Parametric study of multi-wall structural response to hypervelocity impact by non-spherical projectiles

Computers .i Swucrures Vol. 49, No. 4, pp. 719-745. Printed in GreatBritain.

1993

004s7949/93

$6.00 + 0.00

0 1993 PqatttonPms Ltd

PARAMETRIC STUDY OF MULTI-WALL STRUCTURAL RESPONSE TO HYPERVELOCITY IMPACT BY NON-SPHERICAL PROJECTILES W. P.

and J. A.

SCHONBERG

PECK

Department of Civil and Environmental Engineering, The University of Alabama in Huntsville, Huntsville, AL 35899, U.S.A. (Received 5 September

1991)

Ahstrati-As an alternative to experimental testing and analytical models, numerical modelling is often used to analyze structural response under high-speed impact loading conditions. Since the response of multi-wall structures to spherical projectile impact is well documented, the objective of this paper is to present the results of a numerical parametric study of multi-wall structural response to high-speed cylindrical projectile impact. Numerical impact simulation results were generated by the HULL hydrodynamic computer code for a variety of cylindrical projectiles, impact conditions, and structural geometries. Impact response characteristics are reviewed qualitatively and quantitatively in a parametric analysis of structural response to hypervelocity cylindrical projectile impact. Long rod impacts of single-bumper systems were found to be more damaging than equal-weight spherical projectiles because the trailing end of the rods survived the initial bumper plate impacts. Thin disk impacts of single-bumper systems were also found to be potentially more lethal because the impact of a thin disk on a bumper plate caused a relatively intact section of the bumper plate to rip away and impact the pressure wall. Splitting the bumper of a single-bumper system into two equal-weight bumpers was found to alleviate many of the problems associated with long rod and thin disk impact of single-bumper systems.

INTRODUCTION

Over the last three decades, multi-wall structures have been analyzed extensively, primarily through experiment, as a means of increasing the protection afforded to the interior of habitable spacecraft or modules against perforation by high-speed particles (see, e.g., [l-6]). This work has contributed significantly to the design of spacecraft such as the Space Station Freedom that will be exposed to hypervelocity impacts by meteoroids and pieces of orbital space

debris. However, as structural configurations become more varied (material composition, geometry, etc.), the number and cost of the tests required to characterize the response of such structures have begun to increase dramatically. Although several analytical techniques have been developed to model the response of multi-wall structures under high-speed projectile impact, the calculations involved often become unruly for geometries and material properties even slightly removed from the simplest assumptions (see, e.g., ]7,81). As an alternative to experimental testing and analytical models, hydrocode analysis of high-speed impact phenomena has enjoyed a fairly high level of use and success in predicting the response of a variety of structural systems under different kinds of impact loading conditions [9, IO]. One of the values of hydrocode impact analysis is the ability of the hydrocode to provide detailed information about the impact process which may be difficult or impossible

to obtain experimentally. For example, in the study of debris cloud spread in multi-wall structures under hypervelocity impact, while it may be possible to record the spread of the debris cloud experimentally (see, e.g., [1 l-14]), velocity and density distributions within the debris cloud are more easily obtained from a numerical simulation of the impact event [15, 161. Additionally, impact parameters such as velocity, trajectory, etc., can be more precisely controlled in numerical simulations than in experimental tests where a range of uncertainty always exists in the initial impact conditions. While cylindrical projectile impact has long been of interest to the impact mechanics community, the majority of the work performed has been with long rod projectiles (i.e., L/d >>1) and has been focused primarily on the response of thin and thick singleplate targets to impacts at speeds on the order of l-3 km/set (see, e.g., [17-211). Unfortunately, because of the significant changes in target response that occur as impact velocity is increased, it is difficult to extrapolate the results of such ‘low’ velocity singleplate studies to multi-wall structures under ‘high’ velocity or ‘hypervelocity’ impact. Furthermore, hypervelocity impact testing of multi-wall structures with non-spherical projectiles has been very limited in scope. Such testing was often included as a small part of a much larger test program that, for the most part, employed spherical projectiles (see, e.g., [3,6]). Since projectile shape is known to affect the perforation response of multi-wall structures [22], in order to 719

