29.7 24.8 12 2.9 3.1 52 2 -0.2 50g 1.188 8 layer

7 Mat162 29.7 24.8 12 2.9 3.1 52 2 -0.2 50g 1.134 8 layer

8 Mat162 29.7 24.8 12 2.9 3.1 52 1 -0.2 250g 1.08 8 layer

9 Mat162 29.7 24.8 12 2.9 3.1 52 2 -0.4 250g 1.08 8 layer

10 Mat162 26.7 22.3 12 2.9 3.1 52 2 -0.2 250g 1.08 8 layer - 10% decrease XY

11 Mat162 32.67 27.28 12 2.9 3.1 52 2 -0.2 250g 1.08 8 layer - 10% increase XY

12 Mat162 29.7 24.8 12 2.9 3.1 52 1.8 -0.2 250g 1.08 8 layer

13 Mat162 29.7 24.8 12 2.9 3.1 52 1 -0.4 250g 1.08 8 layer

14 Mat162 29.7 24.8 15 2.9 3.1 52 2 -0.2 250g 1.08 20 layer

15 Mat162 32.67 27.38 12 2.9 3.1 52 1 -0.2 250g 1.08 8 layer

16 Mat162 26.7 22.3 12 2.9 3.1 52 1 -0.2 250g 1.08 8 layer

17 Mat162 17.82 14.88 12 2.9 3.1 52 2 -0.2 250g 1.08 8 layer

18 Mat162 29.7 24.8 12 2.9 3.1 104 2 -0.2 250g 1.08 8 layer

19 Mat162 29.7 24.8 15 2.9 3.1 52 2 -0.2 250g 1.08 8 layer

20 Mat162 29.7 24.8 9 2.9 3.1 52 2 -0.2 250g 1.08 8 layer

21 Mat162 29.7 24.8 12 3.625 3.875 52 2 -0.2 250g 1.08 8 layer

22 Mat162 29.7 24.8 12 2.175 2.325 52 2 -0.2 250g 1.08 8 layer

23 Mat162 26.7 22.3 12 2.9 3.1 52 2 -0.2 50g 1.08 8 layer

24 Mat162 29.7 24.8 12 2.9 3.1 52 2 -0.2 50g 1.08 1 part

25 Mat162 29.7 24.8 12 2.9 3.1 52 2 -0.2 50g 1.08 8 layer

26 Mat02 29.7 24.8 12 2.9 3.1 52 2 -0.2 50g 1.08 1 part

27 Mat02 29.7 24.8 12 2.9 3.1 52 2 -0.2 50g 1.08 8 layer

28 Mat162 29.7 24.8 12 2.9 3.1 52 2 -0.4 50g 1.08 8 layer

29 Mat162 29.7 24.8 12 2.9 3.1 52 1 -0.4 50g 1.08 8 layer

30 Mat162 29.7 24.8 12 2.9 3.1 52 1 -0.2 50g 1.08 8 layer

Table 13: Simulations run where a number of parameters were modified

43

The scale factor that was used to calculate the equivalent mass of TNT was 1.08. However, the accuracy of

this value is not guaranteed as there are many factors which affect it. The simplest way of estimating the

equivalent mass of TNT, is to use Equation 1, which multiplies the mass of explosive used by the ratio of the

Chapman-Jouguet (C-J) detonation velocity squared of the explosive used to the C-J detonation velocity

squared of TNT.

Equation 1

As mentioned previously, the explosive used in this project was PETN. This causes a problem when using

this method of obtaining the TNT equivalent. As PETN has many different compounds, the detonation

velocity can vary slightly, so the exact detonation velocity was not known. As a result of this it was decided

that, in order to attempt to match the simulation results to the experimental results, the value of this scale

factor should be increased. Simulations were run using the 50g charge at 100mm using scale factors of

1.134 and 1.188, a 5 and 10% increase respectively. Figure 28 shows the results of these compared with the

results of the original simulations and the experimental data.

Figure 28: Comparing scale factors with 50g blast

It can be seen from Figure 28 that although increasing the scale factor does increase the maximum

deflection of the plate, even the increase of 10% did not bring the deflection of the simulation to that of

44

the deflection in the experiment. Because of this it was decided to return to using the original scale factor

and try to match the results by altering other properties.

From analysing the simulation it was evident that no damage had occurred within the plate with a blast of

50g. The damage parameters and X and Y moduli were modified for the 8 layer plate with a 50g blast. If no

damage is present in the simulation result, re-running the simulation with modified damage parameters

should have no effect on the result.

Figure 29: Displacement-time graph for listed simulations comparing with 50g blast

The graph shown in Figure 29 illustrates that only the modification of the x and y moduli would affect the

displacement of the plate shown from simulation 23. As expected, modifying the damage parameter values

has no effect on the result of the simulation.

Thereafter, the same process was carried out with the 8 layer plate using Mat162 and a charge size of 250g

to try to achieve the same displacement and shape of curve as the average of the experiments carried out.

45

Firstly, simulations 8 to 13 were run and compared to both the experimental results and simulation 2 which

used all values specified in the data sheet. Simulations 8 to 13 investigated the effects of the AM

parameters 1, 2 and 4 and also the X and Y moduli.

