SOME ASPECTS OF MACHINE GUN PENETRATION OF … Mechanical/Hub_S… · some aspects of machine gun...

ANSYS konference 2010

Frymburk 6. - 8. října 2010 1

SOME ASPECTS OF MACHINE GUN PENETRATION OF

THE ALUMINIUM SHEET-METAL PLATE USING ANSYS

AUTODYN

Authors:

Ing. Juraj HUB, Ph.D., Department of Aerospace and Rocket Technologies, UNIVERSITY OF DEFENCE, Brno, e-mail: [email protected] Mjr. Ing. Luděk JEDLIČKA, Ph.D., Department of Weapons and Ammunition, UNIVERSITY OF DEFENCE, Brno, e-mail: [email protected]

Anotace:

Článek předkládá simulaci průstřelu duralového plechu střelami vojenských nábojů ráže 7,62x54R (7,62-59) a 12,7x108 (12,7-PZ32) pomocí numerického kódu Ansys Autodyn v.11. Plechy jsou vyrobeny z duralové slitiny D16AT, která se používá v konstrukci letadel; mají kruhový tvar a jsou po svém vnějším okraji vetknuty. Tloušťky materiálu jsou v rozsahu 0,6 až 2,5 mm. Článek předkládá simulační materiálový model pro střelu i cíl založený na experimentech, výsledky simulace a experimentu jsou vzájemně porovnány a dále jsou komentovány faktory ovlivňující proces průstřelu i tvorby modelu. Dále je uveden balistický limit prostřelovaného plechu ve tvaru mezní rychlosti střely, která nedokáže uvažovaný plech plně proniknout. Simulace poskytují vhled do procesu penetrace. Výsledky mohou být využity při pevnostních analýzách leteckých konstrukcí poškozených střelou v průběhu bojových operací.

Annotation:

The paper deals with numerical simulation, through the numerical code Ansys Autodyn v.11, of the penetration of 7.62-59 and 12.7-PZ32 bullets into a sheet metal plate. Fully clamped cylindrical plates are made of aluminium alloy D16AT used in aircraft structures. The thicknesses of the plates are from 0.6 to 2.5 mm. The paper presents material models used for the numerical system parts: both kind of bullets and the sheet metal. The simulation conditions are based on experiments, the results are compared and influencing factors are discussed. Next the ballistic limit of the sheet metal is introduced in terms of an ultimate bullet velocity when no full perforation of the sheet metal occurs. The simulations provide some useful insight into the penetration mechanisms. The results obtained can be useful in the analysis of the airframe structures with battle damage caused during war operations.

Introduction

Air operations bring the possibility of battle damage caused by vyrious anti-aircraft systems. Aircraft damage influences operational capabilities, aircraft abilities to fly, to return to the airbase, landing, reusing in mission and servicing. Finding a tool for airframe ballistic



resistance estimation will help to evaluate the flying, operational and combat capabilities. The paper introduces the contribution to the estimation of the ballistic resistance of the airframe structure using the Finite Element Method (FEM).

Two of the possible anti-aircraft machine gun ammunitions used in war operations are the projectile of caliber 7.62-59, known also as 7.62x54R, with armour piercing full metal jacket bullet with steel core and the projectile 12.7-PZ32, known also as 12.7 API or 12.7 B-32, with steel core and incendiary composition in tip. The probability of hitting the aircraft increases for take-off and landing and is essential especially for low attitude and slow speed target as helicopter. The helicopter fuselage is the largest aircraft area of possible impact and penetrating the airframe and sequential damage of inner systems can be fatal. The work is focused on Mi-8 helicopter rear fuselage part of a semimonocoque structure consisting of spars, ribs and skin made of alluminium alloy. A semimonocoque structure allows carrying the load even when damaged enabling the load distribution to adjacent parts.

The goal of this paper is to describe the effect of the 7.62-59 and 12.7-PZ32 bullets penetrating the sheet metal plates made of aluminium alloy D16AT using FEM. The thicknesses of the plates are of the values from 0.6 to 2.5 mm, which are typical values used for airframe skins of airplanes used also within Czech Air Forces. First step is to find a FEM model for the both bullets and the target based on real experiments. Next goal is to examine the ballistic limit of sheet metal plates in terms of an ultimate bullet velocity that is not sufficient to penetrate the target completely.