W. P. SCHONBERGand J. A.

720

optimize the design of a structure destined for the orbital debris environment, it is important for the design engineer to be aware of the many damage modes possible in multi-wall structures under a variety of hypervelocity projectile impact conditions. Because orbital debris particles are in general not spherical and can impact an orbiting spacecraft at speeds in excess of 5 km/set, it is important to characterize the response of typical space structure wall configurations to high-speed non-spherical projectile impact. Since the response of multi-wall structures to spherical projectile impact has been relatively well analyzed, the objective of this investigation was to perform a numerical parametric study of multi-wall structural response to high speed cylindrical projectile impact. The numerical impact simulation results were generated on the NASA/Marshall Space Flight Center Cray X/MP supercomputer by the HULL hydrodynamic computer code (hereafter referred to as the ‘HULL code’), a Eulerian finite difference code with explicit time integration. In the HULL code, an elastic/plastic constitutive law with work hardening and thermal softening was employed with an ultimate strength failure criterion and the MieeGruneisen equation-of-state. Following these introductory comments, an overview of processes involved in the hypervelocity impact of multi-wall structures and an overview of the HULL code are presented. After a discussion of the numerical impact simulation parameters, the results of the numerical parametric study of the response of multi-wall structures under cylindrical projectile impact are then presented and discussed. Impact simulation results for a variety of different cylindrical projectiles and impact conditions are reviewed qualitatively and quantitatively. Impact damage in the structural systems is characterized according to the extent of pressure wall perforation and crater damage as a result of the impact loadings. The parametric analyses performed revealed many interesting features of multi-wall structural response to hypervelocity cylindrical projectile impact conditions. THE HYPERVELOCITY

PECK

Fig. 1. Normal

unyawed cylindrical projectile single-bumper structure.

impact

of a

4 = 0” and $ = 90”. In the single-bumper system impact, the projectile collides initially with the protective bumper (thickness t,), which is usually a relatively thin layer of material placed at a small distance S in front of the pressure wall (thickness t,) of the structural system. Upon impact, strong shock waves propagate through both the projectile and the bumper plate. The pressures associated with these shocks typically exceed the strength of the projectile and bumper plate materials. As the shock waves propagate, the projectile and bumper materials are heated adiabatically and non-isentropically. The release of the shock pressures occurs isentropically through the action of rarefaction waves that are created as the shock waves interact with the free surfaces of the projectile and bumper plate. This process leaves the projectile and bumper materials in high energy states and can cause either or both to fragment, melt, or vaporize, depending on the material properties, geometric parameters, and the velocity of impact. The bumper plates in the single- and doublebumper systems protect the pressure wall plates against perforation by causing the disintegration of the impacting projectiles and the creation of diffuse debris clouds which impart significantly lower impulsive loadings to the pressure wall plates. In the

d+i

7I

IMPACT PROCESS

Consider the hypervelocity impact of a multi-wall structure by a cylindrical projectile of diameter d and length L travelling at velocity V. Figures 1 and 2 illustrate the normal impact of an unyawed cylindrical projectile on a single- and double-bumper system, respectively. In Fig. 3(a), coordinate axes are superimposed on a cylindrical projectile in order that trajectory yaw angles may be defined. Specifically, the yaw angles 4 and $ are defined to be the yaw angles in the x-z and y-z planes, respectively (see, e.g., Fig. 3b). In this manner, a normal ‘straight-on’ disk or cylinder has yaw angles of 4 = $ = 0” while a normal ‘edge-on’ disk or cylinder has yaw angles of

1 S, SECONDARY s2

Fig. 2. Normal

unyawed cylindrical projectile double-bumper structure.

