Investigations on material casualty of plates under impact load conditions

IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
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Volume: 02 Issue: 09 | Sep-2013, Available @ http://www.ijret.org 321
INVESTIGATIONS ON MATERIAL CASUALTY OF PLATES UNDER
IMPACT LOAD CONDITIONS
H. Raghavendra Rao 1
, A. Siva Kumar2
, M. Venkateswar Reddy3
, K. Vijaya Kumar Reddy4
1
M.Tech Student, 2
Professor & HOD, 3,
Asst. Professor, Dept. of Mechanical Engineering MLR Institute of Technology,
Dundigal, Hyderabad-43, Andhra Pradesh, India. siva_appisetty1@yahoo.co.in
4
Professor, Dept. of Mechanical Engineering, JNTUHCEH, Kukatpally, Hyderabad, Andhra Pradesh-85, India
Abstract
Impact problems are typical in nature since they involve geometry, boundary and material non-linearity. The impact of projectiles at
sub-ordnance velocities against mild steel, stainless steel and aluminum plates has been studied. In this paper, target plates of 3mm
thickness of materials Mild steel, Titanium are made to impact by Tungsten fragment with different velocities 300, 500, 700 and 1000
mm/ms. On impact, kinetic energy and residual velocity of this fragment is plotted to visualize the damage of the respective target
plate. It is observed that the element size significantly affects the numerical results. Hence a sufficiently refined mesh is used. Kinetic
energy is an essential parameter to be determined in order to study damage behavior of target. Higher the kinetic energy absorption,
leads to higher is the damage target. So, higher initial velocities are required for the fragment in order to create the necessary
damage in the target.
Index Terms: Projectile, Target plate, Mild steel, Tungsten, Titanium
-----------------------------------------------------------------------***-----------------------------------------------------------------------
1. INTRODUCTION
The response of any structural element, when subjected to
dynamic (impact) loading such as projectile hitting a target is
significantly different compared to its response to a static
force. Dynamic strength characteristics of projectile/target
undergo considerable changes due to impact. When the impact
is made with high velocities, projectile and target experience
plastic deformation, material failure, and increase in strength,
cracks formation and propagation etc. All these effects need to
be accounted in numerical simulation tools in order to get
accurate representation of the actual behavior.
Simulation of penetration events requires a numerical
technique that allows one body (fragment) to pass through
another (target). Lot of research has gone into the study of
high velocity impact behavior of projectile impact a hard
target. Since the duration of the impact is of the order of 1e-4
sec to 1e-3 sec, stress wave propagation effects need to be
considered in the problem.
Target damages when it is subjected to impact load by high
velocities of fragment. The damage to the target depends on
various factors such as:
 The geometric shape of the fragment and Target
 The geometric size of the fragment and Target
 The material of the fragment and Target
 The number of fragments hitting the target
 The velocity of the fragment
 The angle of hit with the normal direction of the
target
 The thickness of target
2. FINITE ELEMENT MODELLING OF TARGET
PLATE AND PROJECTILE
2.1 Geometric and Finite Element Model
Geometric and finite element modeling is done using Hyper
Mesh with user profile LS-DYNA. Finite element Meshing
involves dividing the physical domain into small zones called
finite elements. Mesh size and element type chosen plays an
important role in the accuracy of the results obtained from LS-
DYNA. For the present work 103794 elements exists for the
model. At impact zone fine mesh is chosen as it involves
penetration of elements into other elements.
Eight noded hexahedral elements are considered for both the
fragment and target with fully integrated selective reduced
property. Wherever necessary, six noded pentagonal elements
are used for smooth mesh.
