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Analytical model for cratering of semi-infinite metallic targets by long rod penetrators

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Abstract

Analytical model is presented herein to predict the diameter of crater in semi-infinite metallic targets struck by a long rod penetrator. Based on the observation that two mechanisms such as mushrooming and cavitation are involved in cavity expansion by a long rod penetrator, the model is constructed by using the laws of conservation of mass, momentum, energy, together with the u-v relationship of the newly suggested 1D theory of long rod penetration (see Lan and Wen, Sci China Tech Sci, 2010, 53(5): 1364–1373). It is demonstrated that the model predictions are in good agreement with available experimental data and numerical simulations obtained for the combinations of penetrator and target made of different materials.

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Abbreviations

ρ :

density

ρ p :

density of penetrator

ρ t :

density of target

v :

velocity of the undeformed rear of a long rod penetrator

u :

penetration velocity

Y p :

penetrator strength

R t :

target resistance

S :

static target resistance

C :

constant of the dynamic resistive pressure

U F0 :

critical penetration velocity, defined as U F0 = (HEL t/ρ t)1/2

δ :

a function of u, defined by eq. (17)

n :

constant, defined in eq. (17)

HEL :

Hugoniot Elastic Limit

HEL t :

HEL of target material

r :

initial radius of the cross section of a long rod penetrator

R m :

radius of the penetrator mushroom

A p :

initial area of the cross section of a long rod penetrator

A e :

cross-sectional area of the debris

V e :

ejecting velocity of the debris

ϕ :

Ap/Ae

θ :

tangle between arbitrary radius of the semispherical surface and penetration centerline

p :

pressure on the surface of a spherical nose

u n :

normal component of penetration velocity on the surface of the penetrator nose, viz. u n = ucos θ

F tN :

integration of p over 0 ⩽ θ ⩽ π/2

R crater :

total crater radius

I :

F tN /(πr2)

d m :

mushroom diameter, viz. d m = 2R m

d t :

total crater diameter, viz. d t = 2R c

V 0 :

impact velocity

V C :

critical velocity corresponding to u = U F0

A 0 :

initial cross-sectional area of a long rod penetrator

A c :

total crater area

E 1 :

elastic modulus

E 2 :

plastic modulus in a bilinear material model

Y 0 :

yield stress or proof stress in a true tress-strain curve

Y :

yield stress in a bilinear material model

V :

poisson ratio

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Authors and Affiliations

  1. CAS Key Laboratory for Mechanical Behavior and Design of Materials, University of Science and Technology of China, Hefei, 230027, China

    HeMing Wen, Yu He & Bin Lan

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  1. HeMing Wen
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  2. Yu He
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  3. Bin Lan
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Correspondence to HeMing Wen.

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Wen, H., He, Y. & Lan, B. Analytical model for cratering of semi-infinite metallic targets by long rod penetrators. Sci. China Technol. Sci. 53, 3189–3196 (2010). https://doi.org/10.1007/s11431-010-4101-6

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