impact

of a

Parametric study of multi-wall structural response to hypervelocity impact

Fig. 3. Coordinate system for yaw angle definitions. single-bumper system impact shown in Fig. 1, the debris cloud (with cone angle y) travels towards and impacts the pressure wall plate. In the double-bumper system impact shown in Fig. 2, the debris cloud created as a result of the impact on the outer bumper plate first travels toward and impacts the inner bumper plate. This creates another debris cloud which then travels toward and impacts the pressure wall plate. In either case, the impact of the debris cloud creates an area of crater damage A,, on the pressure wall plate. The size of this area on the pressure wall over which the impulsive loading of the debris cloud is distributed is governed by the manner in which the projectile and bumper plate(s) fragment, melt, or vaporize, and by the spacing(s) between the bumper(s) and the pressure wall plate. THE HULL HYDRODYNAMIC

COMPUTER

CODE

Introductory comments The HULL code consists of a series of computer programs that solve dynamic continuum mechanics problems in either an Eulerian or a Lagrangian framework. The HULL code also provides a means

721

for linking solutions in these two types of configurations. For example, two-dimensional Eulerian and Lagrangian solutions can be linked interactively (i.e., both frameworks running and solving portions of the problem simultaneously) or by using the velocity and stress fields from a completed Eulerian run as the initial conditions for the subsequent Lagrangian run required to complete the problem. The discussion that follows is a summary of the two-dimensional mathematical framework used by the HULL code in solving the hypervelocity impact problems discussed in this paper and is taken from the HULL code user’s manual [23]. Equations of motion The HULL code Eulerian module solves the partial differential equations of continuum mechanics in finite difference form without including heat conduction and viscosity effects. Specifically, the equations that are solved simultaneously are written as follows: ap /at

+ paui/ax, = 0

(1)

paujlat - aTg/axi + pgj = 0

(2)

paE/at - a (Tyuj)/axi + pu,g, = 0

(3)

TO=f (p,Z,&lax, + aa,lax,),

(4)

where p is the material density, uj is the material velocity in the jth coordinate direction, TV= S, - P6,, S,, and P are the stress tensor, the deviatoric stress tensor, and hydrostatic pressure, respectively, g, is the gravitational body force in the jth coordinate direction per unit mass, E = I + u,uj/2 and Z are the total and internal energy per unit mass,

Table 1. Material properties Material _ property _ Ambient density_ (am/cm3) .Speed of sound (km/set) Shock velocity-particle velocity slope Initial Gruneisen coefficient Poisson’s ratio Initial yield strength ( x 10” dynes/cmr) Saturation yield strength (x 10” dynes/cm*) Plastic strain at saturation yield strength (ultimate failure strain) Ultimate failure stress (x IOr dynes/cm*) DeBye temp. (K) Vapor coefficient Ambient melt energy per unit mass ( x IO9ergs/gm) Fusion energy per unit mass ( x 109ergs/gm) Ambient vaporization energy per unit mass (x lo9 ergs/gm) Sublimation energy per unit mass ( x lo9 ergs/gm) Ambient energy per unit mass at vaporization end ( x 10” ergs/gm)

Projectile 1100-O 2.71 5.38 1.337 2.10 0.33 3.44738 8.96318

Pressure wall 2219-T87 2.80 5.38 1.337 2.10 0.33 3.79212 4.41264

Bumper 6061-T6 2.71 5.38 1.337 2.10 0.33 2.48211 2.89580

0.35 1.00 375 0.1

0.06 1.16 375 0.1

0.10 1.16 375 0.1

7.30 3.96

7.30 3.96

7.30 3.96

3.20

3.20

3.20

1.192

1.192

1.192

1.512

1.512

1.512

W.

722

P. SCHONBERG and J. A. PECK

Table 2. Numerical impact simulation parameters Numerical

V

d

run no.