Figure 30: Displacement-time graph for listed simulations comparing with 250g blast

From Figure 30, increasing the X and Y moduli by 10% shows an increase in the displacement. This was

unexpected as it was thought that increasing the stiffness of the material in these directions would make it

less flexible and therefore decrease the displacement. The two simulations with a displacement around

30mm refer to simulations 8 and 13, where both AM 1 and AM 2 were reduced by half to 1. For simulation

13, AM 4 was also decreased from -0.2 to -0.4. This indicates that the AM 4 value has no effect on the

maximum displacement.

46

Simulations 9 to 12 all produce similar displacements; therefore it was necessary to determine the strain of

each simulation.

Simulations 9 to 12 had similar displacements to the experiments but Figure 31 highlights that they all

produce strains of approximately 100%. Figure 32 illustrates that both simulations 8 and 13 produced

similar strains to the experimental results. However, no simulation produced both accurate strain and

displacement graphs suggesting further investigation was needed.

Figure 31: Displacement-time graph for listed simulations

Figure 32: Strain-time graph for listed simulations

47

The displacement-time graph was plotted for the further simulations that were run shown in Figure 33.

Simulations 16 and 17 both produced maximum displacements around 30mm, considerably lower than the

experiments. Simulations 15, 18 and 19 all produced similar displacements to the experiments. Therefore,

it was necessary to determine the strain for each of these simulations.

Figure 33: Displacement-time graph for listed simulations

Figure 34 shows the strains present in the simulations where simulations 16, 17 and 19 all produce strains

similar to those of the experiments. However, as previously shown 16 and 17 produced lower

displacements. Simulation 19 produced both strain and displacement graphs very similar to those of the

experiments.

Figure 34: Strain-time graph for listed simulations

48

For this simulation, the Z modulus was increased by 25% and all other parameters were kept the same.

Considerable noise can be seen in the strain graphs; however the trend of the graph is very similar to that

of the experiments. This could suggest that there is a possible error with this parameter in the data sheet.

Further information on how the data was obtained for the panels would be helpful in order to find a

possible reason for this discrepancy. A simulation was run with the same parameters as simulation 19 but

for 10ms instead of 2ms. This was to determine if the trend of the graph would follow that of the

experiments. The experimental results showed that the displacement varied like a damped sine wave,

whereas the simulation response did not decrease in amplitude.

If more time was available, a full material parameter study would have been completed. This would have

allowed the optimum parameters to be determined.

7.7 Comparison between S-Glass and E-Glass Although, this project focuses on S-Glass Composite material, one of the group’s supervisors had carried

out a considerable amount of work on E-Glass Composite material. Therefore, it is interesting to compare

the strengths of the two materials and the energy both are able to absorb.

One test carried out during the blast testing, test number 7, used E-Glass material and a hole was created in

the centre of the panel using a charge mass of 250g. Comparing this with tests one to three, highlights that

there is a significant difference between the strengths of the two materials and the energy they are able to

absorb before complete failure occurs in the panel.

Table 14: Comparison between E-Glass and S-Glass

S Glass E Glass Difference

X Modulus (GPa) 2.97E+10 2.21E+10 7.60E+09

Y Modulus (GPa) 2.48E+10 2.21E+10 2.70E+09

Z Modulus (GPa) 1.20E+10 1.60E+10 -4.00E+09

UTS X (MPa) 5.49E+08 3.87E+08 1.62E+08

UTS Y (MPa) 4.57E+08 3.87E+08 7.00E+07

UTS Z (Mpa) 5.20E+07 1.90E+07 3.30E+07

G12 4.50E+09 8.00E+09 -3.50E+09

G23 2.90E+09 8.00E+09 -5.10E+09

G31 3.10E+09 4.66E+09 -1.56E+09

Shear Strength XY (MPa) 7.30E+07 2.24E+08 -1.51E+08

Shear Strength YZ (MPa) 4.90E+07 2.24E+08 -1.75E+08

Shear Strength XZ (Mpa) 4.90E+07 1.90E+07 3.00E+07

Strain in X 1.85E-02 1.75E-02 9.74E-04

Energy 5.07E+06 3.39E+06 1.69E+06

Strain in Y 1.84E-02 1.75E-02 9.16E-04

Energy 4.21E+06 3.39E+06 8.22E+05

Strain in Z 4.33E-03 1.19E-03 3.15E-03

Energy 1.13E+05 1.13E+04 1.01E+05

49

Strain in XY 1.62E-02 2.80E-02 -1.18E-02

Energy 5.92E+05 3.14E+06 -2.54E+06

Strain in YZ 1.69E-02 2.80E-02 -1.11E-02

Energy 4.14E+05 3.14E+06 -2.72E+06

Strain in XZ 1.58E-02 4.08E-03 1.17E-02

Energy 3.87E+05 3.87E+04 3.49E+05

Cost £12-20/kg £1-2/kg

From Table 14 it is evident that a greater tensile strength in the X, Y and Z directions enables a greater

amount of energy to be absorbed by the S-Glass material before failure.

There is a large difference between the costs of the two materials. The purpose of the material is to save

the lives of soldiers operating military vehicles; therefore cost is of little importance [14].

7.8 Post-test Material Examination Following the blast test, each panel was quartered in order to determine whether any internal damage had

occurred within the panels. The panel that was tested, using a charge size of 50g, showed no damage had

occurred within the panel. This result agrees with the results achieved using LS-DYNA. The three tests that

were tested with a charge size of 250g at a distance of 100mm from the panel were compared. Only two

out of the three panels showed internal damage, therefore it is difficult to distinguish whether the damage

was initiated from the blast or the process used to cut the panels.