The results can be useful for airframe structure ballistic resistance estimation exposed to the impact of mentioned ammunition. Penetration is defined as an event during which a bullet creates a discontinuity in the original surface of the target. Perforation requires that, after bullet or its remnants are removed, light may be seen through the target [1]. The ballistic resistance of the target means the ability of the tareget to avoid the complete penetration of the target upon the impact of ballistic object with specific energy, e.g. the bullet or a part of it, fragment. The target is considered to be ballistic resistant in case of bringing the ballistic object to stop or pushing the object aside [2].

Experimental Shooting

Shooting experiments are the basis for creating the the simulation model and were carried out using 7.62-59 and 12.7-PZ32 projectiles firing into the aluminium alloy sheet metal samples of the material of the thickness 0.6, 1.2, 1.8 and 2.5 mm for the 7.62 bullet and of the thickness 1.2, 1.8 and 2.5 mm for the 12.7 bullet, both in the perpendicular direction towards the target [3,4]. The sheet metal plates had the rectangular dimension of 200 mm x 400 mm. Each plate thickness was subjected to impact and perforation by bullets travelling at velocities within the range of 873.4 – 900.1 m·s-1 for 7.62 bullet, respectively of 811.1 – 821.3 m·s-1 for 12.7 bullet, in an upright direction towards the plate. The firing distance was 10 m, see Fig. 1.

The bullet 7.62-59 is a boat-tailed cylinder of 9.45 g mass, 7.87 mm diameter in cylindrical part and 31.24 mm length. The bullet is of a three-part design with the hard steel core, a



relatively soft lead filling and a gilding metal jacket (tombac). The bullet 12.7-PZ32 is a boat-tailed cylinder of 49.5 g mass, 12.98 mm diameter in cylindrical part and 64.5 mm length. The bullet is of a three-part construction with the steel core, a soft incendiary composition in tip and a gilding metal jacket.

In each case the velocity of the bullet was measured using optical gates before the impact with the target vexp1 and after it had perforated the target vexp2 according to Fig. 1. The mean measured velocities were modified with respect to the distance between measured and the target positions to the values v1, v2 and shown are in Tab. 1. The modified striking velocity before penetration v1 was used for the FEM simulations to represent the initial bullet velocity vsim1 = v1 and the modified residual velocity after penetration v2 was used for the comparing with simulation velocity vsim2 after the complete penetration of the target.

2m 1m

10m 1m0.5m

barrel

optical gatevexp1 vexp2

target

v1

v2

opticalgate

Figure 1. Experimental shooting Bullet Target Experimental velocity Simulation velocity

caliber thickness t v1 v2 vsim2 ∆ [mm] [mm] [m·s-1] [m·s-1] [m·s-1] [%] 7.62 0.6 881.2 876.7 876.2 -11.1 1.2 881.3 875.0 874.0 -15.9 1.8 880.3 869.9 869.2 -6.7 2.5 880.1 861.5 864.3 15.1 12.7 1.2 808.0 805.3 805.0 -11.1 1.8 813.8 808.5 808.4 -1.9 2.5 818.2 809.7 810.0 3.5 Table 1. Experimental and simulation results

FEM model

All FEM models were prepared using the explicit non-linear transient hydrocode Autodyn v.11 inplemented in the system Ansys Workbench with 2D symmetry so only a half of all



parts were modelled. The model of both bullets was created upon the real geometry with equal outer dimensions. The geometry of the bullets was a little bit simplified in order to creating the suitable mesh. The volume and density of both steel cores, lead filling for the bullet 7.62 and both gilding metal jackets were modified to achieve also equal total weight of the bullets.

The model of the targets has the thickness upon the experimental parts and has in 2D projection a rectangular shape that creates a thin disc using axial symmetry. The periphery of the disc is clamped. The simulation methodology is taken from [5-7]. The character and discretization of the model of the bullet and the target is shown in Fig. 2. The incendiary filling in the tip of the bullet 12.7 is ignored due to its soft nature so there is a cavity in the front of the bullet. The initial condition for the bullets is initial bullet velocity vsim1. The rotation of the bullets causing by barrel bore and air drag are not considered.

