Design for Dynamic and Impact loading Ballistics Laboratory

8/2/2019 Design for Dynamic and Impact loading Ballistics Laboratory

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MM528: Design for Dynamic and Impact loading

Ballistics Laboratory

Name: Neville LawlessStudent no: 10212298

Date: 22/12/10


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Table of Contents

Introduction..........................................................................................................................................1

Experimental rig setup.....................................................................................................................2

Dynamic loading of a cantilever beam.................................................................................................3

Theory..............................................................................................................................................3

Experimental method.......................................................................................................................4

Results & discussion........................................................................................................................4

Sources of error................................................................................................................................5

Spallation of a long cylindrical rod......................................................................................................6

Theory..............................................................................................................................................6

Experimental method. .....................................................................................................................6


Impact of a finite length uniform bar with a rigid flat anvil.................................................................9

Experimental method. .....................................................................................................................9


Introduction

The ability to understand the mechanics of materials is of huge importance to engineers when

designing structures. The design of automotive vehicles and military crafts are two sectors where

this of particular significance. Their ability to withstand, and also to impart loads, can provide

strength, stability and protection to cargo and people alike. To maintain these properties they need

to be able to withstand two forms of loading, Static and dynamic loading.

Static loading does not change in magnitude or position over time. Ideally it is applied over an

infinite length of time and causes a deformation which can easily be predicted. For example, with a

cantilever beam, when a static load exerts a force that causes plastic deformation, the deformation

only occurs at the root of the beam (once the the load is above the yield strength), whilst the rest of

the beam remains straight.

Dynamic loading occurs over a very short time period with high rates of deformation or stress

loading. The deformation that occurs with objects under dynamic loading varies depending on the

magnitude of the load, mainly varying with the speed of the projectile. The main objectives of this

investigation were to observe the reactions of different types of objects subjected to different

dynamic loads and to associate the results with knowledge previously gained from theory in the

module. The three types of reactions to be observed were:


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Dynamic loading of a cantilever beam.

Spallation of a long cylindrical rod.

Impact of a finite length uniform bar with a rigid flat anvil.

Experimental rig setup

A compressed air firing mechanism was used in the lab to apply the dynamic loads required for this

investigation. Figure 1 below shows both a photo and schematic of the apparatus.

A regulator controls the pressure of the compressed air being released to the barrel. When the valve

is opened, the gas enters into the pressure chamber of a ballistic rig and fires a specimen down the

throat of a barrel once the switch is pressed.

The specimen to be fired is placed into the loading throat shown in Figure 2. This is located at the

top of the firing barrel.

Once the specimen leaves the barrel it hits a rigidly held anvil. This causes the dynamic loading of

the specimen. In this case there are three different types of experimental setup and these shall be

explained in the following sections.

Figure 1: Laboratory apparatus and schematic


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Dynamic loading of a cantilever beam.

Theory

From theory studied in the classroom, it was shown how the

deformation of a cantilever beam changes as the dynamic load

increases. As the moment caused by the load causes the cross

section of beam to pass the yield stress of the material, a plastic

hinge develops towards the free end of the beam. As the length

of the new beam formed (with its root at the hinge) begins to

decrease, due to a vertical load being applied. The plastic hinge

starts to grow towards the root of the beam to compensate.

When the force is not great enough to completely develop the

hinge to the root, it may sometimes stop the growth of the hinge

and jump to the root of the beam and continue to bend the beam

as a whole. Finally when there is an excessive dynamic load

exerted at the tip the plastic hinge will develop and travel at

high speed towards the root of the beam and cause severe

bending and excessive curling of the beam.

Figure 2: Schematic diagram of the

loading throat for firing of projectiles


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Experimental method.The Cantilever beams used in this investigation have been fabricated from 2mm aluminium sheets,

its dimensions are: 35mm x 150mm.

The beam was rigidly clamped at one end ( see Fig. 3) and inserted beneath the barrel of the

ballistic rig.

The projectile was a small Hardened tool steel cylinder. It was then placed in the loading throat

(Fig. 2) and fired at the free end of cantilever beams. This was done at the following pressures; 4

Bar, 6 Bar, 8 Bar.

Results & discussion.

On comparison of the experimental results with that of the theory explained above, it was found that

the experimental results hold well with the predictions made and meet the requirements for these

type of loading situations.

Figure 3: Aluminium beam in locking clamp prior to experiment

Figure 4: Cantilever beams subjected to dynamic loads withresultant plastic hinge bending


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@ 4 Bar:

There is evidence of a small plastic hinge and some bending at the root which suggests that the

force created by the 4 bar of pressure was not great enough to completely develop the hinge to the

root and it simply jumped to the root of the beam and started to bend the beam about the root.