Figure 35 compares panel SP5, where internal damage is clearly visible and panel SP6 where no damage can

be seen. SP5 clearly shows that delamination occurred in the panel.

Figure 36, shows the areas where delamination was expected in simulation 19. When comparing this to

Figure 35 it is clear that the simulation did not correspond to the real experiment in terms of the amount of

delamination.

Figure 35: Left, shows the internal damage of panel SP5 and right, shows no visible internal damage in panel SP6

50

7.9 Blast Conclusions

After carrying out numerous simulations and varying a number of their parameters it was found that

Simulation 19 gave the most similar response to the blast experiments. The 10ms simulation, which used

the same parameters as Simulation 19, highlighted that only the first peak of the response could be taken

into consideration when comparing the simulations to the experimental results. It was decided that this

was adequate as the initial peak was the most important to investigate. Further to this, due to the

differences seen with the 20 layer model, it could also be suggested that the material card had been

optimised for the 8 layer model.

It was extremely challenging to obtain the optimum simulation which accurately represented the blast

experiments. Representing the exact boundary conditions in the simulation that perfectly match those of

the blast test proved difficult. During the blast experiments the bolt holes deformed during the test and as

these were not modelled in the simulations this could not be taken into account. The bolts would also

prove complex to model using LS-DYNA.

From the results of the blast test, it would appear that the S-Glass Phenolic composite is far stronger than

the E-Glass epoxy material. However, it cannot be concluded that this is due to the materials alone. The S-

Glass panels had a woven fabric structure and therefore this could be the reason for the increased strength

of the material.

Figure 36: Delamination of Simulation 19

51

8 Split Hopkinson Pressure Bar

8.1 Background At the beginning of the 20th century Bertram Hopkinson began carrying out dynamic experiments on steel.

The result of these experiments showed that the dynamic strength of the material was double the strength

at a low strain rate. However, all materials are known to act differently when tested under high strain rates

making it necessary to test individual materials to understand how they perform.

The Split Hopkinson Pressure Bar (SHPB) was first developed by Hopkinson but the apparatus today has

been further developed by both Davies and Kolsky. In recent years, the apparatus has been used for a

number of different applications which include; steel used in offshore platforms in the North Sea, ceramics

used in advanced armours and steels used in nuclear pressure vessels [15].

8.2 Theory To characterise materials, they are generally tested under quasi-static loading conditions, however, this

characterisation is not valid when the material is subjected to high strain rates. Standard material testing

machines that are used to test materials under low strain rate conditions are unable to obtain the same

material information when testing under high strain rates for high impact loading conditions [16]. In order

to obtain accurate material models to be able to perform numerical simulations, numerous stress/strain

curves are required at various strain rates.

One way of obtaining stress-strain curves for high strain rates is through the use of the Split Hopkinson

Pressure Bar. Testing using this method can determine the properties of a material at strain rates between

200 - 104 s-1. Figure 37 illustrates the SHPB apparatus which will be used in this project.

The Split Hopkinson apparatus consists of a specimen that is held between an incident bar and a

transmitter bar. During the test, the gas gun propels the striker bar which impacts the pulse shaper end of

the incident bar and produces an elastic compressive stress wave in the incident bar. The elastic wave

travels along the incident bar, where it makes contact with the specimen. At this point, the wave separates

into two components, one is reflected back along the incident bar as a tensile wave, and the other travels

Transmitter Bar Incident Bar Striker

Gas Gun

Momentum

Trap

Specimen

Strain Gage Strain Gage

Pulse

Shaper

Figure 37: SHPB rig set up

52

through the specimen into the transmitter bar until it impacts the momentum trap and the specimen has

fractured. Strain gauges mounted on both the incident and transmitter bars are used to measure the strain

of the incident wave, the reflected wave and the transmitted wave. These values can then be used to

obtain a stress-strain curve for the material.

For an ideal Split Hopkinson experiment, the specimen is required to be in dynamic stress equilibrium and

deform at an almost constant strain rate throughout the test.

8.2.1 One Dimensional Wave Propagation Theory

Figure 38: Simplified Split Hopkinson Bar Diagram with stresses shown [17]

The way in which the stress wave propagates through the steel bars can be explained using basic wave

theory. The wave equation can be written as:

Equation 2

In this equation, √

, the longitudinal wave speed in the bar, and represents displacement. The

wave equation can be rewritten in order to give the stress in the bars as:

Equation 3

In Equation 3, ρ is the density of the bar and V is the velocity of the particles in the bar that are subjected to

the pulse.

The stress at the interface between the specimen and incident bar, σs1, can be calculated using Equation 4.

This equation states that the stress on the front of the specimen is equal to the difference between the

53

incident and reflected stress pulses in the bar, multiplied by the ratio of the bar’s cross sectional area, ABAR,

to instantaneous specimen cross sectional area, As(t).

( )

( )

Equation 4

Similarly, the stress at the interface between the specimen and transmitter bar, σs2, is equal to the stress in

the transmitted bar, σt,, multiplied by the ratio of bar cross sectional area, ABAR, to instantaneous specimen

cross sectional area, As(t). This equation is shown below in Equation 5.

( )

Equation 5

Soon after the initial impact the specimen will be in a state of stress equilibrium where the stress on the

front of the specimen will be equal to the stresses on the back of the specimen i.e. .

The displacement of the two bars can be used to calculate the true strain, εtrue, in the specimen. This is

shown in Equation 6.