L/d

(cm)

Single-bumper NR-24 NR-67 Single-bear NR-38 NR-42 NR-43 NR-44 NR-45 NR-46 NR-48 NR-49 NR-66 NR-68 Double-bumper NR-39 NR-47

@

(km/=4

t

42

(n&)

(mm)

0 0

-

-

1.6 1.6

-

3.175 3.175

10.16 il.25

-

0 0 0 0 0 60 0 0 0 0

0 0 0 0 0 0 0 60 0 0

0 0 0 0 0 90 90 0 0 0

1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6

-

3.175 3.175 3.175 3.175 3.175 3.175 3.175 3.175 3.175 3.175

10.16 10.16 10.16 10.16 IO.16 10.16 IO.16 10.16 11.25 Il.25

-

0 0

0 0

0 0

0.8 0.8

0.8 0.8

3.175 3.175

2.54 2.54

respectively, and 6, is the Kroenecker delta function. In eqns (l)-(4) and in those following, a repeated index such as &+/ax, or r+u,.implies a sum over the

7.62 7.62

where Y is the tensile flow stress. If the deviator% stresses do not satisfy eqn (8), they are brought back to the yield surface through the relationship

directions i = 1,2,X

three orthogonal

P is calculated by noting that it is a

function only of density and internal energy. The governing equations of motion are then manipulated to yield

aP/at = -pc,2(au,/ax,),

For the work presented in this paper, failure initiation is determined using the maximum principal strain theory. The onset of failure is determined by solving for the principal strains using the equation

where C, is the material isentropic sound speed. The deviator% strain rate tensor is given as

a6 ;/at = (auiiaxi + auj/ax,yz Deviatoric through

(n&i

(c$

systems, spherical projectiles 0.500 6.0 0.890 10.5 systems, cylindrical projectiles 0.350 2.00 6.0 0.913 0.11 6.0 1.440 0.0277 6.0 0.437 1.00 6.0 0.635 0.31 6.0 0.913 0.11 6.0 0.913 0.11 6.0 0.913 0.11 6.0 0.519 3.00 10.5 0.606 2.00 10.5 systems, cylindrical projectiles 0.350 2.00 6.0 1.440 0.0277 6.0

The pressure

(dzg)

(de&

strains

are related

- (6,i/3)(atfjiaxi). to deviatoric

(6)

stresses

sq= 2f-A $

(7)

where G is the elastic shear modulus. The onset of plastic flow is determined using the von Mises yield criterion, that is, the response is elastic so long as

1ti, - 16, / = 0

and assuming failure occurs whenever max(l) 2 6, where 4 is the material tensile strain to failure. Equations (l)-(3) are solved on an Eulerian finite

difference grid composed of discrete spatial intervals. Two-dimensional axisymmetric and two- and threedimensional Cartesian coordinate systems are available for mesh discretization. The solution is advanced explicitly from the initial conditions by discrete time intervals. The variables computed by HULL at each point of the finite difference mesh at each time-step are the pressure, the orthogonal velocity components, the internal energy, the normal deviatoric stresses, and the shear deviatoric stresses. In addition, for each grid cell (i.e., the region bounded by straight lines

Table 3. Comparison of numerical spherical and cylindrical projectile impact test results, single-bumper systems, 0 = + = $ = 0” d,,

A,

y

N Y Y

D (cm) 1.8 1.4 1.4

(=n) 1.3 1.4

(cm2f 20.2 28.3 Il.4

(de& 22.5 26.5 17.0

N Y N N

1.0 1.0 1.1 1.3

0.9 -

40.9 11.8 32.8 -

41.0 11.5 37.0 -

L/d

(kJ)

Pressure wall perforated?

NR-67 NR-66 NR-68

Sphere 3.0 2.0

55.197 49.255 52.273

NR-24 NR-38 NR-44 NR-45

Sphere 2.0 1.0 0.31

3.196 3.196 3.200 3.196

Numerical run

no.

Energy

(10)

723

Parametric study of multi-wall structural response to hypervelocity impact Table 4. Effect of cylindrical projectile L/d ratio on single-bumper system response,

e=d=$=oo

Numerical N!l

YlO.

Lid

2.0 1.0 0.31 0.11 0.0277

NR-38 NRA4 NR-45 NR-42 NR-43

Energy &J)

Pressure wall perforated?

