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Proceedings of the NATIONAL CONFERENCE ON ADVANCES IN MECHANICAL ENGINEERING (NCAME) held from 27-29 Nov.

2010 at University Polytechnic, AMU, ALIGARH, INDIA [ISBN 978-93-80697-33-8]

Numerical Simulation of Ogive Nose Projectile Impact on

Aluminum Plates of Different Thicknesses

Sanaan H. Khan 1 and R. Ansari

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Mechanical Engg Deptt, Zakir Husain College of Engg and technology, Aligarh Muslim University, Aligarh, 202002

Present study deals with the numerical investigation of aluminum target plates impacted by ogive nose rigid

projectile on aluminum target plates of 0.5 and 1 mm thickness at different velocities. Effect of ogive nose projectile

is studied with respect to impact velocity on plate thickness and attempt is made to simulate the deformation

behavior of aluminum plates. The numerical simulations of this problem have been performed using a finite element

code, ABAQUS-Explicit with an adaptive mesh for the plate. To define the thermo-viscoplastic behavior of the

material constituting the plate, the Johnson–Cook model has been used. This homogeneous behavior has been

coupled with the Johnson–Cook fracture criterion to predict completely the perforation process. The numerical

results predict correctly the behavior of projectile-plate in agreement with experimental data published by Ansari,

R.U. Various parameters like choice of element and aspect ratio, which plays an important role in numerical

simulation, has been studied.

I. Introduction

Impact on plates is a complex phenomenon involving dynamic behavior, fracture, damage

initialization and evolution. It has been observed during this kind of projectile-plate impacts

(metal–metal) that the nose shape of the projectile used changes the energy absorbed, the failure

mode and the ballistic limit [1,2]. Numerically, several previous studies of structural impact on

aluminum plates have been performed using FE LS-DYNA code [3, 4]. In these previous studies

numerical problems occur when fixed meshes are used, specially using conical projectile.

Therefore, it is recommended to use an adaptive mesh for this configuration. The same

observation was reported by Gupta et al. [2] studying numerically the problem of aluminum plate

impact with ABAQUS FE code. In conclusion, the problem of plate impact perforation is not so

easy to solve numerically due to element distortion caused by severe local loading. In this work,

finite element simulations of aluminum plates impacted by ogive nosed projectiles are performed

using an explicit finite element code ABAQUS-Explicit [8], currently used for dynamic loading

problems [2,9–11]. The numerical configuration used in terms of dimensions and boundary

conditions is based on experimental set-up proposed by Ansari, RU. [7]. Numerical simulation is

performed on 0.5mm and 1mm thick aluminum plates of 255mm external diameter and results

obtained, allows predicting properly the complete process of perforation as it will be discussed in

this paper.

1 Research Student, Mechanical Engg. Deptt. ZHCET, AMU, Aligarh. (er.sanan@rediffmail.com.)

2 Professors, Mechanical Engg. Deptt. ZHCET, AMU, Aligarh. (ruansari@rediffmail.com )

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II. Material response characterization

In this study, Johnson and Cook model (JC), has been used to describe the elasto-

viscoplastic behavior observed in aluminum at high impact velocity because it takes into account

high strain rates sensitivity, larger deformation and thermal softening. Moreover, this model is

pre-implemented in ABAQUS-Explicit. The explicit formulation of the JC model is given by:

Johnson-Cook hardening

The Johnson-Cook Flow Surface is:

Where A, B, C, n and m are constants.

The non-dimensional temperature

Where is the current temperature, is the ambient temperature, and is the melting

temperature.

The non-dimensional strain rate is the ratio of the effective plastic strain rate to the reference

strain rate (usually equal to 1.0), i.e.

Johnson-Cook dynamic failure

Failure accumulation in the Johnson-Cook model does not directly degrade the yield surface. The

model, more fully described in reference 5, 6 defines the strain at fracture as

Where is the ratio of the pressure to the effective stress, i.e.

