Paper: ASAT-13-ST-24 th
13 International Conference on AEROSPACE SCIENCES & AVIATION TECHNOLOGY, ASAT- 13, May 26 – 28, 2009, E-Mail:
[email protected] Military Technical College, Kobry Elkobbah, Cairo, Egypt Tel : +(202) 24025292 – 24036138, Fax: +(202) 22621908
Impact of Ceramic/Composite Light-Weight Targets by High-Speed Projectiles M.A. Shaker* and A.M. Riad*** Abstract: In this paper, an analytical model has been proposed to describe the perforation process of ceramic/composite lightweight targets by high-speed small caliber projectiles. The present model consists of two parts; the first part is concerned with the modeling of ceramic fragmentation and its penetration by a projectile [1], whereas the second is concerned with modeling of projectile penetration into composite failed by tensile failure [11]. Two modes are considered to be associated with projectile and ceramic materials during their perforation; these are erosion and rigid. Main assumptions and governing equations of the proposed model are introduced. These equations are arranged and compiled into a computer program. The input data needed for running the program are easily determined. The predictions of the proposed model are compared with the available experimental measurements of other investigators; good agreement is generally obtained. In addition, representative samples of the model predictions are presented with relevant analysis and discussions. The introduced results prove the predictive capabilities of the proposed model which could be used as a quick tool for designing a ceramic/composite target capable of defeating high-speed projectiles of certain threat.
Introduction In the last few decades, non-metallic materials such as ceramics and composites have been incorporated into more efficient lightweight armors. In particular, ceramics become widely used in such armors because of their low density, high hardness, rigidity and compressive strength. Moreover, ceramic/composite armors become the subject of many investigations because of their performance against small and medium caliber projectiles, especially when the weight is the design condition, for instance in lightweight vehicles, airplane and helicopter protection or body armors. Investigating the penetration process through lightweight armors is necessary for design optimization of such armors. Three main research directions are used for studying the penetration of lightweight armors by small and medium caliber projectiles. These directions are: (i) analytical, (ii) experimental, and (iii) numerical simulation. Analytical work represents the fastest, less expensive and probably most accurate research direction in this field as it simulates the impact process in a few seconds using personal computers.
*
Egyptian Armed Forces Egyptian Armed Forces,
[email protected] 1/21
**
Paper: ASAT-13-ST-24
Benloulo and Galvez [1] studied analytically the penetration of a ceramic/composite lightweight target by a projectile. They assumed that the penetration process consisted of three main phases; ceramic fragmentation, penetration into fragmented ceramic and post failure of composite plate. In each penetration phase, ceramic and projectile erosion as well as deformation of composite plate were modeled. Their model was based on equating the pressure at the projectile targetinterface. Moreover, it required the use of a single empirical parameter that may be determined from residual velocity data of one firing test. Predictions of their model gave good agreement with the measurements of their experimental program. Benloulo et al. [2] developed one-dimensional analytical model of ballistic penetration of ceramic/composite armors. The predicted results of their model was compared with those of ballistic tests and numerical simulation; good agreement was obtained. The model was capable of calculating the residual velocity, residual mass, projectile velocity and the deflection or the strain histories of the backup material. The development of their analytical model for the composite penetration was based on previous studies of the impact in yarns, fabrics and finally composites [3]. Yakoub [5] studied the penetration of ceramic/Kevlar and Ceramic/GFRP by two different calibers of armor-piercing projectiles. His analytical work was based on Benloulo and Galvez model [2]. In his experimental work, the limit velocities due to the impact of the smallest caliber projectile into the constructed composites with different thicknesses were measured and used as input data to run the model. In addition, the constructed bi-layered targets were impacted by the highest caliber projectile. The predicted results of the analytical model were compared with the results of his experimental program and with the numerical results of other investigators. Good agreement was generally obtained. Ravid et al. [6] investigated analytically the penetration of ceramic/composite armor by a projectile. Their model consisted of four stages, these were: (i) impact and penetration into ceramic, (ii) penetration into broken ceramic, (iii) penetration in combined (broken ceramic and backup) media, and (iv) backup plate perforation. Stages (i) and (ii) were concerned with wave propagation and projectile penetration through the frontal ceramic layer. Damage of the projectile nose would occur during the initial impact process and broken fragments were ejected. In stage (iii), the projectile passed through the fragmented ceramic, held in place, and supported by the backing layer and inertia effects. This stage generated additional comminuted ceramic. In the fourth stage, the combined fragmented ceramic and the backing layer were considered as a single isotropic plate. They performed a series of ballistic tests on AD98 ceramic AD98 bonded to Kevlar backup plate to validate the predictions of their analytical model. The model predictions were slightly overestimated their ballistic measurements. Fawaz et al. [7] presented a three dimensional finite element model that investigated the performance of ceramic/composite armors when subjected to normal and oblique impacts by 7.62 AP projectiles. The simulation of penetration process as well as the evaluation of energy and stresses distributions within the impact zones, was done using LS-DYNA 3D finite element code and the results were compared with the experimental data reported by Mayseless [8]. The simulation showed that the distributions of global kinetic, internal and total energy versus time are similar for normal and oblique impact. However, the interlaminar stresses at the ceramic/composite interface and the forces at the projectile-ceramic interface for oblique impact were found to be smaller than those for normal impact. Finally, they observed that the projectile erosion in oblique impact was slightly greater than that in normal impact. 2/21
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Hetherington and Rajagopalan [9] investigated experimentally the perforation process of a range of ceramic/GFRP composite targets. In their work, 12.7 mm projectiles were fired against different combinations of ceramic and GFRP thicknesses. The characteristic requirements of targets were selected such that complete perforation took place by the projectile so that the amount of energy absorbed by the target could be estimated. The results of their experiments were compared with that ones estimated from Florence's analytical model [10]. Good correlation between the theory and experiments was obtained. Moreover, they suggested that Florence's model could be used to generate design graphs which assisted the armor designers in selecting the optimum combination of armor components to provide the lightest, cheapest protection system against any perceived level of threat. In the following, two-part model is proposed to describe the penetration process of ceramic/composite targets and to evaluate their ballistic resistance against small caliber projectiles. The proposed model consists of two parts; the first is used to model the projectile penetration into a ceramic tile [1], whereas the second uses the tensile strain as a failure criterion for modeling the projectile penetration into composite plate [11]. The predictions of the two-part model are compared with the experimental measurements and analytical results of other investigators. In addition, Samples of the obtained analytical results due to the impact of highspeed steel projectiles into ceramic/composite targets with different materials are presented with relevant analyses and discussions.