Equation 6

And by differentiating Equation 7, the true strain rate, , is shown to be:

( )

Equation 7

This wave theory assumes that there is no wave propagation within the specimen. Although there would be

some reverberations within the specimen, equilibrium within the specimen is reached comparatively

quickly.

54

9 SHPB Simulation

For the initial simulations, simple elastic models were used, where the correct stiffness and density of the

specimen and bar materials were used. Figure 39 shows a part view of the Split Hopkinson Model in LS

Prepost. The model that was created only included the incident bar, transmitter bar and specimen. The

loading pulse produced from the striker bar was applied to the nodes on the incident bar that would have

come into contact with striker bar.

Figure 39: Part view of Split Hopkinson model in LS Prepost

In an attempt to reduce computational time, shorter incident and transmitter bars were modelled.

However, the output files of the simulation differed from the files produced using the correct length of

bars. Therefore, it was necessary for each simulation to be carried out using bars of length 1900mm.

9.1 Determining Size/Shape of Specimens

It was necessary to carry out numerous simulations to determine the most appropriate size and shape of

specimen to be used in the experiments. In order to select the most suitable size of specimen for the SHPB

experiments, twelve simulations were carried out using different sizes and shapes of specimens, which are

described in Table 15.

Incident Bar

Transmitter Bar

Specimen

55

Table 15: Split Hopkinson Pressure Bar Simulations

Simulation Shape of Specimen

Specimen Size (mm)

Element Size Specimen

z-direction (mm)

Element Size Bar

z-direction (mm)

Length of Each Bar

(mm)

SHPB 1 Square 15 × 15 × 15 1 2 1900

SHPB 2 Square 15 × 15 × 10 1 2 1900

SHPB 3 Square 15 × 15 × 5 1 2 1900

SHPB 4 Square 7 × 7 × 7 1 2 1900

SHPB 5 Square 7 × 7 × 5 1 2 1900

SHPB 6 Square 7 × 7 × 3 1 2 1900

SHPB 7 Circle 8.5 radius × 15 1 2 1900



SHPB 10 Circle 4 radius × 7 1 2 1900



Each simulation was run in LS Dyna using a sampling rate of 20MHz and the results were viewed in LS

Prepost. Figure 40 illustrates the elements on the front of one of the square specimens, from which the z-

stresses were plotted, although these element numbers varied from specimen to specimen. The stresses

were plotted for the five individual elements and an average curve was then created. Thereafter, the z-

stresses were plotted from the corresponding elements on the back of the specimen and the same plotting

procedure was followed. This method was used for all simulations.

Figure 40: Elements on specimen that were used to plot z-stresses

56

Using MATLAB, with scripts created by Rasmus Eriksen, the stresses on the front of each specimen were

compared for the twelve different simulations that were carried out. It can be concluded from the graph

shown in Figure 41 that increasing the thickness of the specimen will lead to an increased instability of the

stresses through the specimen. A specimen with a relatively small thickness should ensure that the stress is

uniformly distributed through the length of the specimen [18].

Figure 41: Comparison of stresses on the front surface of specimen for all simulations

Following this, the MATLAB could also be used to plot the stress difference between the front and back of

each specimen for each of the simulations shown in Table 15.

57

Figure 42: Stress difference between front and back of specimen

It is evident from Figure 42 that as the thickness of the specimen is decreased the stress difference also

decreases. This result was as expected as the distance the wave travelled was decreased.

Errors were encountered with the MATLAB scripts and numerous changes needed to be made. A sampling

rate of 20MHz was written in the ‘Masterfile’ which was run in LS-DYNA. It was assumed that this sampling

rate was constant, however errors discovered in the MATLAB graphs suggested that the sampling rate isn’t

always constant. A number of parameters written in the MATLAB scripts depended on a constant sampling

rate. The sampling rate, TRp was determined in the MATLAB scripts using Equation 8.

Equation 8

Strain gauge

𝑥

Figure 43: SHPB rig explaining distance ‘x’

58

If the samples per second value, taken from the data produced in LS-DYNA is incorrect, the time at which

the reflected wave occurs at the strain gauge will also be incorrect. The time taken for the incident wave to

reach the strain gauge should be the same as the time for the reflected wave to reach the strain gauge. The

sampling rate was discovered to be approximately 21MHz which was considerably greater than specified in

LS-DYNA which created a time lag of around 17µs. In order to solve this problem, an average of all the time

steps was calculated. The inverse of this value enabled the mean sampling rate to be calculated.

9.2 Dispersion Dispersion is the inertia effects which occur in long rods/bars due to the propagation of waves. A

compressive wave propagates along the bar in the z-direction causing the bar to be pushed towards the

specimen. The maximum frequencies of the wave travel slower through the bar than the minimum

frequencies of the wave.

In order to correct some of the errors found in the MATLAB graphs, a dispersion correction code was

created in MATLAB and could be applied to the MATLAB script to correct for the dispersion effects of a

wave. This dispersion correction was taken from Pochhammer-Chree explained in a paper by Marais [17].

9.3 Pulse Shaping The input pulse applied to the striker bar of the Split Hopkinson Pressure Bar equipment can be controlled

using a pulse shaper. A pulse shaper is a small piece of material, commonly copper or brass, placed on one

end of the incident bar. The striker bar makes contact with the pulse shaper causing it to plastically deform,

which sequentially changes the input pulse fed into the incident bar. Pulse shapers have been known to

smooth the input pulses produced from explosive behaviour [19].