Fracture occurs in the Johnson-Cook model when the damage parameter D exceeds 1.0. The

evolution of D is given by the accumulated incremental effective plastic strains divided by the

current strain at fracture

The first set of brackets in the Johnson-Cook fracture model is intended to represent the

observation that the strain to fracture decreases as the hydrostatic tension increases. The second

set of brackets in the strain to failure expression represent the effect of an increased strain rate on

the material ductility, while the third set of brackets represent the effect of thermal softening on

the material ductility. Johnson-Cook hardening and failure parameters for aluminum used in this

study, have previously been published [2], and taken from there.

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III. Numerical Modeling using Abaqus Explicit

Numerical analysis of the problem was carried out using ABAQUS finite element code.

An axisymmetric geometric model of the projectile and target plate was created in the

preprocessing module of the code. Target plate was modeled as a deformable body and projectile

as rigid body with single node reference point to assign mass, inertia and impact velocity.

Surface to surface contact was modeled between the projectile and the plate using penalty

contact algorithm. The bullet was considered as master surface and impact zone of the plate as

node based slave surface. The effect of friction between projectile and plate was considered as

negligible due to thinness of the plate. The target was restrained at its periphery with respect to

all degree of freedom by using Encastre boundary condition. Displacement of the bullet across

the axis was also curtailed.

Mesh definition

The numerical simulations have been performed using axisymmetric mesh on aluminum plates

of 230mm p.c.d by using four noded axisymmetric quadrilateral elements (CAX4R) with single

integration point, on both the thickness [0.5 and 1 mm] .The mesh is made finer in the contact

zone of the projectile-plate to satisfy the conditions proposed by Zukas [8]. The aspect ratio of

the elements were taken unity [8] in the impact zone, however, it was allowed to increase as the

distance from the impact zone increases. The number of elements has been taken in the thickness

direction to approach unity aspect ratio condition in the impact zone.

Table 1

Thickness in

mm

Number of elements along

thickness

Total no. of elements in

plate

0.5 09 6,247

1 18 12,494

ALE Adaptive meshing

Two kinds of procedures may be used during numerical simulations. The first was to use

a fixed mesh in terms of length elements while the second was to use an adaptive mesh allowing

regenerating the mesh of the plate during time calculations. The first option is well defined and

robust for problems involving small or moderate deformation (without severe distortion). For

large deformation with strong element distortion, the algorithm does not work efficiently and

problem of convergence appears. Thus, the second option using adaptive mesh is better and does

not alter the topology (elements and connectivity) of the mesh. The adaptive meshing in

ABAQUS-Explicit combines the features of pure Lagrangian analysis (in which the mesh

follows the material, as is usually the case in ABAQUS) and Eulerian analysis (in which the

mesh is fixed spatially and the material flows through the mesh) currently referred as Arbitrary

Lagrangian–Eulerian (ALE) analysis [9]. In an adaptive mesh increment, a new, smoother mesh

is created by sweeping iteratively over the adaptive mesh domain. During each mesh sweep,

nodes in the domain are relocated based on the current positions of neighboring nodes and

elements to reduce element distortion. In a typical sweep a node is moved as a fraction of the

characteristic length of any element surrounding the node. In our case the sweep mesh value has

been chosen 20. This choice solves convergence problems during numerical simulation.

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IV. Computational results and discussion

Numerical results of ogive nose projectile impact on 0.5mm and 1mm thick aluminum plate

are discussed and compared with Ansari, R.U [7] and good co-relation between the two was

found. Figure 3 show the predicted progress of the deformation of the target plate impacted by

ogive nosed projectile. Ogive nosed projectile hits the target plate at the center. The tip of the

projectile initiates the perforation process, and finally emerges from the rear of the target. The

target deforms gradually like the shape of the projectile. Johnson cook material model helps to

flow the yield surface exactly that might have happened during experiments. One of the major

disadvantages with axisymmetric model comes out with a fact that petalling could not be

predicted by it. As the material of the target plate is pushed forward, thinning of the target plate

is observed.

Stress strain contours of the target plate are shown in figure 4 and 5. It was observed that the

peak values of shear stress is reached when ogive portion of the projectile perforates the plate,

after that the stress decreases and becomes constant. The intensity of equivalent plastic strain

however reaches maximum value at the beginning of perforation when nose burst the target

plate. Else everywhere on plate the concentration of plastic strain was found negligible.