Analytical Model In this model, the projectile is idealized as a cylindrical rod with initial length Lo and initial diameter DP. Similar to the one-dimensional model developed by Tate [12,13], the projectile material is assumed to behave as rigid-perfectly plastic with respect to nominal stressengineering strain relationship. Therefore, the present model identifies two modes associated with the penetrating projectile through the target; these are erosion and rigid. The projectile is assumed to strike the target normally with a high velocity. The present model considers that the lightweight armor to consist of a ceramic tile of thickness HCo backed by a composite of thickness Hb. As mentioned before, the model divides the penetration process of ceramic/composite targets into three main phases: (i) ceramic fragmentation, (ii) penetration of fragmented ceramic, and (iii) penetration of textile composite backing plate. The first and the third phases consist of only one stage, whereas the second phase consists of different penetration stages. The backing composite is assumed to be failed by tensile failure. The model is based on equating the pressure at rod-target interface. The momentum conservation principle is used to derive the main equations representing each penetration stage. The sequence of penetration stages depends on the relative velocities between projectile, ceramic and composite masses ahead of projectile. For each penetration stage, a system of first order dependent differential equations has been derived. The penetration time is taken as independent variable. The system of equations is solved numerically to determine the parameters associated with the penetration process as functions of time. The current value of penetration velocity U is determined using its respective interface equation. The end conditions of the current stage are considered as initial conditions for the subsequent stage. The penetration process terminates when the composite fails or when the projectile stops inside the target (i.e. it attains zero velocity).
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In the following, the main assumptions considered during analysis are introduced. In addition, main equations and end conditions of each penetration stage are presented.
Main Assumptions
The projectile-target interface area does not change during the penetration process. The remaining mass of fragmented ceramic ahead of projectile is taken into consideration during the penetration process of the composite plate; this mass is added to the remaining mass of projectile; both masses are moved as a rigid mass with the current projectile velocity. Textile/resin composites are homogeneous. The laminate constituting the composite is deformed due to its impact by the projectile, forming a conical shell shape with straight sides. There is no lateral (in-plane) displacement of the composite material. The full thickness of the composite plate material ahead of the projectile moves with the current projectile velocity. Friction between composite yarns and projectile is neglected. The crossover (crimp force) between yarns of the composite is neglected. The maximum tensile strain failure of the fibers is considered to stop the model calculations. Bending stresses caused by the projectile are not considered in the analysis. The inertia forces of the mass of the vertically moving fabric are not considered in the analysis. The resin used (epoxy) is brittle and broken locally due to impact. Therefore, the projectile is considered to penetrate the textile under the point of impact.
Main Equations of Penetration Phases Phase (i): Ceramic Fragmentation During this phase, both the projectile and the fragmented ceramic in-contact with projectile front are subjected to erosion, whereas both the remaining ceramic and composite backing plate are assumed to be stationary. By applying the modified Bernoulli's equation which equates the pressure at the projectile-target interface:
Yp
1 1 2 2 p v u Yco c u w 2 2
(1)
where YP is the flow stress of projectile material, Yco flow stress of intact ceramic material,
p
density of projectile material, c density of ceramic material, v velocity of projectile rigid part, u penetration velocity, w velocity of remaining fragmented ceramic and back plate ahead of projectile (w=0). From Eqn. (1), the current penetration velocity can be calculated as a function of velocity (v):
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u
v
v 2 1 1
(2)
where:
c , P
and
2 Y p YCo p
.