@ 6 Bar:

It is apparent that the hinge has developed more towards the root, however the force created was not

sufficient enough to completely develop it to the root.

@8 Bar:

It can be said that any force larger than this would cause excessive curling and bending as the

plastic hinge has curled much more than the previous 3 stages, and the bend about the root has

formed an angle at the root of the beam against the undeformed plane of approximately 60 o. It also

can be seen that excessive curling is beginning to develop at the tip of the cantilever.

It can now be said that no excessive force has been applied in any cases. From the theory of

dynamic loading of a cantilever beam, it was expressed, that the hinge created in the beam should

travel at high speed towards the root of the beam which would in turn causes excessive curling if an

if an excessive force was applied. It can be seen in Figure 4 that there is a section of the beam that is

straight followed by the bending at the root. This confirms that the moment applied jumped to the

root to cause the final deformation and was not excessive.

Sources of error

Discrepancies can arise in the deformation of the beam, some of these can be accounted for with the

following reasons:

The positioning of the projectile as it hit the beam. From Figure 4 it is evident that the

projectile did not hit the centre of the beams which cause some twisting in the beams, this is

especially evident in the 8 bar projectile strike. Although the twisting did not hinder the

results beyond credibility, hitting the beam at the centre of the end of the beam would

maximise the dynamic deformation.

The Adjustable regulator and inaccuracies in the compressed gas pressure that arise from it.

Misplacement of the cantilever beam when it is being clamped into position. A longer length

or a skew angle on it may result in deformations which cannot be accounted for.


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Spallation of a long cylindrical rod.

Theory.

Spalling is the term used for the fracture and subsequent propelling of a particle, a piece or a flake

from the surface of a material. This process occurs when stress waves propagates through the

material, usually applied from an external source such as an explosion or projectile.

Take for example a cylindrical bar of length L, when a stress wave of wave length L/2 is transmitted

through one end of the bar. If the tensile fracture stress is less than the stress wave, a tensile

fracture will occur when the wave is reflected, as soon as the net stress is greater than the tensile

fracture stress. This fractured piece is termed the spall and the process is called spalling. The

particle speed when measured is then shown to be twice that of the speed associated with the stress

wave applied.

Experimental method.

The rods used in this experiment were cylindrical Perspex bars. The bars had 6 small groovings at

equal intervals to create 6 sections along the bar, these section were numbered with a marker. The

groovings ensure that spalling would occur. The bars were placed at the end of the barrel fixed with

adhesive tape to ensure they would not drop (Figure 5). Once the bar was in position, the tool steel

projectile that was used in the previous experiment was placed into the loading throat of Ballistic rig

and the compressed gas was set to 3 bar. The projectile was then fired down the barrel and

contacting the end of the bar, giving rise to a stress wave to which was transmitted through the bar.

This process was repeated for 4, 6 and 8 bar test.

Figure 5: Perspex rod in place-holder prior to experimentation


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Results & discussion.

The resulting spalling patterns are displayed below in Fig 6-9.

Figure 8: 4 Bar: three spalls develop. Numbers 4,5 & 6

Figure 9: 8 Bar: Full spallation occurring with fracture of the top of the perspex rod

Comparing the theory to what was seen in the results of the experiment. It is evident that the stress

wave induced by the projectile was a triangular wave. The reason for this is that there are multiple

fractures throughout each specimen used in the experiment. When a stress wave being transmitted

through a bar is triangular, the resultant reflected tensile wave does not have to travel a lot to matchthe compressive wave. The leaves a surplus compressive wave travelling which in turn reflects back

once again from the new end of the bar in a tensile wave. When the tensile force passes the point of

Figure 7: 6 Bar: three spalls develop. Number 2-4 in a long spall and numbers 5 and 6broken off.

Figure 6: 3 Bar: two spalls develop.


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alignment, it may break off another piece, as shown in the above images.

On Comparing the theory to the results, it can be said that all waves induced were greater than

the Tensile Fracture value as all specimens were fractured. Also:

@3 Bar:

The stress induced was greatest at the end of the sixth section, causing spallation here. The stress

wave transmitted through the entire rod and reflected, in tensile form, back from the end and

matched the compressive wave just after the beginning of the fifth section and caused a second spall

to fracture off.

