Design for Dynamic and Impact loading Ballistics Laboratory
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Transcript of 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
Results & discussion........................................................................................................................7
Impact of a finite length uniform bar with a rigid flat anvil.................................................................9
Experimental method. .....................................................................................................................9
Results & discussion........................................................................................................................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