(3)
From the equation of motion of projectile rigid part, the deceleration of projectile rigid mass during penetration process is represented by:
Yp dv dt p .L
(4)
where L is the length of projectile rigid mass. The other equations which govern this phase are: - The time rate of change of mass of projectile rigid part is:
dM p dt
p Ap v u
(5)
where Ap is the cross-sectional area of the projectile. - The time rate of change of length of projectile rigid part is:
dL v u dt
(6)
Finally, the time rate of change of penetration depth of projectile is:
dX u dt
(7)
where X is the projectile penetration depth. End conditions The present phase terminates when the projectile tip and cracking front positions coincide [14], i.e. when ceramic conoid is detached from the ceramic tile as shown in Fig. 1a, i.e. X S crack H Co ,
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i.e.
X Vcrack .t H Co
(9)
where Scrack is the distance traveled by radial cracks front through ceramic thickness, t is the penetration time, and Vcrack the velocity of radial cracks front propagated through ceramic thickness. The velocity "Vcrack" is assumed to be equal to one-fifth the value of ceramic's longitudinal elastic wave velocity "C" [15].
Phase (ii): Penetration of Fragmented Ceramic When the projectile front meets the cracking front, the penetration proceeds into a volume of damaged ceramic whose mechanical properties have been reduced. The volume of fragmented ceramic has a conoid shape. This conoid has been physically separated from the remaining intact ceramic tile by cracks. It is accelerated in the impact direction and distributes the pressure on the backing composite plate. According to the relative velocities between the velocity of projectile rigid mass "v", the penetration velocity "u" and the velocity of conoid/composite "w"; this phase may be divided into three stages as shown in Table 1. Due to the motion of projectile and the cylindrical part of fragmented ceramic ahead of projectile, the composite backing plate begins to stretch. A circumferential resisting force, which acts at the ceramic/composite interface, will resist the motion of the moving masses. The end conditions of the first phase will decide the initial conditions of the subsequent stage of phase (ii).
Stage (1): Penetration of eroding projectile into eroding fragmented ceramic In this stage, the projectile front at the interface is still eroded, cf. Fig. 1b. Bernoulli's energy balance equation is applicable:
Yp
1 1 2 2 p v u Yc c u w . 2 2
(10)
Table 1 The possible stages of the second phase. No.
2 3
Condition
Penetration of eroding projectile into eroding v>u,u>w fragmented ceramic Penetration of rigid projectile into eroding v=u,u>w fragmented ceramic Penetration of eroding projectile into rigid v>u,u=w fragmented ceramic
X < Hco
1
Stage
Ceramic penetration strength is dramatically decreased after fragmentation and its mechanical properties are reduced. So, the penetration resistance decreases and the flow stress of fragmented ceramic is given by [14]:
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v w Yc Yco . v f 1st
2
(11)
where Vf1st is the velocity of projectile rigid mass at the end of first phase, and w is the instantaneous velocity of conoid-composite mass. From Eqn. (11), the current penetration velocity can be calculated as a function of velocity (v) and back plate velocity (w) as:
u
v
w
v w 2 1 Y c Y p p 2
1
(12)
The current deceleration of projectile rigid mass during penetration process can be calculated using Eqn. (4), the time rate of change of mass of projectile rigid part is calculated using Eqn. (5), whereas the time rate of change of length of projectile rigid part is calculated using Eqn. (6). The current acceleration of the back face of cylindrical part of fragmented ceramic ahead of the projectile and the composite backing plate can be calculated as follows:
M mov
dw Yc Ap Fresis. dt
(13)
and:
Mmov c . Ap . Hcf b . Ap . Hb
(14)
where Mmov is the total mass of moving parts ahead of the projectile, Hcf is the current thickness of fragmented ceramic ahead of projectile, Hb is the total thickness of composite backing plate, b is the density of the fabric material, and Fresis is the resisting force of backing plate against moving parts which equals to the length of circumference of the projectile multiplied by the circumferential force of composite backing plate. The resisting force of composite plate is represented as follows:
Fresis 2 R 1 .F
(15)
where F is the axial load per unit of circumference and R1 is projectile radius. The role of this force is appeared and explained in details when modeling the penetration of composite backing plate by a projectile alone or projectile and remaining ceramic. As the ceramic is subjected to erosion, the rate of change of fragmented ceramic thickness can be calculated as follows:
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dH cf dt
u w
(16)
Finally, the time rate of change of penetration depth of projectile is computed using Eqn. (7). End conditions: The current stage terminates if any of the following conditions is met. Then, a new stage or phase may be started as shown in Table 2. Table 2 The end conditions of stage (1)/phase (II) and the subsequent stage. No.
End condition
Subsequent Stage/Phase
1 2 3
X = Hco v=u u=w
Case(1)/Phase (III) Stage (2)/Phase(II) Stage (3)/Phase(II)
Stage (2): Penetration of rigid projectile into eroding fragmented ceramic This stage starts when the penetration velocity "u" is equal to the velocity of projectile rigid mass "v". So, Bernoulli's equation at the projectile-ceramic interface becomes:
Yp Yc
1 2 c u w 2
(17)
The deceleration of projectile rigid mass during penetration process can be calculated using Eqn. (4). In this stage, mass and length of projectile rigid part remain constant and equal to the mass and length of projectile at the end of first stage. The acceleration of the back face of cylindrical part of fragmented ceramic ahead of the projectile and the composite backing plate can be calculated using Eqn. (13) and the rate of change of fragmented ceramic thickness can be calculated using Eqn. (16). Finally, the time rate of change of penetration depth of projectile is computed using Eqn. (7). End conditions: This stage terminates if any of the following conditions is met. Then, a new stage or phase may be started as shown in Table 3. Table 3 The end conditions of stage (2)/phase (II). No.