Mesh size plays a very important role in the accuracy of the
results. Choosing appropriate element type and the mesh size
is utmost important. With increase in mesh quality and size,
results tend to converge and stabilize. Lot of effort has gone in
choosing the appropriate element type and mesh size for this
impact study. The mesh was refined in the impact zone. The
mesh density was reduced as the distance from the impact area

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increased. Care was also taken to maintain correct aspect ratio
in the grid especially in and around the impact zone where the
aspect ratio of the elements was maintained close to unity. The
aspect ratio was allowed to increase towards the periphery of
the plate. Fig.1 shows the Discretisation of geometry model
Fig.1 Discretisation of geometry model
2.2 Material Model
Because of the impact, projectile and target undergoes severe
deformations, stresses and the induced stresses go beyond
yield. To properly depict the projectile/target behaviour,
selection of correct mathematical (material) model for the
projectile/target are important. These material models depict
the material flow (elastic and plastic) and stress wave
propagation and strain rate effects. Since stresses cross the
yield point, uniaxial stress-strain curve beyond yield and up to
failure are required. Definition of material stress-strain curve
plays an important role in the accuracy of the results obtained
from the programme – LS-DYNA.
The projectile is assigned with AT_PLASTIC_KINEMATIC
material model (available in LS-DYNA). This model is suited
to model isotropic and kinematic hardening plasticity with the
option of including strain rate effects. The target is assigned
with MAT_PIECEWISE_LINEAR_PLASTICITY material
model. This is an elasto-plastic material with an arbitrary
stress versus strain curve and arbitrary strain rate dependency
can be defined. Also, failure based on a plastic strain or
minimum time step size can be defined. Material Properties.
The projectile is assigned with tungsten material properties.
Different materials such as mild steel, Titanium alloy were
considered for the target. Definition of material stress-strain
curve plays an important role in the accuracy of the results
obtained from the programme – LS-DYNA. Hence stress
strain curves are defined for the target materials. The material
properties and stress strain curves defined for the materials are
shown in figures 2&3.
Fig 2 Stress-Strain curve for Mild steel
Fig 3 Stress-Strain curve for Ti alloy
2.3 Contact Definition
Contact is the only way of load transfer between the projectile
and the target. Eroding surface-to-surface contact with failure
is defined between the target and the projectile. The fragment
was considered as the master surface and the contact surface
of the target plate as the slave surface.
2.4 Loads and Boundary Conditions
Any type of service loads or mechanical loads can be applied
to structure or fluid. In this case, the main load is impact
pressure, generated due to projectile impact and the resulting
stress wave propagation. The impact pressure is transferred to
target by contact surface. Proper modeling of contact interface
between the projectile and the target is critical for accurate
impact load transfer.
The target is constrained in all degrees of freedom along the
periphery and projectile is allowed to travel in space freely
with defined velocity in a direction normal to the target. For
all the solution cases presented in this report only half of the
mesh is used, as shown in the figure 4, due to symmetry of the
problem.

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2.5 Analysis
Once all the necessary steps are completed, simulation is
carried out using LS-DYNA. As stated earlier, the impact lasts
for very short duration and the maximum damage to the
projectile/target is observed during this period. This calls for
collection of data (like impact pressure, KE (Kinetic Energy),
momentum, deformation, stress, strain, etc) during this period
using very small time steps. Several simulations have been
carried out before the actual problem was studied. The main
objective of these studies is to establish the correctness of the
material model used to define the projectile/target, time step
calculations, problem setup etc.
After defining all the input data, dynamic impact analysis is
carried out using LS-DYNA. Various checks on input data are
performed before submitting the job to LS-DYNA. Since LS-
DYNA is an explicit code, the time step is determined by the
program automatically to maintain the stability and
convergence during the analysis.
Various results from the study are extracted and presented in
the subsequent pages. Efforts are made to capture the impact
data as accurately as possible for the complete cycle of
simulation.
2.6 Case Studies
The similar cases for which simulation has been carried out
are tabulated in 1. Simulation has been carried out for all the
cases and results have been documented.
Table 1 Case studies
Fig 4 Finite element model with boundary conditions
3. RESULTS AND DISCUSSIONS
The following parameters are measured and discussed:
a. Velocity
b. Kinetic Energy
c. Von Mises stress
d. Effective plastic strain
e. Damage (measured in terms of hole diameter).