31.24 mm 2.5 mm

1.8 mm1.2 mm0.6 mm

100 mm

gilding metaljacket core

- steel

filling- lead target - aluminium alloy

2.5 mm

1.8 mm1.2 mm

12.98 mm

64.5 mm

100 mm7.87 mm

core - steelgilding metal jacket

target - aluminium alloy

7.62-59 12.7-PZ32

Figure 2. FEM model of the bullet and the target

All material models for the bullet and the plate were retrieved from the Autodyn material libraries [8] due to the fact, that experimental searching for the dynamic material characteristics facing high strain rates needs very special equipment [9] and there is still limited published data available on the dynamic material properties of used materials.

A sheet metal plate of the target made of the aluminium alloy D16AT is considered to be equivalent to ASTM 2024-T3 alloy [10-11], which is to some extend available in the Autodyn library.

The hydrodynamic shock equation of state relating stress to deformation and internal energy is in the Grüneisen form [8,12]

( )HH eepp −+= ρΓ , (1)

where p is hydrostatic pressure, pH is Hugoniot pressure, Γ is Grüneissen Gamma, ρ is density of the alloy 2024-T3, e is internal energy, eH is Hugoniot energy. The pressure is based on a linear Hugoniot relation between shock velocity us and particle velocity up

p10s uSCu += , (2)



where C0 is initial sound speed and S1 is Hugoniot slope coefficient. The values are shown in Tab. 2.

The constitutive model expressing the relation between the shear stress and strain uses Johnson-Cook model representing the strength behaviour of materials subjected to large strains, high strain rates and high temperatures as it is the solving high-speed impact. The empirical Johnson-Cook model [13] for the von Mises flow stressσ , decouples the effect of strain, strain rate and temperature, namely,

( ) [ ][ ][ ]m**nT1 lnC1 BAT,,f −++== εεεεσ && , (3)

where ε is the equivalent plastic strain, 0

*/ εεε &&& = is the dimensionless plastic strain rate

for -1

0 s0.1=ε& and T* is the homologous temperature. The five material constants are as

follows: A is the yield uniaxial stress, B is strain hardening coefficient, n is strain hardening exponent, C is strain rate hardening coefficient and m is thermal softening exponent. The actual values of the constitutive constant used for the material 2024-T3 are shown in Tab. 2 according to [14-15].

In order to describe the damage of the material it is necessary to consider also the failure criterion. Very convinient model has been proposed by Johnson-Cook [8,16]. This model assumes that damage accumulates in the material element during plastic straining and that the material breaks when the damage reaches a critical value. This model is constructed in a similar way to the Johnson-Cook strength model in that it consist of three independent terms that define the dynamic fracture strain as a function of pressure, strain rate and temperature

[ ][ ][ ]*

5

*

4

D

21

fTD1 lnD1 eDD

*3 +++= εε σ

& . (4)

The damage variable D takes values between 0 and 1. D = 0 corresponds to undamaged material and D = 1 corresponds to the fully broken material. The evolution of D is given by the accumulated incremental effective plastic strain divided by the current strain at fracture

∑=f

Dε

ε∆. (5)

The values for the fracture Johnson-Cook material model of 2024-T3 alloy according to [14-15] are in Tab. 2.

The bullet parts are described through various material models. The steel cores of both bullets are modelled using a shock equation of state and the

Johnson-Cook constitutive model of STEEL 1006 retrieved from the Autodyn library. The parameters used in simulation are shown in Tab. 2.

The lead filling of the bullet 7.62 is represented also by retrieved model LEAD from Autodyn library using shock equation of state and Steinberg-Guinan constitutive model [17]. This constitutive model is a semiempirical strain-rate independent model for the yield stress and the shear stress:

( ) ( )[ ] ( )

−

′−

′+++= 300T

G

GP

Y

Y11YT,PY

0

T

31

0

Pn

i0η

εεβ , (6)



( ) ( )

−

′−

′+= 300T

G

GP

G

G1GT,PG

0

T

31

0

P

0η

, (7)

where Y is the yield strength, G is shear modulus, ε is strain, and η is the compression. This model is an elastic-perfectly plastic model and includes the enhacement of strength due

to pressure P and work hardening β with hardening exponent n, and softening due to tempereture T. The constitutive material model values for lead filling are shown in Tab. 2. 2024-T3 Steel 1006 Lead Copper