Figure 6 and figure 7 show the plot between impact velocity and corresponding residual

velocities for observed and computed part. It was observed that numerical analysis over-

predicted the ballistic limit velocities in most of the cases. The predicted ballistic limit velocities

computed by Abaqus/CAE were found satisfactory with some error bounds. The relative error of

19% was found for 0.5mm thickness between experimental and predicted results. Somewhat

similar error was found for 1mm thick plate too.

Figure 1: The assembly of plate and bullet Figure 2: Finer mesh in impact zone

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Fig 3. Deformation behavior and von-Mises contours for aluminum plate

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Fig. 4: shear stress contour Fig. 5: Equivalent plastic strain contour

10 20 30 40 50 60 70 80

10

20

30

40

50

60

70

80

impact velocity (m/s)

resid

ual velo

city (m

/s)

impact velocity versus residual velocity

Ansari [7]

Abaqus

quadratic fit

quadratic fit

h=0.5mm

Fig 6: Impact verses residual velocity for 0.5mm thickness Fig 7: Impact velocity verses Residual velocity for 1mm thickness

20 30 40 50 60 70 80

10

20

30

40

50

60

70

80

impact velocity (m/s)

resid

ual velo

city (m

/s)

impact velocity versus residual velocity

Ansari [7]

Abaqus

quadratic fit

quadratic fit

h=1mm

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V. Conclusion

In conclusion it is possible to predict accurately with numerical simulations the impact

failure mode as observed during experiments by ogive nose projectile of CRH 2. Perforation by

the ogive nosed projectile caused petal formation in the target plate as the bending of these petals

was found to decrease as the thickness of the target plate increases from 0.5 to 1mm.

It was also noticed that the global as well as local deformation (in the impact zone) of the plate

decreases as the projectile velocity is increased.

It is not possible, for the case of ogive nose projectile, to predict the ballistic limit and

the fracture time in agreement with experimental values published [7] without strong effect

between adaptive or fixed mesh. The difference between these two approaches is linked to the

convergence during numerical simulation. In some cases using fixed mesh, the calculation is

stopped due to element distortion. Using ALE approach, this problem is reduced maintaining the

high quality mesh throughout the process.

VI. References

[1]. Borvik T, Langseth M, Hoperstad OS, Malo KA. Perforation of 12 mm thick steel plates by

20 mm diameter projectiles with flat, hemispherical and conical noses Part I: experimental

study. Int J Impact Engng 2002;27:19–35

[2]. Gupta, N.K., Iqbal,M.A., Sekhon, G.S., 2006. Experimental and numerical studies on the

behavior of thin aluminum plates subjected to impact by blunt- and hemispherical nosed

projectiles. International Journal of Impact Engineering 32, 1921–1944.

[3]. Borvik T, Langseth M, Hoperstad OS, Malo KA. Ballistic penetration of steel plates. Int J

Impact Engng 1999; 22:855–86.

[4]. Borvik T, Hopperstad OS, Langseth M, Malo KA. Effect of target thickness in blunt

projectile penetration of Weldox 460 E steel plates. Int J Impact Engng 2003;28:413–64

[5]. Johnson, G.R. and Cook, W.H., “Fracture Characteristics of Three Metals Subjected to

Various Strain, Strain Rates, Temperatures and Pressures,” Engineering Fracture Mechanics,

Vol. 21, No 1, pp. 31-48, 1985.

[6]. Johnson GR, Cook WH. A constitutive model and data for metals subjected to large strains

high strain rates and high temperatures. In: Proceedings of the seventh international

symposium on ballistics; 1983.

[7]. Ansari R. Normal and oblique impact of projectiles on single and layered thin plates. Ph.D.

thesis, IIT Delhi, 1998.

[8]. Zukas JA, Scheffler DR. Practical aspects of numerical simulations of dynamic events:

effects of meshing .Int J Impact Engng 2000:925–45.

[9]. ABAQUS Analysis User’s manual, 2009. Version 6.9.3, vol. 2.