3.1 Target as Mild Steel
The results of first four cases are shown where a 15 mm cube
shaped tungsten fragment is made to impact with wide range
velocities of 300, 500, 700, 1000mm/ms onto two Mild steel
target plates of size 300x300x3 mm which are separated by
100mm apart. The fragment is positioned at a distance of
0.5mm from the first target plate.
It is observed that the fragment penetrated easily through two
plates by reducing its velocity and kinetic energy. The amount
of damage caused by the impact of a projectile with target
plate is determined primarily by the factor kinetic energy
released. Table 4.1.1 shows the change in velocities and
kinetic energies of the fragment after impact with two target
plates.
The velocity drop and kinetic energy drop for each case is
calculated. The drop is given by the difference of initial value
and the value obtained after 2nd plate. Graphs are drawn
between initial velocities taken as x-axis and drops taken as y-
axis. Figures 5&6 show the graph plots for velocity drop and
kinetic energy drop. It is found that as initial velocity of the
fragment is increased both velocity drop and kinetic energy
drop are increased. Hence it can conclude that for higher
impact velocities more kinetic energy is transferred.
S.
N
O
FRAGME
NT
MATERIA
L
IMPAC
T
VELOC
ITY
(mm/ms
)
TARGE
T
MATERI
AL
TARGE
T
PLATE
THICKN
ESS
(mm)
GAP
BETW
EEN
TWO
PLATE
S
(mm)
1 Tungsten 300
MS +
MS
3 + 3 100
2 Tungsten 500
MS +
MS
3 + 3 100
3 Tungsten 700
MS +
MS
3 + 3 100
4 Tungsten 1000
MS +
MS
3 + 3 100
5 Tungsten 300 Ti + Ti 3 + 3 100
6 Tungsten 500 Ti + Ti 3 + 3 100
7 Tungsten 700 Ti + Ti 3 + 3 100
8 Tungsten 1000 Ti + Ti 3 + 3 100

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Table 2 Velocity and Kinetic energy drop
Initial
After 1st
plate (MS)
After 2nd
plate (MS)
Velocity
(mm/ms)
300 280.00 261.0
500 476.25 456.0
700 676.25 653.0
1000 976.25 952.5
Kinetic
energy
(kg-
mm/ms2
)
1465 1200 970
4070 3410 2750
7980 6800 5300
16280 14000 11300
0
10
20
30
40
50
60
0 150 300 450 600 750 900 1050 1200
Initial Velocity
VelocityDrop
Fig 5 A schematic diagram of Initial Velocity Vs Velocity
drop
0
1000
2000
3000
4000
5000
6000
0 150 300 450 600 750 900 1050 1200
Initial Velocity
KEDrop
Fig 6 A schematic diagram of Initial Velocity Vs KE drop
Maximum Vonmises stress for the fragment material was
found to be about 0.5516 KN/mm2. The maximum Vonmises
stresses obtained for each case are tabulated. Much difference
is not found when the stresses are compared for all 4 cases.
Table 4.1.2 shows list of maximum Vonmises stress obtained
for each case.
Table 3 Vonmises stress
Initial velocity
(mm/ms)
Plate 1
(KN/mm2)
Plate 2
(KN/mm2)
300 0.4062 0.4078
500 0.4030 0.4078
700 0.4066 0.4054
1000 0.4060 0.4064
The maximum effective plastic strains for the target plates and
fragment are measured and listed in the table 4 for all the
above four cases but no much difference is found.
Table 4 Effective Plastic Strain
Initial velocity
(mm/ms)
Plate 1 Plate 2 Fragment
300 0.3326 0.3315 0.2547
500 0.3259 0.3456 0.2747
700 0.3413 0.3323 0.2800
1000 0.3307 0.3303 0.2800
Damage of the plates due to impact is measured by means of
hole diameter produced in the plates. The following table 5
shows the hole diameter produced in the target plates due to
impact with fragment.