In order to reduce the effect of dispersion, it is recommended that a slowly rising incident pulse is applied

to the incident bar compared with a pulse which rises sharply, which can be controlled using the pulse

shaper material.

The length of the striker bar can also be altered to change the incident pulse. Therefore, it was necessary to

explore the effect that different lengths of striker bars and various sizes of pulse shapers had on the input

pulse. A MATLAB script was created that allowed each possible combination of striker bar and pulse shaper

to be compared to ensure that the most suitable combination could be chosen.

From these MATLAB scripts it was decided that a pulse shaper with 6.4mm diameter and 1.6mm thick

would be used. This information was used in the MATLAB script and the graph shown in Figure 44 was

produced. It was decided to choose the result that gave the highest strain rate at a range of around 30.

59

Figure 44: Mean strainrate against range of strainrate for pulse shaper and striker bar combinations

Thereafter, the most suitable combination of specimen, pulse shaper and striker bar was chosen, enabling

the best results to be achieved.

9.4 Manufacturing of Test Specimens The size of specimen that was chosen was the square shaped specimen of 15 × 15 × 10mm. A circular

specimen with similar cross sectional area was also chosen with 8.5 radius × 10mm thickness. This was in

order to compare the results when using square and circular shaped specimens.

For the square shaped specimens, ten specimens were manufactured in the in plane direction and ten

specimens were manufactured in the out of plane direction. This meant that the characteristics of the

material could be investigated in two directions of the material.

For the circular shaped specimens, only out of plane specimens were manufactured due to the difficulties

and time needed to cut in plane specimens. The circular specimens were manufactured using a water jet

cutter. This was the first time this method had been used to cut composite plates within the University and

it was unclear whether it would be suitable. On inspection, it was found that the manufactured specimens

had absorbed a small amount of water slightly altering the density and making a comparison between the

circular and square specimens impossible. Because of this, it was concluded that water jet cutting isn’t a

suitable method to cut this type of composite panel.

60

10 SHPB Experimental The Split Hopkinson Pressure Bar tests were all performed at The Technical University of Denmark,

Copenhagen. The SHPB rig was designed as part of a previous student’s Masters Project in 2012 [20].

10.1 Procedure of SHPB Experiments

10.1.1 Set up of Test Rig

A picture of the apparatus used in the experiments is shown in Figure 45. All of the main components of the

SHPB rig are numbered and Table 16 provides the name of each part.

An I-Beam was mounted between two sets of supports, on which supports to hold the incident and

transmitted bars were attached. Thereafter, the gas gun, momentum trap and incident, transmitted and

striker bars were all fixed in their correct places. Two plastic covers were manufactured by the workshop,

which could be used to alter the velocity of the striker bar by covering the holes in the gun barrel.

Figure 45: SHPB rig at DTU

Table 16: Component of SHPB

Part Number Part Name

1 Power supply 2 Gas gun chamber 3 I beam 4 3 point adjustable support (x12) 5 Gas gun barrel 6 Plastic hole covers (x2) 7 Incident bar 8 Transmitter bar 9 Momentum trap

2

1

3

4

7 8

9

6 5

61

The incident, transmitter and striker bars used in the experiments were made from an identical material.

The incident and transmitter bars had the following characteristics, shown in Table 17.

Table 17: Characteristics of the incident, transmitter and striker bars

Characteristics Incident and Transmitter Bars

Length 1900mm

Diameter 25mm

Material Mn20V6

Density* 7818kg/m3

In order to determine the correct density of the material, a small section of the material was weighed and

measured and the density was calculated.

The first stage of preparing the rig was to align the gas gun barrel with the incident and transmitter bars.

The position of the bars was adjusted using screws on the three point adjustable supports. Sliding a finger

over the interface between bars allowed a rough alignment to be completed. The easiest way to ensure this

alignment was accurate was to hold a light at all interface points between bars to guarantee that no light

could pass through. If this was the case, the bars were perfectly aligned.

Test firing was carried out to ensure that the compressed air supply was connected correctly and the firing

mechanism was operating as desired.

The SHPB rig was set up to ensure that two strain gauges were attached to each bar. The strain gauges on

the incident bar were positioned on the top and bottom of the bar, exactly 180° apart, half way along the

incident bar at 950mm. The strain gauges on the transmitter bar were also positioned on the top and

bottom of each bar at ten diameters (250mm) from the specimen interface. A Wheatstone bridge set up

was created for the two strain gauges on both of the bars. Thereafter, amplifiers were connected to each

Wheatstone bridge which was then connected to the data acquisition software [21]. A diagram of this set-

up is shown in Figure 46.

62

The Wheatstone bridges were set up with two active and two passive strain gauges which is known as a full

bridge circuit. This configuration was used as it is sensitive to bending strain and compensates for

temperature variations.

Four strain gauges each of 120Ω resistance were used in the bridge set-up. Figure 47 details the set-up of

each strain gauge.

After setting up the Wheatstone bridges, the amplifier needed to be configured for each circuit, by altering

the circuit according to the FYLDE amplifier operating manual. The diagram shown in Figure 48 highlights

this layout.

Figure 47: Strain gauge set up for each bar

Figure 46: Diagram of Wheatstone Bridge, amplifier, data acquisition and computer set up

Incident Transmitter

Wheatstone

Bridge

Wheatstone

Bridge

Amplifier

Data

Acquisition

Computer

63

The strain gauge wiring set up was modified from its previous set up to avoid using connector blocks with

the aim of improving the connections and therefore the accuracy of the results.