End condition
Subsequent Stage/Phase
1 2
X = Hco u=w
Case(2)/Phase (III) Stage (3)/Phase(II)
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Stage (3): Penetration of eroding projectile into rigid fragmented ceramic This stage starts when the penetration velocity "u" is equal to the velocity of conoid-composite "w". So, Bernoulli's equation at the projectile-ceramic interface becomes:
Yp
1 2 p v u Yc 2
(18)
The deceleration of projectile rigid mass during penetration process can be calculated using Eqn. (4). From Eqn. (18), the current penetration velocity can be calculated as a function of velocity (v):
u v
2(Y c Yp )
(19)
ρp
while the time rate of change of the projectile rigid mass computed from Eqn. (5) and the time rate of change of length of projectile rigid mass from Eqn. (6).Finally, the time rate of change of penetration depth of projectile is computed using Eqn. (7). End conditions: This stage terminates if the following condition is met. Then, a new phase may be started as shown in Table 4. Table 4 The end conditions of stage (3)/phase (II). No.
End condition
Subsequent Stage/Phase
1
v=u
Case(2)/Phase(III)
Phase (iii): Penetration of Composite Backing Plate During this phase, penetration of backing plate may occur in the form of some cases according to the relative velocities between the moving masses in addition to the penetration depth "X". The present phase includes the following cases: Case (1): The penetration may continue by the projectile only (if the fragmented ceramic conoid ahead of the projectile is completely eroded at the end of the previous phase), cf. Fig. 1c. Case (2): The penetration may continue by the projectile and the remaining mass of fragmented ceramic (if this mass is greater than 0.1 g) [Ref.]. A single projectile is considered to penetrate the composite backup having a mass consisting of the masses of remaining projectile and fragmented ceramic and the same total kinetic energy [2], cf. 1d. During the penetration process of composite, projectile only or projectile and the mass of remaining fragmented ceramic is considered to be rigid and moves with current velocity v until composite is failed. 9/21
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Modeling of composite backing plate penetration The mathematical model introduced by Vinson and Zukas [16] and then developed by Taylor and Vinson [11] is selected herein for determining the structural response of textile composite fabric subjected to ballistic impact by a projectile. The analysis of this model is based on the theory of linear conical shells under axially symmetric loads. The variables required into such analysis are those describing the geometry of the impact body, mass and radius of the projectile, as well as the properties of the fabric. This analysis also used the tensile strain as failure criteria to stop model calculations when penetration occurs. In our case, the target consists of ceramic tile backed by composite. Therefore, output of the ceramic tile part model are the input of the textile composite backing plate model. These input are the remaining masses of both the projectile and the ceramic conoid ahead of the projectile and the final velocity of them after terminating the ceramic penetration process. Upon transversely impacting the fabric by a projectile, a conical deformation results analogous to the V-shaped deformation of a single fiber. Figure (1)e shows a horizontal yarn transversely impacted by projectile "A" traveling in the vertical direction with velocity "V". Because of impact, two longitudinal strain waves are initiated and propagated horizontally with velocity "C" in opposite directions away from the impact point "A". Concurrently, a transverse wave of velocity " U " is generated which causes the inverted V-shaped deformation pattern to propagate to point "P" at time "t". The strain wave velocity C relative to such unstrained points on the yarn, at more distance away from ‘C t’ is given by:
C
1 dT M d 0
(20)
where M is the mass per unit length of the unstrained yarn, and (dT/dε)ε=0 is the initial slope of the yarn tension-strain curve. The vertical velocity V and the velocity of transverse wave front U are represented by [11]: V C ( 1 )[ (1 ) ] 2
(21)
U C[ (1 ) ]
(22)
and:
where ε is the yarn strain. The velocity V at ε =0 is represented by the velocity at which the projectile alone or projectile and remaining ceramic starts to penetrate the backing composite. Equation (22) derived by Vinson and Zukas [16] is modified by Taylor and Vinson [11] who represented the velocity of transverse wave front as a function of projectile velocity V as:
U 64(0.74V )
(23)
The linear conical shell theory is used to drive the equations necessary for determining the displacements, stress resultants, and couples for the generalized case of truncated conical shell 10/21
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under axially symmetric loading. The axial displacement of conical shell Utot, at incremental time ∆t is represented by (cf. Fig. 1f):
U
tot
R 1 .F E.H b .sin βsinβ
R2 .ln 2 β R1
(24)
where R1 is projectile radius, F is the axial load per unit of circumference, E is the elasticity modulus of the fabric, Hb is the total thickness of the fabric, β is the rotation angle of the fabric with respect to the normal of the middle surface, and R2 is the product of the transverse wave velocity U and time t in addition to the radius R1. Equation. (24) can be used to determine the axial load F caused when the fabric is elongated an amount Utot. as follows:
E .H b U tot . . sin . cos F . R1 ln R 2 R 1
2
(25)
and, the rotational angle "β" is given by:
tan 1R2 Utot .