Table 5 Hole Diameter
Initial velocity
(mm/ms)
Plate 1 (mm) Plate 2 (mm)
300 15.910 15.96
500 15.975 16.46
700 16.090 16.87
1000 16.150 16.80
3.2 Target as Titanium
This is similar to section 4.1 but instead of Mild steel material,
titanium material properties are assigned to both targets. The
velocity and kinetic energy results were listed in the following
table 6 showing the change in velocities and kinetic energies
of the fragment after impact with two target plates.
The velocity drop and kinetic energy drop for each case is
calculated. Graphs are drawn between initial velocities taken
as x-axis and drop taken as y-axis. Figures 7 and 8 show the
graph plots for velocity drop and kinetic energy drop.
Similarly it is found that as initial velocity of the fragment is
increased both velocity drop and kinetic energy are increased.

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Table 6 Velocity and Kinetic energy drop
Initial
After 1st
plate (MS)
After 2nd
plate (MS)
Velocity
(mm/ms)
300 293.80 288.30
500 492.80 485.50
700 691.20 680.20
1000 988.75 978.25
Kinetic
energy
(kg-
mm/ms2)
1465 1408 1355.0
4070 3955 3837.5
7980 7780 7450.0
16280 15900 15280.0
0
5
10
15
20
25
30
0 150 300 450 600 750 900 1050 1200
Initial velocity
VelocityDrop
Fig 7 Plot showing Velocity drop
0
200
400
600
800
1000
1200
0 150 300 450 600 750 900 1050 1200
Initial velocity
KEDrop
Fig 8 KE drop
Maximum Vonmises stress for the fragment material was
found to be about 0.5516 KN/mm2. The maximum Vonmises
stresses obtained for each case are tabulated. It is found to be
increased as impact velocity is increased for this material.
Table 7 shows the maximum Vonmises stress obtained for
each case
Table 7 Vonmises stress
Initial velocity
(mm/ms)
Plate 1
(KN/mm2)
Plate 2
(KN/mm2)
300 1.081 1.129
500 1.157 1.350
700 1.384 1.423
1000 1.818 1.643
The maximum effective plastic strains for the target plates and
fragment are measured and listed in the table 8 for all the
above four cases but no much difference is found.
Table 8 Effective Plastic Strain
Initial
velocity
(mm/ms)
Plate 1 Plate 2 Fragment
300 1.366e-2 1.294e-2 0.1925
500 1.335e-2 1.297e-2 0.2440
700 1.403e-2 1.416e-2 0.2763
1000 1.416e-2 1.324e-2 0.2826
The following table 9 shows the hole diameter produced in the
target plates due to impact with fragment.
Table 9 Hole Diameter
Initial velocity
(mm/ms)
Plate 1 (mm) Plate 2 (mm)
300 15.475 15.77
500 15.385 15.77
700 15.485 15.67
1000 15.485 15.68
CONCLUSIONS
The conclusion of the present work are enumerated and
presented as shown hereunder
 The deformations caused due to various impact
velocities for different materials were analyzed. It has
been found that velocity drop is increased as the
impact velocity is increased.
 The kinetic energy drop is increased by the increment
of velocity i.e. energy absorption is more for higher
velocities.
 For Mild steel material velocity drop and kinetic
energy drop is high compared to Tungsten and
Aluminium material.
 Velocity drop is less when target plates of 3mm are
used, when compared to 6mm Plates.
 More damage i.e. average hole diameter is found for

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the second plate compared to first plate in all the
cases.
 Effective gap was found to be about 100 mm between
two target plates.The increasing order of effective
plastic strain is Ti Alloy, Al Alloy, Tungsten and
Mild steel.
REFERENCES
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[8] N.K. Gupta, M.A. Iqbal, G.S. Sekhon. Experimental
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[9] Leonard E. Schwer. Preliminary assessment of Non-
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[10] Vijay K. Goyal, Carlos A. Huertas, Jose R. Borrero,
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