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Dynamic response of alumina ceramics impacted by long tungstenprojectile

Jianguo Ning a, Huilan Ren a,*, Tingting Guo a, Ping Li b

a State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijng 100081, PR Chinab National Key Laboratory of Shock Wave and Detonation Physics, Institute of Fluid Physics, CAEP, Mianyang 621900, PR China

a r t i c l e i n f o

Article history:

Received 31 July 2012

Received in revised form

27 April 2013

Accepted 8 June 2013

Available online 22 June 2013

Keywords:

Anti-penetration ability

Long rod projectile

Ceramic target

Penetration damage

a b s t r a c t

In this paper, the dynamic response characteristics of ceramic targets impacted by a long tungsten

projectile at a high speed are investigated through an improved theoretical model. The model, based on

conventional quasi-static cavity expansion theory, takes the effect of the target damage caused by

penetration on the constitutive equation into account. A few useful relations of the target resistance and

the penetration velocity are derived from the model and the stationary incompressible hydrodynamic

theory. In order to examine the dynamic damage response of alumina ceramics to projectile impact and

the theoretical model, we set up the experimental system of a high-speed, long tungsten projectile with

its sabot separation device penetrating ceramic targets with/without cover plate, carried out a series of

penetration experiments, and compared the experimental results with theoretical calculation and nu-

merical simulation results. Theoretical and experimental results show that 1) the anti-penetration ability

of AD90 ceramic is higher than that of 45# steel, especially, in the low-speed stage of the projectile; 2)

material parameters of AD90 ceramic obtained from the numerical simulation of projectile penetration

are reasonable; 3) the cover plate covered on the front of the ceramic target can improve the anti-

penetration ability, while the constraint sleeve enclosed the ceramic target has little effect on the

anti-penetration ability; 4) from the numerical simulations, the damage caused by penetration in the

target with the cover plate is initiated by the tensile wave reected from the back of ceramic, while thedamage in the non-plate target is initiated by direct impact, and then develops at the target back by

tensile wave; and 5) the theoretical model presented in this paper is proven to be reasonable, can be used

to further studying on dynamic response of target materials under penetration.

2013 Elsevier Ltd. All rights reserved.

1. Introduction

In a war in the future, tank is still a major military strike force,

thus many countries have been and are studying novel armour

protection materials and structures to improve its anti-penetration

ability. Recent years, brittle ceramic materials, such as Al 2O3 and

AlN, have been investigated as possible substitutes for steel as tankarmour materials against kinetic energy projectiles and shaped-

charge jets. Their excellent ballistic performance against penetra-

tion comes from their unique dynamic mechanical properties, such

as low density and high compressive strength. The dynamic me-

chanical response, dynamic damage and fracture of ceramic com-

posite armour are also the important factors for analyzing ballistic

performance against penetration[1].

Studies [2e5] on penetration mechanics indicated that the

impact and penetration process included wave propagation,

elasticeplastic deformation, crack initiation and propagation,

plugging process, petal-shaped reaming, spallation, shear zone,

melting and phase transformation, fragmentation, etc. These

phenomena belong to certain different scientic elds, thus it

becomes very complicated if all these phenomena need to bestudied. Penetration theory is generally based on the phenome-

non produced in the impact and penetration process, therefore

the empirical formulas are developed on the basis of a series of

simple formulas by responsible simplication. The target resis-

tance is usually used to measure the ability of a target to resist

penetration. Cavity expansion analysis (CEA) plays a signicant

role in studying the penetration behavior of target materials like

brittle ceramics[6].

Since CEA was rst put forward in the mid-20th century, it has

been widely used in many aspects. Hill [7] proposed that the

cavity expansion pressure can be considered as the work required* Corresponding author. Tel.: 86 10 68913557.

E-mail addresses: 396785294@qq.com,huilanren@bit.edu.cn(H. Ren).

Contents lists available at SciVerse ScienceDirect

International Journal of Impact Engineering

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . co m / l o c a t e / i j i m p en g

0734-743X/$ e see front matter 2013 Elsevier Ltd. All rights reserved.

http://dx.doi.org/10.1016/j.ijimpeng.2013.06.006

International Journal of Impact Engineering 62 (2013) 60e74

mailto:396785294@qq.commailto:huilanren@bit.edu.cnhttp://www.sciencedirect.com/science/journal/0734743Xhttp://www.elsevier.com/locate/ijimpenghttp://dx.doi.org/10.1016/j.ijimpeng.2013.06.006http://dx.doi.org/10.1016/j.ijimpeng.2013.06.006http://dx.doi.org/10.1016/j.ijimpeng.2013.06.006http://dx.doi.org/10.1016/j.ijimpeng.2013.06.006http://dx.doi.org/10.1016/j.ijimpeng.2013.06.006http://dx.doi.org/10.1016/j.ijimpeng.2013.06.006http://www.elsevier.com/locate/ijimpenghttp://www.sciencedirect.com/science/journal/0734743Xhttp://crossmark.dyndns.org/dialog/?doi=10.1016/j.ijimpeng.2013.06.006&domain=pdfmailto:huilanren@bit.edu.cnmailto:396785294@qq.com

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by opening per unit volume of the cavity. Chadwick[8]solved the

spherical cavity expansion pressure of the Mohr-Coulomb mate-

rials. In 1989, Sternberg [9] applied the CEA to ceramic material

and discussed the application of cavity expansion pressure as a

strength item in the Tate equation. He also studied the inuence

of material properties on the anti-penetration resistance and

found that the constitutive relationship of ceramic above the

elastic limit could not well describe the material behaviour,

indicating that the cavity expansion model for ductile materials

can not be directly used for brittle materials. Forrestal [10]

considered the cracks of porous rock when performing CEA and

found that the theoretical results using the Mohr-Coulomb

strength criteria and the linear pressure relationship were

consistent with the experimental results. Satapathy and Bless[11]

and Forrestal and Longcope [12] extended and applied the

quasi-static cavity expansion theory to ceramic materials.