(26)
In addition, the projectile deceleration is calculating by dividing the circumferential force by the projectile mass as:
ap 2R1.F mp
(27)
In addition, the maximum strain at R = R1 is represented by conical shell theory as:
0y R 1 0y max .
U tot . . sin . cos R 1 . ln R 2 R 1
(28)
As the projectile deflects the fabric, both the level of strain and strain rate change considerably with time. Hence, the modulus of elasticity of the fabric will also change with time. From Eqn. (22) and knowing the strain of the fabric from Eqn. (28), the instantaneous modulus of elasticity E is calculated using the following equation:
E ρb .C 2 Where
b
(29)
is the density of the fabric material, and C is the velocity of sound in this material.
The main equations representing the different stages of the proposed model are arranged and compiled into a MATLAB program. The sequence of penetration stages that representing the complete penetration of ceramic/composite target by a projectile can be shown in Fig. 2. The input data to the two-part model are easily determined. The output of the model are the time histories of velocities of moving masses, projectile penetration depth and its length into the 11/21
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target. The model is capable of predicting projectile residual velocity, losses in projectile velocity and energy due to penetration and total time of penetration process. Moreover, the model is also capable of predicting the time histories of the transverse wave velocity, angle of fiber, strain of fiber, modulus of elasticity and the axial force acting on the fiber during the penetration of composite backing.
Results and Discussions In the following, the present results are classified into: (i) model validation, (ii) predictions where samples of predicted results using the present model are introduced with relevant analyses and discussions.
i) Model Validation In the following, the residual velocities obtained by the analytical model are compared with the analytical, numerical and experimental results of other investigators. Benloulo and Galvez [2] presented the values of residual velocities obtained numerically and analytically for 14 mm tungsten projectiles after they perforated AD99.5 ceramic/Dyneema targets. Table 5 lists the projectile residual velocities obtained analytically by their model and numerically by Autodyn2D due to the impact of ceramic/Dyneema composite targets with different thicknesses by tungsten projectiles with different impact velocities. The corresponding predicted residual velocities obtained by the present model are also listed in Table 5.The absolute maximum relative differences in percent between the predictions of their analytical model and numerical results and the analytical results of the proposed model, ΔVr1and ΔVr2, are listed in the same table; these are 14.7 % and 13.4, respectively. In addition, the residual velocities obtained by the analytical model are compared with the experimental measurements of Hetherington and Rajagopalan [9]. They investigated experimentally the perforation process of a range of ceramic/GFRP composite targets. In their work, 12.7 mm projectiles were fired against different combinations of ceramic and GFRP thicknesses. The predicted results of the proposed model are obtained considering the value of strain to failure of GFRP fiber. The experimental measurements of Ref. [9] and the corresponding predicted results of the proposed model are listed in Table 5. It is clear from the table that both the experimental measurements of Ref. [9] and the corresponding analytical results of the present model are in good agreement. The absolute maximum relative difference between the experimental measurement of Ref. [9] and the corresponding prediction of the present model is 9.4% when the projectile impacts a target consisting of 9 mm ceramic tile backed with 10 mm GFRP composite at Vi = 882.9 m/s.
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Table 5 Comparison between predicted residual velocities and that obtained numerically and analytically by Benloulo and Galvez [2] due to the impact of 14 mm Tungsten projectiles into Cer./Dyneema targets.
Impact vel., Vi [2] [m/s]
Cer. thick., HCo [mm]
Comp thick. Hb [mm]
1 2 3
1250 1500 1250
20 20 20
4 5
1250 1250
25 25
Target No.
Residual velocity, Vr [m/s]
Abs. max. difference [%]
Anal. [2]
Num. [2]
Current
ΔVr1
ΔVr2
20 20 25
950 1280 930
940 1220 910
1032 1306 1016
8.6 2.0 9.2
9.8 7.05 11.6
20 25
850 820
890 830
961 941
13.0 14.7
7.9 13.4
Table 6 Comparison between measured residual velocities of Ref. [9] and the corresponding predictions of the present model. Ceramic thickness, HCo [mm]
Composite Thickness, Hb [mm]
Measured impact vel. Vi [9], [m/s]
Measured residual vel. Vr [9], [m/s]
Predicted residual vel., Vr [m/s]
Abs. relative difference, [%]
4
5 8 10
898.2 882.3 881.4
832.6 826.3 802.4
814.33 775.09 758.55
2.1 6.2 5.4
6
5 8 10
880.7 893.9 878.1
800.5 802.5 760.6
779.63 762.1 723.94
2.6 5.0 4.8
9
5 8 10
898.2 880.1 882.9
693.9 658.3 621.5
759.14 702.78 679.67
8.2 6.7 9.4
ii) Predictions In the following, samples of the model predictions are presented and discussed. The obtained results are due to the impact of tungsten projectiles with different velocities into AD99.5/Dyneema targets with different thicknesses. Input data to the computer program for the considered projectile and targets are that used in experimental program of Ref. [2]. All these data are listed in Table 7. The introduced results are: (i) effect of impact velocity, (ii) effect of target thickness and (iii) time histories results.