3.196 3.200 3.196 3.210 3.172

Y N N Y Y

D

dh

A,

fern) (cm) 1.0 1.1 1.3 1.5 1.8

Y

(cm21 (dea)

0.9 0.4 t

11.5 37.0 22.5 29.0

3.0 32.8 11.8 19.3

tSevere necking of pressure wall plate near debris cloud impact site.

connecting adjacent grid points), the HULL code computes the mass contained within each grid cell. When material failure occurs within a cell, the material in the failed cell is replaced by air. Cells which contain air cannot support either distortional or tensile forces. Slip is presumed to occur when more than one solid material occupies a cell. Such a cell can sustain a compressive stress, but cannot support either a shear or a tensile stress. If a grid cell contains more than one material, an iterative procedure is called to equilibrate the pressure of each material in the cell to a common value.

A constitutive equation that describes the relationship between pressure, density, and internal energy is referred to as the material’s equation-of-state (EOS). Constitutive equations can also describe the relationship between elastic and plastic stresses and strains. Both of these types of relationships are contained within the HULL code material response routines. The elastic/plastic constitutive relationships are the standard equations developed using classical elasticity and plasticity theory (see, e.g., [24,25]). A number of EOSs are available to the user within the HULL code to characterize the release of a material from a shocked state. The Mie-Gruneisen EOS is a valid thermodynamic description of most materials in the solid matter state and can even be used to describe the release of a material in which some melt has occurred [26]. For an aluminum projectile impacting an aluminum target, melt is only expected to begin at an impact velocity of approximately 5.8 km/set [27]. Thus, since most of the impact conditions considered in this paper were such that at most only some melt of the projectile and target materials was expected to occur, the EOS selected for use was the Mie-Gruneisen EOS. The following is a brief description of the Mie-Gruneisen EOS as used by the HULL code based on the in-

formation contained manual 1231.

within the HULL code user’s

Mie-Gruneisen equation -of-state

The form of the Miffiruneisen EOS utilized by the HULL code can be written as P = P,(l-o.S

r#f) + Tp (i - 1,) t P*,

where P is the pressure in the material, PH is the pressure along the Hugoniot at a density p, r is the Gruneisen ratio, ~1= p/p,, - 1 is the material compression, and Z,, pot and POare the ambient internal energy per unit mass, ambient material density, and ambient pressure. The ambient internal energy is calculated using I0 = 2C,T;‘/3T,,

(12)

where C, = 3R/A,, R = 8.317 x 10’ is the universal gas constant, A, is the atomic weight of the material, TR = 288 K is room temperature, and T, is the material’s DeBye temperature. The ambient pressure is taken to be 1 atm. For solid materials it can be shown that r = Z-l&P>

(13)

where To is the value of the Gruneisen ambient density and is given by

L/d

(d:g)

(d$

(d:g)

NR-42 NR-46 NR-48 NR-49

0.11 0.11 0.11 0.11

0 60 0 0

0 0 6:

9: 90 0

‘;:y 3.210 3.210 3.210 3.210

ratio at

where K = E/3( 1 - 2 v) is the adiabatic bulk modulus of the material, B = 3 a is the material volumetric coefficient of thermal expansion, a is the linear coefficient of thermal expansion, and C, is the specific heat of the materiat at constant pressure. The pressure along the Hugoniot PH can be found in any one of several ways. In some equations-of-state it is simply represented by tabular P,, vs p data taken

Table 5. Effect of cylindrical projectile orientation on single-bumper system response Numerical run no.

(11)

Pressure wall perforated?

D (cm)

d& (cm)

Y Y

1.5 1.8 1.4 1.3

0.4 1.4 1.2 -

(~2) 11.8 14.6 25.6 30.6

(dzg) 22.5 17.5 33.0 35.0

W. P. SCHONBERG and J. A. PECK

724

Table 6. Comparison of numerical single- and double-bumper test results, cylindrical projectiles, g=b=*=O” Numerical

s,

s,

Lid

(cm)

(cm)

Energy (kJ)

Pressure wall

run no.