The specimen was then mounted between the incident and transmitter bars. A pulse shaper was placed on

the end of the incident bar that interacted with the striker bar. Both the specimen and pulse shaper were

mounted on the bars by applying a small amount of grease, although it was important that only the

minimalist amount was used in order that it did not affect the results.

10.1.2 Test Procedure

A LabVIEW program was previously created in order to control and fire the SHPB rig. This program allowed

the user to obtain the required strain and velocity data for each test as it controlled the data acquisition

system. The pressure in the gas gun was set to the desired value. The LabVIEW program was “Armed” and

the rig was triggered by touching the positive input of the valve to the positive output of the power supply.

Before testing could commence, the SHPB apparatus needed to be calibrated. Initially, a wave speed

calibration was carried out. This was done by firing the rig ten times, with no specimen or pulse shaper, and

recording the output data from the LabVIEW program. This data was then used in a Matlab script created

to determine the elastic wave speed in the bars and the Young’s Modulus shown in Table 18.

Figure 48: Internal set up of amplifier for each strain gauge

64

Table 18: Calibration of elastic wave speed and Young’s Modulus

Test Number

Wave Speed Young’s Modulus

Incident Bar

Transmitter Bar

Incident Bar

Transmitter Bar

1 5331.4 5174 222.2176 209

2 5160 5160 208 208

3 5259.001 5145 216.2396 207

4 5115 5168 205 209

5 5179 5179 210 210

6 5198 5166 211 209

7 5172 5168 209 209

8 5217 5164 213 208

9 5172 5168 209 209

10 5172 5168 209 209

Average 5173 5166 209 209

Standard deviation 30 9 2 1

The position of each strain gauge was found using the same data from the tests used to obtain the wave

speed. The average wave speed was calculated using Matlab which allowed the gauge position to be found

relative to the specimen-bar interface. The average gauge position on the incident bar was found to be

964mm from the specimen and on the transmitter bar was found to be 253mm from the specimen.

A striker bar velocity calibration was also carried out. This was done by firing the SHPB rig five times using

the same pressure in the gas gun. This series of tests showed that a relatively constant velocity could be

obtained if the pressure was kept constant.

In order to get a measurement of strain as an output rather than simply a voltage, a “strain gauge shunt

calibration” was carried out using the LabVIEW software shown in Figure 49. This calibration was

performed before each test.

65

Figure 49: LabVIEW software

A high speed camera was used to record the response of the specimen after the rig was fired, this is shown

in Figure 50. Photron FastCAM Viewer was used to take slow motion videos where the resolution of the

camera was set by drawing a box around the area of interest and the number of frames per second could

be chosen from a range. In the case of SHPB tests the number of frames per second was set to 60,000. A

grey-scale calibration was completed which ensured the camera recognised the colour black due to the

resolution that was used. The camera was set to trigger when it received a positive signal into its general

input. This positive signal came from the output of the data acquisition board. This method of triggering the

camera was adequate for the requirements of the SHPB tests as it allowed a recording time of five seconds,

half the time before the trigger and half after.

66

Once the camera was set up, the data acquisition system had to be armed before firing, which was

completed using the main user interface shown in Figure 51.

Figure 51: Main user interface for obtaining readings from strain gauges

The pressure in the gas gun chamber was set as required and the ‘ARM’ button, shown in Figure 51, was

selected. Thereafter, the positive wire of the valve was connected to the positive power supply to fire the

striker bar.

Figure 50: SHPB high speed camera and spotlight set up

67

10.1.3 Safety

In order to ensure the tests were carried out safely, ear protection was worn. In addition, all personnel had

to stand to the right (behind) of the gas gun.

10.2 Static Compression Tests

To determine whether the specimens would break and at what load they would fail, static compression

tests were carried out using the Instron 6025 machine with a 100kN load cell. Digital image correlation was

used on the specimens to obtain accurate stress-strain data from each test. Due to difficulties calibrating a

3-D DIC system because of the dimensions of the specimens being too small, a 2-D uncalibrated system was

used. This meant that only the in plane strain could be measured. Figure 52 shows the compression test

set-up with the high speed camera.

The first test carried out used an out of plane square specimen with the aim of finding out if it could be

broken using the SHPB rig. The test was set up to stop if the load reached a 100kN. This test reached the

maximum load of 100kN without failing. It was expected that this specimen would not fail during the test as

the material has a high strength in the z-direction. As a result of this, it was unlikely that the out of plane

specimens could be broken using the SHPB rig.

Thereafter, the in plane square specimens were tested as the material has lower strengths in the x and y

directions. Five tests were carried out which are explained in Table 19.

Figure 52: Static compression test rig and high speed camera

68

Table 19: Static compression tests

Test Number Specimen Name Specimen Width (mm) Specimen

Thickness (mm)

Cross-sectional

Area (mm2) Width 1 Width 2

1 Inplane 1 15 15.16 10.16 227.4

2 Inplane 2 15.04 15.22 10.16 228.91

3 Inplane 3 15 15.16 10.16 227.4

4 Inplane 4 15 15.22 10.14 228.3

5 Inplane 5 15 15.24 10.16 228.6

The stress-strain curves from the above tests can be seen in Figure 53. The maximum failure stress

indicates that the in plane specimens were cut so that the test operated in the materials y-direction. The

failure stress measured is far closer to the value in this direction in the supplied data sheet than for the

failure stress in the x compressive direction.