Density ρ 2780 7222.2 11340 8800 kg·m-3 Shock C0 5328 4569 2006 3958 m·s-1 EOS S1 1.338 1.49 1.429 1.497

Γ 2.00 2.17 2.74 2.00 G 28000 81800 8600 46400 MPa J-C A 368.5 350 MPa strength B 683.9 275 MPa model C 0.0083 0.022 m 1.7 1.0 n 0.73 0.36 Steinberg Y0 8 MPa

-Guinan β 110 strength n 0.52 model G’P 1 G’T -9.976 MPa Y’P 93000 Piecewise Y0 120 MPa

J-C εP1 0.3

strength εP2 1x1020 model Y1 450 MPa Y2 450 MPa m 1 J-C D1 0.112 failure D2 0.123 model D3 1.5 D4 0.007 D5 0 Table 2. Material characteristics

The gilding metal jacket uses a shock equation of state as well and the Piecewise Johnson-Cook constitutive model of modified COPPER retrieved from Autodyn library. This model is



860

865

870

875

880

885

880.0 880.5 881.0 881.5

v1, vsim1 [m.s-1]

v 2, v

sim

2 [m

.s-1

]

sim 0.6 sim 1.2 sim 1.8 sim 2.5

exp 0.6 exp 1.2 exp 1.8 exp 2.5

v1 0.6 v1 1.2 v1 1.8 v1 2.5

7.62-59

804806808810812814816818820

805 810 815 820v1, vsim1 [m.s-1]

v 2, v

sim

2 [m

.s-1

]

sim 1.2 sim 1.8 sim 2.5exp 1.2 exp 1.8 exp 2.5v1 1.2 v1 1.8 v1 2.5

12.7-PZ32

a modification of the Johnson-Cook model, where the dependence on effective plastic strain

represented by the term (A+Bεn) in equation (3) is replaced by a piecewise linear function of

yield stress Y versus effective plastic strain εp. The strain rate dependence and thermal softening terms remain the same as in the Johnson-Cook model. The parameters used in gilding metal jacket simulation are shown in Tab. 2.

In all cases for the target and bullet the erosion in form of instantaneous geometric strain of the value 2.0 was used except the value 1.5 for target penetration by projectile 12.7. The friction coefficient of the value 0.3 was considered for the contact between gilding metal jacket of the bullet 7.62 and the aluminium target.

Results of simulation and comparison with experiments

The simulation velocities of the bullets after perforation vsim2 derived from FEM

simulations are shown in Tab. 1. Deviations ∆ express the ratio of the difference of simulation and experimental velocities after perforation vsim2 – v2 with respect to the change of experimental velocity before and after perforation v1 – v2. The experimental and simulation results are shown in graph in Fig. 3 in terms of comparison both experimental and simulation velocities after perforation v2 and vsim2; also is consiederd the striking velocity before penetration v1.. The example of FEM solution is shown in Fig. 4.

Figure 3. Experimental and simulation results The results show an excelent correspondence between the experimental and simulation

velocities after perforating the target. The simulation bullet velocity values almost copy the experimental values.

The target is perforated in all cases with sulprus of energy during the impact process. The target material is partly shearing and partly bending and some debris occurs. The plane of the target is slightly distorted and during the penetartion is springing. The both bullets show just



little deformation on the tip for higher thicknesses of the target; the deformation on the tip is more obvious with the bullet 12.7. The bullet 7.62 is a little bit distorted for higher thickness.

The difference between the experimental and the numerical results could be caused by various influencing factors. First one is due to some of the uncertainties that exist with the material model of the bullet gilding metal jacket. There is limited amount of exact dynamic material data for this kind of material. Next influencing factor are boundary conditions. In the simulation the target perimeter is perfectly clamped. On the other hand, the experimental fixing the plate could deal with a certain value of flexousity. Next factors are bullets fired on experiments as their actual weight and change of shape after perforating the plate are unknown. Also is unknown the accuracy of the bullet velocity measurement. Simplifying the bullet shape, neglecting the incendiary in tip and leaving out the rotation of the bullet can also play a significant role in simulation correspondence with respect to real behaviour. And finally, the actual experimental shape of penetrated plate was rectangular and the shape used in simulations is circular due to the axial symmetry. This discrepancy is considered neglecting due to the same minimal size of the specimen of the value 200 mm.