NR-39 NR-38

2.0 2.0

2.54 7.62 10.16 -

3.196 3.196

NR-47 NR-43

0.0277 0.0277

2.54 10.16

3.206 3.172

1.62 -

directly from Hugoniot data. If the relationship between shock velocity and particle velocity can be represented by a straight line, that is, if u,=

c,+su,

(15)

then the conservation equations across a shock front (known as the shock jump conditions) lead to p, = P,C;rll(l

- Srl)2,

(16)

where 9 = 1 - pO/p, U, is the shock velocity, Up is the particle velocity, Co is the ambient bulk sound speed, and S is the slope of the U, - U, line. It is noted that the right-hand-side of eqn (16) has a pole at S = l/q. The HULL code avoids such a potential difficulty by approximating the right-hand-side of eqn (16) with a three-term sum P,=Ap+Bp2+cp3,

(4

15.0 13.5 I 120

10.5

(17)

D1

02

d,,

(cm)

(cm)

(cm)

A, (cm21

N Y

0.8 I.0

1.3 -

0.9

25.6 3.0

N N

2.0 1.8

4.3 -

-

11.8 19.3

perforated?

where B = A (1 + 2(S - l)], and A = pot;, C = A [2(S - 1) + 3(S - 1)2]. The right-hand side of eqn (17) is the sum of the first three terms of the infinite series obtained by performing the division indicated in eqn (16). Using all three terms in eqn (17) has been found to lead to problems for negative values of p. Thus, the HULL code uses all three of the terms only for positive values of p; for negative values of p, only the first term is used. The internal energy used in the EOS is adjusted to reflect the phase changes expected as a material passes from the solid state into the melt phase. The amount of energy required to initiate material melt is also modified by the HULL code due to the compression of the material using the relationship I,=[,,,,,(1

+Fq

+Gq2)

(18)

where I,,, is the energy per unit mass required initiate melt in a material that is compressed

to to

Densitv

C&r

Vap$

mo.oo~~pm’mI 6.oOxlo“ 9 00x10-' 1.20 1.50 1.80 2.10 2 40

3.00x10-' 6.00x10-' 9.00x10-' 120 150 180 210 2 40 2 81

: :

: I

725

Parametric study of multi-wall structural response to hypervelocity impact

(b)

Density

15.0

13.5 -I

1.80 2.10 2.40 2 a1

1.50 1.60 2.10 2.40

8

B

_

_ -

7.5

:

1.

.. .

=._-‘_

;,*

.

b P 3

6.0

_

_

_

_

4.5

3.0

1.5

0.0

r; 1

Time S B 4.5

a

Radius cm

9.000 IN SEP.

C de ps - 1 GR !PR

.

1309 R=.445CM

Rodhan p?%8%

Ktvd”f6&EG

Density

Cc)15.0

COkU 1.00X1 O-Pm’m 3.M)xIo-' 6.00x10-' 9.00x10“ 1.20 1.50 1.80 2.10 240

12.0

10.5

V.!,, 3.00x10-' 6.00x10-' 9.00x10-' 120 1.50 180 2.10 240 285

9.0 E i? i 0 .? 3

7.5

6.0

.5 Time B 4.5

I 6.0

I

1

3.0

4.5

RlldiU~ cm

Id458E?

“1

I

1.5

C de GR 5PR

I

0.0

115

2400 R=.445CM

I 3.0

I 4.5

Ldiwcm

pc”,“‘l’or5

I 6.0

KM/??bEG

Fig. 4. (a) HULL code simulation NR-67-spherical projectile t = Opsec. (b) HULL code impact simulation NR-67-spherical projectile t = 9.000 psec. (c) HULL code impact simulation NR-67-spherical projectile t = 14.836 psec.

(a)

SCHONBERG

W. P.

726

and J. A.

PECK

15.0

color

13.5 ,

oox,

3.00x10-’ 6.00x10-’ 91 00x10-’ 20 I 50 1 80 2.10 2 40

B 2

V$lCS

o_P’cm 3.QOx

IO“ 6.ooxto-’ 9ooxto-’ 20 1t 50 1 .a0 2.10 2 40 2 61

I I I : 1 I I

6.0

4.5

3.0

I

1.5

0.0 .5

I

6.0

I 4.5

I 3.0

I 1.5

I 0.0

115

1 3.0

I 4.5

I 6.0

1

; ‘5

Density

(b) 15.0

7

C&M

13.5

V+l@S

l.oox**-~m’cm 6~oOx,0_; i 3.00x10-

3.00x 6.00X 12.0

:.z’” 1.50 1 80 2.10 2 40

10.5

6

9.0

:: % ii .Y A!