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Table 7 Input data to the computer program [2]. Parameter
Projectile
Ceramic
composite
Material Caliber [mm] Length [mm] Mass [kg] Density [kg/m3] Elasticity modulus [GPa] Flow stress [MPa] Failure strain ε [%]
tungsten 14 35.2 114.3 18100 300 3200 -
AD 99.5% 3840 310 7500 -
Dyneema 970 100 3.5
(a) Effect of impact velocity Figure 3 plots the predicted change of residual velocity with impact velocity for AD99.5 cer./Dyneema targets with different thicknesses. The straight line fit that correlates the residual velocity with impact velocity for each bi-element target is also plotted on the same figure. For each considered target, It is seen from the figure that the residual velocity increases with impact velocity. In addition, the model predicts that the ballistic limit of the target consisting of 40 mm AD99.5 ceramic backed by 40 mm Dyneema is close to 1000 m/s. Figure 4 plots the predicted change of residual length of projectile with impact velocity for the different bi-element targets considered. The straight line fit that correlates the residual length of projectile with impact velocity for each bi-element target is also plotted on the same figure. For each considered target, it is shown from the figure that the residual length decreases with increasing the impact velocity. This is could be attributed to the increase of erosion rate of projectile length during ceramic penetration (cf. Eqn. (6)) with impact velocity. Figure 5 plots the predicted change of projectile energy loss ratio, ΔE/Ei, with impact velocity for the different bi-element targets considered. The straight line fit that correlates the projectile energy loss ratio with impact velocity for each bi-element target is also plotted on the same figure. For each considered target, it is seen from the figure that the projectile energy loss ratio decreases with increasing the impact velocity. This is may be due to the earlier tensile failure of the backing composite with the increase of impact velocity which, in turn, decreases the target resistance against projectile penetration. In addition, the model predicts that the target consisting of 40 mm AD99.5 ceramic backed by 40 mm Dyneema is capable of absorbing the total impact energy when Vi is close to 1000 m/s. (b) Effect of backing composite thickness of bi-element target Figure 6 plots the predicted change of projectile residual velocity as function of ceramic thickness for different backing thicknesses at Vi = 800 m/s. For each Dyneema backing thickness, it is seen from the figure that the residual velocity decreases with increasing of ceramic thickness. In addition, the drop in residual velocity, at each ceramic thickness, due to the change of backing thickness is relatively small. This reflects the influence of Dyneema backing thickness on the ballistic resistance of the whole bi-element target. The great ballistic resistance of the bi-element target is achieved by ceramic tile while the backing composite is only for containing the ceramic fragments which resist the projectile advancement into the target.
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Figure 7 plots the predicted change of projectile residual length as function of ceramic thickness for different backing thicknesses at Vi = 800 m/s. For each Dyneema backing thickness, it is seen from the figure that the projectile residual length decreases linearly with increasing of ceramic thickness. This is could be attributed to the erosion time of projectile front which increases with ceramic thickness. Moreover, the present model predicts that the projectile penetrates the Dyneema composite backing thickness as a rigid mass and the increase of its thickness does not have any influence on the decrease of residual projectile length. Figure 8 plots the predicted change of projectile energy loss ratio, ΔE / Ei, with ceramic thickness for different thicknesses of composite backing of the bi-element targets considered. For each Dyneema thickness, it is seen from the figure that the projectile energy loss ratio increases linearly with increasing ceramic thickness. Moreover, the increase in projectile energy loss ratio due to the change of backing thickness only is relatively small which indicates that the influence of composite backing thickness on the projectile energy loss ratio is not significant.
(iii) Time Histories Results The model was run using the data of AD99.5 ceramic/ Dyneema targets that were struck by 14 mm tungsten projectiles. In the following, a set of time histories results are presented for Ceramic/Dyneema targets. The set of time histories include velocities of moving masses, depth of penetration, and projectile length. a) Velocity of moving masses-time history Figure 9 plots the time histories of the velocity of projectile rigid mass, v, penetration velocity, u, for a bi-element target consisting of 30 mm-thick AD99.5 ceramic backed by 10mm-thick Dyneema at Vi = 800 m/s. It is seen from this figure that both the velocity of projectile rigid mass and the penetration velocity decrease during the first penetration phase with the increase of time. During the second penetration phase, the rate of increasing the penetration velocity u is great. When the velocity of rigid mass of projectile v is equal to the penetration velocity u, the projectile penetrates the remaining ceramic as a rigid mass. The velocity V continuously decreases until the moment at which the penetration of fragmented ceramic terminates and the projectile starts to penetrate the Dyneema composite backing. Penetration phase III continues until the tensile fail of fabric occurred. The present model predicts that the total time of penetration of the considered target is 192 µs and the residual velocity of projectile is 48 m/s. b) Depth of penetration-time history Figure 10 plots the time histories of projectile penetration depth x for the bi-element target consisting of 20 mm AD99.5 ceramic backed by 20 mm Dyneema at different impact velocities, respectively. For each impact velocity, it is seen from this figure that the trends of projectile penetration depths are similar. In the second phase where the strength of ceramic is degraded due to its fragmentation, the rate of projectile penetration depth increases. When the projectile reaches the third phase of penetration, the only resisting force is the tensile strength of the Dyneema which reaches to the failure value at the end of this phase. Therefore, the rate of penetration depth of Dyneema is too high compared with the penetration rate of ceramic. The present figure also shows that the total time of penetration decreases with increasing impact velocity. The model predicts that the total times of penetration are 48, 36, and 31 µs when the projectile impacts the considered target with velocities of 800, 1000 and 1200 m/s, respectively.