7.62-59 12.7-PZ32

t = 0.6 mm t = 1.2 mm

t = 2.5 mm t = 2.5 mm

Figure 4. Simulation results of penetration

Ballistic limits

A methodology for estimation the ballistic limit of considered helicopter fuselage structure impacted by projectiles 7.62-59 and 12.7-PZ32 using FEM will be presented in this chapter. First, the main parameters of the structure will be described and its parts consisting of. Next, the ballistic limit will be introduced as an evaluating factor for the structure damage when hitting by considered bullets. For this estimation of the ballistic limit the FEM model described in previous chapter will be used. Finally, the ballistic limit will be compared to the calculated firing conditions from ground position. The results will help to evaluate the possible damage of considered structure.



A rear conical semimonocoque fuselage structure consists of 26 longitudinal stiffeners, 17 ribs, skin and two flanges on both structure ends. Structure main dimensions: length 5447 mm, outer diameter on the fuselage side 971.2 mm, outer diameter on the side of the tail rotor 553.5 mm, skin thickness 0.8 and 1 mm, the Z shape rib thickness parallel to the skin 1 mm, the L shape stiffeners thickness parallel to the skin 1.6, 2.3 and 2.4 mm, both flanges consist of two parts and their total thickness parallel to the skin except the skin is 2.9 and 3.7 mm. The structure parts are riveted, see Fig. 5. The material of the whole investigated structure is considered of the same type D16AT, respectively 2024-T3, as the experimental samples described above. Description of the fuselage structure is presented more in detail in [18].

Figure 5. Airframe structure of the helicopter fuselage Mi-8

For the slimplified numerical purposes is the composition of particular structure parts considerd as one homogenous part of material of particular thickness without considering the cross section shape of the rib, stiffener and flange. Therefore the total thickness of areas subjected to possible impacting by bullets varies upon the description in Tab. 3. A ballistic limit will be then estimated for every thickness combination.

The ballistic resistance of the targets is objectively defined using limit velocity, respectively limit energy, of a particular bullet design and calibre. The limit velocity, sometimes called ballistic limit when referring to the armour, is the velocity below which a given projectile will not defeat a given target [1,2]. The higher limit velocity of the bullet means higher ballistic resistance of the target; respectively it means the lower penetrating ability of the bullet. Since penetration is somewhat stochastic event, a statistical expression for the limit velocity is used. v50 is the velocity at which a given projectile will defeat a given target 50% of the time and this velocity is commonly used as both experimental measurenets as well as both production check.

The following factors affect the limit velocity [1]: material hardness, yaw at impact, projectile density, projectile nose shape, and length to diameter ratio of the bullet. For the material hardness, in general, the harder the target, the higher v50 becomes; while the harder the penetrator, the lower v50 becomes and there is more residual penetrator. With respect to yaw at impact, the more yaw, the greater chance for breakup or ricochet and the higher v50



becomes. With bullet density, the more dens the bullet is, the lower v50 becomes. A blunter nose translates, in general, to a higher v50. If the target is overmatched significantly, however, the nose shape has negligible effect. The length to diameter ratio can go either way and a great deal depends on the obliquity of impact.

The FEM simulation using Ansys Autodyn enables to estimate the limit velocity in form of velocity v0, which means with respect to the velocity v50, no complete penetration of the target in any case upon simulation conditions and the bullet gets stuck in the target.

The limit velocity of structure areas impacted by bullet 7.62 and 12.7 then is estimated using Ansys Autodyn v.11. The methodology is based on [19,20]. The impact is considered to be of a perpendicular direction with respect to the target plane. The results are shown in graph in Fig. 6 and Fig. 7 for the simulation range of the target thicknesses from 0.6 to 4.5 mm. A linear approximation is introduced for the bullet 7.62 and a square approximation for the bullet 12.7 enabling an easy and quick estimation of the limit velocity for both kinds of bullets, for various thicknesses and easy implementation into analytical ballistic limit calculations. The example of simulation results is shown in Fig. 7 and [21] for both kinds of bullets.

vL = 34.3t + 38.4

R2 = 0.9964

0

50

100

150

200

250

0 1 2 3 4 5Target thickness t [mm]

Lim

it ve

loci

ty v

. L [m

.s-1

] .