The differences between the curves must be due to problems with the experiments, possibly, the speckle

pattern used on the specimens.

Strain

Stre

ss (

Mp

a)

Figure 53: Stress-strain graph of static compression tests

69

10.3 Results of SHPB Tests

Initial SHPB tests were carried out using the out of plane specimens to determine whether the SHPB rig

would be able to cause the specimens to fracture. Both circular and square out of plane specimens were

tested, where neither of them were damaged in the SHPB rig.

Thereafter, the in plane specimens were tested and a description of the tests conducted is explained in

Table 20.

Table 20: SHPB tests carried out

SHPB Test

Number

Specimen name

Date In/Out

of Plane Shape of Specimen

Initial Length of Specimen

(mm)

Initial Cross

Sectional Area of

Specimen (mm^2)

Striker Bar

Velocity Pressure

11 6 15-01-2014 In Square 10.2 228.608 22.635 3

12 7 15-01-2014 In Square 10.22 229.52 23.413 3

13 8 15-01-2014 In Square 10.22 229.5216 23.802 3

14 9 15-01-2014 In Square 10.24 230.124 22.744 3

15 10 15-01-2014 In Square 10.24 228.6 24.396 3

A Matlab script was created in order that the results of each test could be analysed and explained. The

incident, reflected and transmitted waves can be plotted in addition to a stress-strain plot and a strain-

strain rate plot.

10.4 Discussion

The incident, transmitted and reflected waves for In Plane specimen 7 during the SHPB test, can be seen

below in Figure 54. It can be seen that the magnitude of the transmitted wave is much smaller than that of

both the incident and reflected wave. This is as expected as some the energy from the incident wave is

used to deform and break the specimen. Similar plots were obtained for all in plane specimens tested on

the SHPB rig except specimen 8. This was because the strain gauge on the transmitter bar failed during the

test.

70

Figure 55 shows how the stress and strain vary in In Plane specimen 7 during the SHPB test. It can be seen

that the compressive stress rises to a maximum of approximately 175MPa at a strain of -2%. Each of the

other 4 In Plane tests resulted in very similar graphs with the maximum stress occurring at approximately -

2%.

-8 -6 -4 -2 0 2-200

-150

-100

-50

0

50Stress Strain curves

Strain (%)

Stre

ss (M

Pa)

Non equilibrium calculation

Figure 55: Stress-strain graph using non-equilibrium calculation

0 100 200 300-100

0

100

200

300

400Waves

Strain (%)

Stre

ss (

MP

a)

Incident Wave

Reflected Wave

Transmitter wave

Figure 54: Incident, reflected and transmitted wave from In Plane specimen 7

71

The strain-strainrate graph for the same specimen can be seen in Figure 56. It shows that the strainrate is

highest, around 1300 strain/s, when the strain reaches -4%. Once again this was also the case in the other

experiments.

10.5 Post-Test Material Evaluation

Following the SHPB experiments the specimens were examined in order to assess the damage caused.

Figure 57 shows two in plane specimens, one which has been tested (left) and one which has not been

tested (right). It clearly shows a diagonal fracture line across the thickness of the specimen as well as

showing that the specimen deforms during the test. There is also some delamination shown where two

layers have started to separate.

-8 -6 -4 -2 0 2-1500

-1000

-500

0

500Strain Strainrate curves

Strain (%)

Stra

inra

te (

/s)

Figure 56: Strainrate-strain graph

72

10.6 SHPB Conclusion

It was discovered from the tests that it was not possible to fracture the out of plane specimens with the

SHPB rig. This was due to the large difference in compressive failure strength of the material in it’s out of

plane and in plane directions. It may have been possible to cause failure in the material; however this

would have meant increasing the striker bar velocity which, due to the sensitivity of the rig, would have

resulted in further strain gauge breakages.

As the simulations were run with a simple elastic material model, it is not possible to draw any conclusions

by comparing them with the experimental data. As a result of this, any further work on the subject should

include simulations where a more accurate material model was used and also include simulations for both

in plane and out of plane specimens.

Figure 57: Tested specimen compared to untested specimen

73

11 Conclusion

From the results of both blast testing and SHPB testing, it is clear that the S-Glass phenolic material is

exceptionally strong; especially in it’s out of plane direction. However, as mentioned previously it is

impossible to conclude whether this is due to the S-Glass fibres or the weaved structure of the panels,

without further research.

The Mat162 material model had never previously been used within the University and as such one of the

main aims of the project was to determine whether it was suitable for modelling composite materials. The

SEA analysis clearly showed that this material model was far superior, in terms of modelling damage, to any

model that had been used previously. It would also appear from the comparison simulations that if the

correct values are used in the material card, it is possible to obtain very similar results when compared with

experiments.

The water jet process used to cut both the specimens and the panels after testing was a not suitable

method for this application. The material was seen to absorb water which could highly affect the results

that were obtained. It was also difficult to determine if the internal damage within the blast panels was due

to the blast test or the cutting process.

It can be concluded from the experiments carried out within the project that the material is suitable for use

as a protective material for military vehicles. It is significantly lighter than steel and does not fail even when

subjected to large explosions close to the panel.