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c) Projectile length-time history Figure 11 plots the predicted change of length of projectile rigid mass as function of time during its penetration of the bi-element targets with different thicknesses, respectively. It is seen from the figure that the length of projectile rigid mass decreases with increasing the ceramic thickness. Moreover, the decreasing rate of length of rigid mass of projectile is high after the projectile starts the penetration process of each target. This is may be due to the increase of erosion time of projectile front until it reaches the moment at which it starts to move as rigid mass (v=u). After the moment at which v=u, the projectile completes the penetration process of the remaining fragmented ceramic and the backing composite without change of its length.
Conclusions
The proposed analytical model is capable of simulating the penetration process of small caliber projectiles into bi-element targets consisting of ceramic tile backed by composite. The predicted projectile residual velocities using the present model are in good agreement with the corresponding experimental measurements of other investigators who used different ceramics and composites for constructing their bi-element targets. The proposed model predicts that most of the projectile energy loss is dissipated during its penetration into the ceramic tile. However, the projectile energy loss during its penetration through the backing composite is relatively small. The effect of the backing composite of the bi-element targets on the projectile erosion is none. Projectiles are subjected to erosion only during their penetration into ceramic. Experimentation is needed to cover the drawn conclusions.
References [1] [2] [3] [4]
[5] [6]
[7]
[8] [9]
I.S.C. Benloulo and V.S. Galvez, "An Analytical Model to Design Ceramic/Composite Armors", 17th Int. Symp. On Ballistics, Midrand, South Africa, March 23–27 (1998). I.S. C. Benloulo and V.S. Galvez, "A New Analytical Model to Simulate Impact onto Ceramic/Composite Armors", Int. J. Impact Eng., Vol. 21, No. 6, PP. 461–471 (1998). I.S.C. Benloulo, J. Rodriguez and V.S. Galvez, "A Simple Analytical Model to Simulate Textile Fabric Ballistic Impact Behavior", Textile Res. J., July, (1996). C. Navarro, M. A. Martinez, R. Cortes and V. S. Galvez, "Some Observations on the Normal Impact on Ceramic Faced Armors Backed by Composite Plates", Int. J. Impact Eng., Vol. 13, No. 1, pp. 145–156 (1993). A.M. Yakoub, "Ballistic Resistance of Modern Armors", Ph.D. Dissertation, Military Technical College, Cairo (2001). M. Ravid, S.R. Bodner and I.S.C. Benloulo, "Penetration Analysis of Ceramic Armor with Composite Material Backing", 19th Int. Symp. On Ballistics, Interlaken, Switzerland, May 7–11 (2001). Z. Fawaz, W. Zheng and K. Behdinan, "Numerical Simulation of Normal and Oblique Ballistic Impact on Ceramic/composite Armors", J. Composite Structures, Vol. 63, pp. 387–395 (2004). M. Mayseless, "Impact on Ceramic Targets", J. Appl. Mech., Vol. 54, pp. 373–378 (1987). J.G. Hetherington and B.P. Rajagopalan, "An Investigation into the Energy Absorbed During Ballistic Perforation of Composite Armors", Int. J. Impact Eng., Vol. 11, No. 1, pp. 33–40 (1991). 16/21
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[10] A.L. Florence, "Interaction of Projectile and Composite Armor", Internal Report, US Army, August (1969). [11] W.J. Taylor and J.R. Vinson, "Modeling Ballistic Impact into Flexible Materials", J. AIAA, Vol. 28, No. 12, PP. 2098–2103 (1990). [12] A. Tate, “A Theory for the Deceleration of Long Rods After Impact”, J. Mech. Phys. Solids, Vol. 15, pp. 387-399 (1967). [13] A. Tate, “Further Results in the Theory of Long Rod Penetration”, J. Mech. Phys. Solids, Vol. 17, pp. 141-150 (1969). [14] R. Zaera, and V. S. Galves, "Analytical Modeling of Normal and Oblique Ballistic Impact in Ceramic/Metal Lightweight Armors", Int. J. Impact Eng., Vol. 21, No. 3, pp. 133–148 (1998). [15] P.C. den Reijer, "Impact on Ceramic Faced Armor", Ph. D. Thesis, Delft University, (1991). [16] J.R. Vinson and J.A. Zukas, "On the Ballistic impact of Textile body Armor", J. Appl. Mech., Vol. 42, PP. 263–268, June (1975).