Satapathy [13]presented the dynamic cavity expansion solution

to determine the dynamic response of ceramic materials in the

cavity expansion at a constant velocity. However, CEA doesnt

take the penetration damage on target material into

consideration.

In dynamic studies, penetration into targets of ceramics,

ceramic/metal, ceramic/composite and layered ceramics gener-ally means that the penetration of long rod of metal such as

tungsten, molybdenum, tungsten alloy, etc. into the ceramics and

the ceramic/composite target in the speed range of 1500e

5000 m/s. These experiments are generally conducted on the

one-stage or two-stage light gas gun. The most commonly con-

ducted experiment is the direct ballistic experiment, also known

as the penetration depth method (the depth-of-penetration,

DOP) [14,15] because it can reect the anti-penetration ability

of the ceramic target by accurately measuring the residual depth

in the backup metal. The advantage of the DOP method is that

the size of the specimen is close to the actual size, while its

drawback is that the information obtained from it is too little.

Only a residual depth can be got from an experiment. In addition,

since in most cases the size of the target is big, the real-timeobservation of the X-ray radiography is difcult. DOP was rst

tested by Yariv in 1986 for investigation of the ballistic perfor-

mance of ceramic tiles [16]and further improved by Rosenberg

[17], Anderson [15,18], and Wooward [19]. Since then, it was

applied widely in U. S. Army and Materials Research Laboratory

and considered as a standard experiment to evaluate the anti-

penetration ability of the ceramic/composite target. Anderson

et al.[15]used DOP test to examine the ballistic performance of

conned Al2O3 ceramic tiles by changing the type and the

thickness of the cover plates. Kim [20]studied the relationship

between the mechanical properties (Youngs modulus, density,

hardness, exural strength, and toughness) and the ballistic

properties of AD95, AD90, AD99, hot-pressed SiC, hot-pressed

TiB2, and hot-pressed B4C, etc. U. Hornemann and A. Holzwarth[21] conducted a series of experiments to investigate the in-

uences of the thickness, distance and structure of the target on

the anti-penetration ability of the ceramic/steel target against

shaped charge jet.

In this paper, based on the stationary incompressible hydrody-

namic theory and spherical cavity expansion analytic method, we

present our improved CEA theoretical model. In order to examine

the dynamic damage response of alumina ceramics to projectile

impact and the theoretical model, we set up the experimental

system of a high-speed, long tungsten projectile with its sabot

separation device penetrating ceramic targets with/without cover

plate, carried out a series of penetration experiments, and

compared the experimental results with theoretical calculation and

numerical simulation results.

2. Theoretical model for target resistance of ceramics

2.1. Stationary incompressible hydrodynamic theory

Taking the target resistance into consideration, we use the basic

equation of the stationary incompressible hydrodynamic theory,

i.e., Bernoulli equation, to describe the penetration of a projectile at

a high velocity into a target

1

2rpvpu

2Yp

1

2rtu

2 Rt; (1)

where rp and rt are the densities of the projectile and target,

respectively; vp and u are the projectile velocity and its interface

velocity at which it begins to penetrate into the target, respectively;

Yp is the dynamic strength of the penetrator and Rt is the target

resistance. From Eq.(1), we nd

u vp

1 rt=rp

1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffirt=rp

1 rt=rp

2Rt Yprpv

2p

s !: (2)

2.2. Quasi-static spherical cavity expansion model with damage

In Eq. (2),vp, rp, and rt can be determined by experiments, while

Rtcan only be obtained from derivation. According to the degree of

damage, the response regions in the semi-innite ceramic target

due to sudden cavity expansion are shown in Fig. 1.

Boundary conditions are as follows:

a.) srjrb 0 (At the elastic-undisturbed interface, there is no

stress.);

b.) sqjrc sf (Radial cracks appear when the hoop stress reaches

the tensile strength.); and

c.) srjra Y(When the radial stress in the cracked zone rea-

ches the compressive strength of the material, the material will

be crushed.).

In the boundary conditions,ris the radius from the tip or cavity

centre,h, a, c,andbare radii of various regions, respectively, shown

inFig. 1, sr and sare the radial and hoop stresses, respectively

(positive in tension), and sf and Y are the tensile strength and

compressive strength of target material, respectively.

2.2.1. Elastic region (c< r< b)

Since the cavity is spherically symmetric, the material in the

elastic region can be described with following equations:

dsrdr

2sr sq

r 0; (3)

r dur

dr; q 4

urr ; (4)

Fig. 1. Response regions in the ceramic targets.

J. Ning et al. / International Journal of Impact Engineering 62 (2013) 60e74 61

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