74

12 Ideas for Further Work

This project acts as a good initial insight into the characteristics of S-Glass composite material; however,

further investigation could be undertaken in order to gain a greater understanding. The DIC software takes

into account the movement of the blast box during an experiment; however, the large movements which

were observed during testing suggest that an improvement to the set-up could provide a greater accuracy

in the results. This improvement could allow more data points to be detected on Aramis and therefore

provide a greater accuracy in the results.

In real life, it is likely that explosives could be buried beneath road surfaces. This would result in gravel

projectiles impacting the protective panels as well as the shock wave from the blast. This may cause

different types of damage to the panels and as such it is necessary to investigate this before it can be

concluded that the material is suitable for its intended purpose.

Regarding the comparison simulations, in order to gain the best possible representation it would be

necessary to create a 40 layer model, identical to the blast panel. However, this would also mean a further

parameter study would be required as the 20 layer model showed that increasing the number of layers

drastically changes the results of the simulation.

As previously discussed, the S-Glass material has a different structure to the E-Glass material. Therefore, if

a true comparison was desired then testing would need to be completed on panels of the two different

materials, each with the same structure.

Furthermore, the investigation into the internal material damage could also be improved. The water jet

process used to cut the panels could have been a factor in the damage seen in the cross section views of

the panels. This suggests the need for a cutting process that has minimal effect on the material in order

that when viewing the internal structure of the panels, the results are solely based on effects of the blast.

There are also areas within SHPB where further investigation could be carried out. If more time was

available, comparison simulations could be carried out where the Mat162 material card could have been

used for the specimen. This would allow a comparison between experiments and simulations carried out

using LS-DYNA.

Further to this, the set-up of the SHPB rig provided issues which considerably affected the results. The

sensitivity of the strain gauges meant a small number of tests could be completed before they would have

to be fixed. Therefore, the method used to attach the strain gauges could be further investigated to

determine a more effective way of obtaining the strain data from the experiments.

Another area of investigation that should be explored is the differences that exist in the two in plane

directions of the material. It is stated on the data sheet that there is a ‘slight’ difference between the

75

strengths in both of these directions. However, this difference is approximately 70-80MPa. Therefore, the

strength of the material will greatly depend on the way the material is cut. Specimens should be cut in both

in plane directions in order to gain a greater understanding of the strength of the material in these

directions.

76

13 Appendix 1


MID Material Identification. A unique number or label not exceeding 8 characters must

be specified.

RO Mass density

EA , Young’s Modulus – longitudinal direction

EB , Young’s Modulus – transverse direction

EC , Young’s Modulus – through thickness direction

PRBA , Poisson’s ratio ba

PRCA , Poisson’s ratio ca

PRCB , Poisson’s ratio cb

GAB , shear modulus ab

GBC , shear modulus bc

GCA , shear modulus ca

AOPT EQ. 0.0: locally orthotropic with material axes determined by element nodes as

shown in Figure 2.1. Nodes 1, 2 and 4 of an element are identical to the Nodes

used for the definition of a coordinate system by *DEFINE_COORDINATE_NODES.

EQ. 1.0: locally orthotropic with material axes determined by a point in space and

the global location of the element centre, this is the a-direction.

EQ. 2.0: locally orthotropic with material axes determined by vectors defined

below, as with *DEFINE_COORDINATE_VECTOR.

LT.0.0: the absolute value of AOPT is a coordinate system ID number (CID on

*DEFINE_COORDINATE_NODES, *DEFINE_COORDINATE_SYSTEM or

*DEFINE_COORDINATE_VECTOR).

Available in R3 version of 971 and later.

MACF Material axes change flag:

EQ.1: No change, default,

EQ.2: switch material axes a & b

EQ.3: switch material axes a & c

EQ.4: switch material axes b & c

XP YP ZP Define coordinates of point p for AOPT = 1

A1 A2 A3 Define components of point a for AOPT = 2

V1 V2 V3 Define components of point v for AOPT = 3

D1 D2 D3 Define components of point d for AOPT = 2

BETA Layer in-plane rotational angle in degrees.

SAT Longitudinal tensile strength,

SAC Longitudinal compressive strength,

SBT Transverse tensile strength,

SBC Transverse compressive strength,

SCT Through thickness tensile strength,

SFC Crush strength,

SFS Fibre mode shear strength,

S_AB Matrix mode shear strength, ab plane, see below,

S_BC Matrix mode shear strength, bc plane, see below,

77

S_CA Matrix mode shear strength, ca plane, see below,

SFFC Scale factor for residual compressive strength,

AMODEL Material models:

EQ.1: Unidirectional lamina model

EQ.2: Fabric lamina model

PHIC Coulomb friction angle for matrix and delamination failure, < 90

S_DELM Scale factor for delamination criterion, S

OMGMX Limit damage parameter for elastic modulus reduction,

E_LIMT Element eroding axial strain

ECRSH Limit compressive relative volume for element eroding

EEXPN Limit expansive relative volume for element eroding

CERATE1 Coefficient for strain rate dependent strength properties,

CERATE2 Coefficient for strain rate dependent axial moduli,

CERATE3 Coefficient for strain rate dependent shear moduli,

CERATE4 Coefficient for strain rate dependent transverse moduli,

AM1 Coefficient for strain softening property for fibre damage in a direction,

AM2 Coefficient for strain softening property for transverse compressive matrix failure

mode in b direction (unidirectional) or for fibre damage mode in b direction

(fabric),

AM3 Coefficient for strain softening property for fibre crush and punch shear damage,

AM4 Coefficient for strain softening property for matrix failure and delamination

damage,

78

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