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a) Schematic drawing of first phase of penetration process.
b) Schematic drawing of the second phase of penetration process.
c) Schematic drawing of case(1) of third phase.
d) Schematic drawing of case(2) of third phase.
e) Horizontal yarn impacted by a projectile [16].
f) Model of impacted textile fabric in the theory of linear conical shells [16].
Fig. 1 A schematic drawing of some penetration stages of a ceramic/composite armor. 18/21
Paper: ASAT-13-ST-24
START
INPUT DATA
CERAMIC FRAGMENTATION
X + Scrack = HCO
No
Yes
PENETRATION INTO FRAGMENTED CERAMIC v>u , u>w , Xw , Xu , u=w
No
u=w
No
X>H CO
No
Yes
ERODED PROJECTILE PENETRATION INTO BACKPLATE
v>u , X>H CO
X=H CO
No
v=u No
No
v=u
Yes Yes
Yes
rigid projectile penetration into backplate v=u , u>w
u=w
Yes Yes
rigid projectile & remaining ceramic penetration into backplate
v=u=w
No
u=w
ERODED PROJECTILE PENETRATION INTO BACKPLATE
v>u , u=w Yes
No
RIGID PROJECTILE PENETRATION INTO BACKPLATE
max> f
No
Yes
v=u
v=u=w No
Yes
max> f
END
Fig. 2 A flow chart showing the sequences of penetration stages of ceramic/composite target by a projectile. 19/21
Paper: ASAT-13-ST-24
1400
35 Target: AD99.5 / Dyneema Projectile: Tungsten
Target: AD99.5 / Dyneema Projectile: Tungsten
1200
Residual length, Lr [mm]
Residual velocity, Vr [m/s]
30
1000 800 600 400
=10 mm / 10 mm =20 mm / 20 mm
200
25
20
= 10 mm = 20 mm = 30 mm = 40 mm
15
=30 mm / 30 mm =40 mm / 40 mm
0 800
900
1000
1100
1200
1300
10 800
1400
900
1000
1100
1200
1300
1400
Impact velocity, Vi [m/s]
Impact velocity, Vi [m/s]
Fig. 3 Predicted change of residual velocity with impact velocity for different bi-element targets.
Fig. 4 Predicted change of projectile residual length with impact velocity for different bi-element targets.
120
800
100
10 mm 20 mm 30 mm 40 mm
Residual velocity, V r [m/s]
10 mm / 20 mm / 30 mm / 40 mm /
Target: AD99.5 / Dyneema Projectile: Tungsten Energy loss ratio, ΔE / Ei [%]
/ 10 mm / 20 mm / 30 mm / 40 mm
80
60
40
20 800
900
1000
1100
1200
1300
Hb = 10 [mm] = 20 [mm] = 30 [mm] 700
600
500
Target: AD99.5 / Dyneema Projectile: Tungsten Vi = 800 m/s
400
1400
0
Impact velocity, Vi [m/s]
5
10
15
20
25
Ceramic thickness, Hco [mm]
Fig. 5 Predicted change of projectile energy loss ratio with impact velocity for different bi-element targets.
Fig. 6 Predicted change of residual velocity with ceramic thickness for different composite backing.
80
34 Hb = 10 [mm] = 20 [mm] = 30 [mm]
Energy loss ratio, ΔE / Ei [%]
Residual length, Lr [mm]
32
30
28
Target: AD99.5 / Dyneema Projectile: Tungsten Vi = 800 m/s
26
Target: AD99.5 / Dyneema Projectile: Tungsten Vi = 800 m/s
70 60 50 40 30
Hb =10 [mm] = 20 [mm] = 30 [mm]
20 10
24 0
5
10
15
20
0
25
Fig. 7 Predicted change of residual length of projectile with ceramic thickness for different composite backing.
5
10
15
20
25
Ceramic thickness, Hco [mm]
Ceramic thickness, Hco [mm]
Fig. 8 Predicted change of projectile energy loss with ceramic thickness for different composite backing.
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900
40
v u
35
750
Penetration depth, x [mm]
30 mm AD99.5 / 10 mm Dyneema Projectile : Tungesten
Phase (II)
600
Vi= 800[m/s]
450 Phase (III)
300 Phase (I)
150
30 25 20 15 AD99.5+Dyneema Hco=20[mm] Hb=20[mm]
10
Vi=800[m/s] Vi=1000[m/s] Vi=1200[m/s]
5
0
0
0
50
100
150
0
200
5
10
15
20
25
30
Fig. 9 Predicted time history of the velocity of projectile rigid mass and penetration velocity.
AD99.5+Dyneema Vi=800[m/s] 10/10[mm]
VR=679[m/s]
20/20[mm] 30/30[mm]
30 VR=493[m/s]
25
VR=16[m/s]
20
15 0
20
40
45
Fig. 10 Predicted time history of the projectile penetration depth for different impact velocities.
40
35
35
Penetration time, t [µsec.]
Penetration time, t [µs]
Projectile length, LP [mm]
Velocity, v and u [m/s]
Target:
40
60
80
100
120
140
160
180
Penetration time, t [µsec.]
Fig. 11 Predicted time histories of the projectile length for different target thicknesses
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200
50