@ 4 bar:

It can be seen that the wave induced by the fired projectile match the reflected tensile wave at the

beginning of the sixth section which caused the breakage at the last groove. The stress wave can be

concluded to be larger than that of the 3 bar test as the residual stresses were great enough to cause

two more breakages along the rod and fracture off sections 4 and 5.

@ 6 bar:

In this instance a much larger stress wave was produced. As with both previous tests sections 5 and

6 fractured off but this is where the similarity ends. As the stress wave initially moved past section

1 and the groove made in the rod ,it is felt that it caused a weak point to occur here. Once this wasdone the residual stresses that were remaining in the bar travelled along the bar and reflected back

from the new end of the bar, the reflected tensile wave matched the compressive just after the

beginning of the first section and once travelled through the groove allowed sections 2, 3 and 4 to

break off as a whole.

@ 8 bar

it is evident that the stress wave induced was so great that it caused breakages at every section.

Also it can be seen that the breakages are a lot coarser than the other specimens, indicating that

there was a larger force. This is also seen by the shattering of the section held in the place-holder by

sellotape.

Without the introduction of the grooves the cut off points would be a lot more erratic. They cause

weak points in the rod which in turn allow for the breakages to occur.


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Impact of a finite length uniform bar with a rigid flat anvil.

Experimental method.

Small projectiles made from Copper, Lead and Aluminium were placed into the loading throat ofthe

ballistic and fired at different gas pressures onto a rigidly held tool steel Anvil. The finding were

recorded and noted.

Results & discussion

Figure 10 below gives a good visual representation of the different deformation patters which occur

at varying projectile speeds. Tables 1-4 below are the recorded and calculated results from the

investigation.

Figure 10: Impact effect on projectiles manufactured from

3 different materials.


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Table 1 below contains the properties of each material which projectile were machines from. On

inspection it is clear that lead will prove to deform the most.

Table 2 contains the length of projectiles after the impacts, measured using a vernier callipers.

The resulting lengths were then used to calculated the % stain on each projectile by calculating l/L

Table 4 below finally indicates the projectile speeds achieved for each test. These were calculated

by taking the dividing the specimen lengths by the recorded laser times.

Table 2: Table of recorded projectile lengths after impact

Pressure Lead Aluminium Copper

4 Bar 15.36 18.94 18.5

6 Bar 13.54

8 Bar 12.86 18.07 18.19

10 Bar 11.02

12 Bar 9.6 17.58 17.6

14 Bar 8.3

20 Bar 6.5

Table 1: Table of material properties for each

projectile type.

Material Properties

Copper: Youngs Modulus = 130GPa

Density=

Aluminium: Youngs Modulus = 70GPa

Density=

Lead: Youngs Modulus = 16GPa

Density=

8.92g/cm3

2.7g/cm3

11.34g/cm3

Table 3: Table of calculated strain resulting on each projectile after impact

Pressure

4 Bar 3.640 0.192 0.060 0.003 0.500 0.026

6 Bar 5.460 0.2878 Bar 6.140 0.323 0.930 0.049 0.810 0.043

10 Bar 7.980 0.420

12 Bar 9.400 0.495 1.420 0.075 1.400 0.074

14 Bar 10.700 0.563

20 Bar 12.500 0.658

lLead

l/L Strain(%)

lAluminium

l/L Strain(%)

l Copperl/L Strain

(%)


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It is quite evident from the results of this experiment that:

At 4, 6 and 8 bar: small plastic deformation is occurring with the lead projectile, while the

aluminium and copper projectiles show small signs of deformation with slight bending occurring.

At 10 bar: the height of the Lead projectile has reduced in height allowing the base of the projectile

to widen.

At 12 bar: mushrooming of the Lead projectile has begun with the bottom edges of the specimen

cracking in the process. The aluminium and copper projectiles have small bulges developing at their

respective bases.

At 14 bar: the mushrooming of the Lead specimen had developed further while the bulging in the

Aluminium and Copper projectiles increased slightly.

At 20 bar, complete flattening of the Lead specimen has occurred, while the Aluminium and

Copper Specimens show similar sign to that seen at 4 bar pressure with the Lead projectile.

Table 4: Calculated projectile velocities for different pressure settings

Test number Material Pressure (Bar) Time (s) Velocity(m/s)

1 Copper 4 30.11

2 Copper 6 57.23

3 Copper 8 72.80

4 Copper 10 103.83

5 Copper 12 115.15

6 Copper 14 150.79

7 Lead 20 165.22

631 x 10-6

332 x 10-6

261 x 10-6

183 x 10-6

165 x 10-6

126 x 10-6

115 x 10-6

Documents

Design for Dynamic and Impact loading Ballistics Laboratory