7.62-59

vL = -14.0t2 + 112.9t - 41.4

R2 = 0.97020

50

100

150

200

250

0 1 2 3 4 5

Target thickness t [mm]

Lim

it ve

loci

ty v

. L [m

.s-1

] .

12.7-PZ32

Figure 6. Limit velocities of the both bullets

Structure area Thickness Limit velocity vL 7.62-59 12.7-PZ32

[mm] [m·s-1] [m·s-1] Skin 0.8 – 1.0 66 - 73 40 - 58 Skin + rib 1.8 – 2.0 100 - 107 116 - 128 Skin + stringer 2.4 – 3.4 121 - 155 149 - 181 Skin + flange 3.7 – 4.7 165 - 200 185 - 180 Table 3. Thickness and limit velocity of structure areas



Using the linear respective square approximation mentioned above is possible to estimate the limit velocities also for every structure area; see Tab. 3 for the results. We assume that the difference in the tendency of the course between the bullets 7.62 and 12.7 is in the character of deformation of the gilding metal jacket. The bullet of the caliber 7.62 has a compact structure consisting of three parts and the bullet of the caliber 12.7 has a cavity in the front of the bullet while the incendiary filling and the effect of its iniciation is not considered. Therefore the deformation of the gilding metal jacket in the front area of the bullet 12.7 plays an important role in the prosess of penetration. The jacket wrinkles when penetrating the target slowly and causes an additional deformation resistance and friction, see Fig. 7. A different situation occurs with the highest thickness of the value 4.5 mm, see Fig. 7, where is a large difference between the thicknesses of the target with respect to then thickness of the jacket and the shear mode of failure mechanism prevails. This mechanism leads to reduction of the limit velocity. The limit velocities should be proved by experiment.

7.62-59 12.7-PZ32

t = 0.6 mm

t = 2.5 mm

t = 4.5 mm

t = 2.5 mm

t = 0.6 mm

t = 4.5 mm

Figure 7. Simulation results of limit velocity

The course of residual velocity after penetration of the bullets with respect to the striking

velocity is shown on graph in Fig. 8 and it is party linear. The tendency of the residual velocity is not linear and rapidly changes when approaching the limit velocity. There will be a lower limit that develops below which the target is not penetrated or the bullet gets stuck in the target [1]. We assume the increased influence of the friction and bullet jacket deformation during the process of very slow bullet velocity.



7.62-59

0

200

400

600

800

1000

0 500 1000

Velocity before impact [m.s-1]

Res

idua

l vel

ocity

[m

.s -1

]

7.62-0.6 7.62-2.5

12.7-PZ32

0

200

400

600

800

1000

0 500 1000

Velocity before impact [m.s-1]

Res

idua

l vel

ocity

[m

.s -1

]

12.7-1.2 12.7-2.5

Figure 8. Course of the limit velocity

In order to compare the limit velocities with the position of the helicopter with respect to the ground firing position, a ballistic calculation on firing conditions were made for seven angles of departure: 5°, 15°, 30°, 45°, 60°, 75° and 90°. The standard artillery atmosphere was considered with following parameters: temperature 15°, relative moisture of the air 1.206 kg·m-3, wind speed 0 m·s-1, gravity constant 9.80665 m·s-2, altitude at sea level 0 m. The initial velocity of the both bullets is considered of the value 830 m·s-1.

The interesting issue is to estimate, whether the perforation occurs according to the magnitude of angle of departure and which distance is possible for the fuselage to stop the impacting bullet and prove the ballistic resistance.

The simulation limit velocity determines the distance not sufficient to completely perforate the target by the bullet and therefore the structure of the fuselage saves the inner aircraft systems.

It is possible to distinguish three cases of impacting the target on limit velocity. First one is that the bullet will impact the target on limit velocity before reaching the trajectory vertex. Next one is that the bullet will impact the target on limit velocity after reaching the trajectory vertex and the last one is that the limit velocity will not be reached at any phase of the flight trajectory. The last case means the fully perforation of the target by the bullet at any phase of the flight trajectory.

The graph in Fig. 9 shows the results in terms of the straight distance between the point of departure and the impact point on the aircraft structure surface, where the bullet reaches the limit velocity, with respect to the angle of departure and the thickness of the target. A perpendicular direction of the bullet is considered with respect to the structure surface. Solid lines represent reaching the limit velocity when the target is possible to stop the bullet and the target proves its ballistic resistance. Circle marks indicate the reaching the limit velocity after



0

1000

2000

3000

4000

0 50 100

Angle of departure [°]

Dis

tanc

e of

impa

ct p

oint

[m

] .

0.8 0.8 0.8 2.4

2.4 2.4 4.7 4.7

7.62-59

0

1000

2000

3000

4000

5000

6000

7000

0 50 100

Angle of departure [°]

Dis

tanc

e of

impa

ct p

oint

[m

] .

1.2 1.2 2.4

2.4 4.7 4.7

12.7-PZ32

the trajectory vertex. Dashed lines represent the situation that the bullet reached its range of fire earlier than reaching the limit velocity and the bullet is able to perforate the target along the whole phase of its trajectory. The graph covers only three thicknesses of the structure area driven from the Tab. 3 for both bullet calibers as an example of using the results on limit velocities.

Figure 9. Distance of the impact point versus the angle of departure

Discussion

The investigated structure expresses just a little ballistic resistance upon performed FEM simulation when facing the impact of both projectiles 7.62 and 12.7. Every limit velocity exceeds the maximum effective range of the machine gun firing the mentioned projectiles which is about 500 m for the bullet 7.62 and 1500 m for the bullet 12.7, respectively. The most probably impacted structure area is the skin with very low ballistic resistance. On the other hande the investigated semimonocoque structure easily distributes the load to adjacent parts and therefore the effect of skin damage on the airframe strangth and stiffness is supposed to be neglecting. The danger of damaging the inner systems is therefore very high. The solution is providing the structure with addition protection covering sensitive areas using e.g. composite armour materials.

Conclusion

The article presents the methodology of evaluating the limit velocities of the ammunition 7.62-59 and 12.7-PZ32 penetrating the target and ballistic resistance of the airfarme structure using FEM. A numerical model has been developed that simulates the penetration and subsequent perforation of aluminium alloy sheet metal D16AT of four thicknesses used in



aircraft structures by bullets of mentioned projectiles. The SW Ansys Autodyn provides a useful tool for modelling the bullet and the target, to consider the boundary conditions and to take an advantage of implemented material models with the possbility of modification to meet the real behaviour of the simulated object.

The FEM simulation results show:

• a good corelation between the experimental and simulation results in terms of comparison the residual velocities after penetration of the bullets through the targets,

• a crucial influence of material characteristics to simulate the experimental shooting,

• an important influence of the friction for precising the residual velocities,

• a linear dependance of the limit velocity with respect to the target thickness for single sheet metal plate,

• an important influence of the deformation of the gilding metal jacket of the bullet in the region close to the limit vlocity,

• a nonlinear course of residual velocity after penetration of the bullet with respect to the striking velocity of the bullet in the region close to the limit velocity,

• a limited ballistic resistance of investigated aluminium samples and structure facing the impact of the projectiles 7.62-59 and 12.7-PZ32.

Neverthless, the results obtained provide a tool for the analysis of the airframe structures with the bullet impact. An isolated complete penetration of the airframe structure probably will not cause the collapse of the fuselage, even multiplied. On the other hand, the consequently damage of the inner systems can be a crucial issue for flying and operational capabilities of the helicopter.

For further research it is necessary following:

• to prove the simulation ballistic limit by experiments,

• to involve also rotation of the bullets,

• to involve also a different angle of impact with respect to the surface plane,

• to simulate the structure areas with actual composition, shape and cross section of present parts; this leads to the 3D nature of the analysis and higher computational expenses,

• to investigate the whole damaged structure under operational load to predict the structure response facing the battle damage.

REFERENCES:

[1] CARLUCCI, D. E., JACOBSON, S. S., 2007: Ballistics – theory and design of guns and ammunition. CRC Press, New York, 2008. ISBN 978-1-4200-6618-0.



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