7.5

6.0

. ... . . t

4.5

I

3.0

.-

1.5

0.0

d0

4.5

3%

115

do

1:5

3!0

X5

6.0

IO“ 10-z

9.ooxto-’

I

1 20 50 1 .a0 2 IO 2 40 2 61

3 m z

Parametric study of multi-wall structural response to hypcrvelocity impact

727

Density

1.20 1.50 1.80 2.10 2.40

I

7.5

6.0

is

do

I 1.5

do

1:s

f.0

I

4.5

1.50 1.80 2.10 2.40 2.99

I

6.0

Fig. 5. (a) HULL code impact simulation NR-66-spherical projectile t = 0.000 psec. (b) HULL code impact simulation NR-66-cylindrical projectile I = 6.000 psec. (c) HULL code impact simulation NR-66-cylindrical projectile r = 12.71O/lsec.

a state defined

by q, I,,,,, is the incipient ambient melt energy per unit mass, F = 2r, - 2/3, and G = (r, - 1/3)(2r, - l/3) - 1. If the material energy

Z is in the region I,,, c Z < Z,,,+ G, it is maintained at I,,, where hW is the material heat of fusion per unit mass. If Z > I,,, - Z,W,then Z is re-set to Z - Z,. This prevents the pressure from changing due to an energy rise during the melt phase. A similar type of procedure is invoked during the vaporization phase if the energy of the shocked state is high enough to cause vaporization to occur. IMPACT

PARAMETERS AND STRUCTURAL CONFIGURATIONS

The conditions of the numerical impact simulations were chosen to simulate the orbital debris impact of light-weight space structures as closely as possible, and still remain within the realm of numerical feasibility. Kessler er al. [28] state that the average mass density for pieces of orbital debris less than 10 mm in diameter is approximately 2.8 gm/cm3, which is approximately that of aluminum. Therefore, the projectile material in the numerical impact simulations was chosen to be aluminum 1100-o. To assess the effect of projectile shape on structural response, spherical and cylindrical projectiles were used in the numerical simulations. The L/d values of CAS 4914-K

the cylindrical projectiles were varied from 0.0277 to 3.0. Two types of multi-wall structures were considered in this investigation: single-bumper and doublebumper. In each case, the bumper plates were 6061T6 aluminum, the pressure wall plates were aluminum 2219-T87, and the projectiles were aluminum 1100-o. The mechanical and thermal properties of the projectile, bumper plate, and pressure wall plate are presented in Table 1. These are the values used as input by the HULL code in the impact simulations performed for this investigation. In Table 1, ‘ambient melt energy’ and ‘ambient vaporization energy’ refer to the internal energies at the inception of material melt and vaporization, respectively. Additional numerical impact simulation parameters are given in Table 2. In Table 2, the angle 0 is the trajectory obliquity measured from the vertical, that is, 6 = 0” is a normal impact. Tables 3-6 present the results of the numerical parametric study. In Tables 3-6, experimental and numerical results are grouped according to both geometric and impact energy similarity. It is noted that in these tables, dashed entries indicate that certain phenomena, such as pressure wall perforation or front surface crater damage, did not occur. Additionally, d,, is the equivalent single hole diameter of all the holes in the pressure wall plate in the event of

728 (a)

W. P.

.%HOUBERG

and J. A.

PECK

Density

(4.0

1 Color V$¶S

12.6

l.aOxlo-~m'm ;:jg;;:: 11.2

9.00x10-' 1.20 150 1.80 2.10 240

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129

Parametric study of multi-wall structural response to hypervelocity impact (c)

14.0

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Fig. 6. (a) HULL code impact simulation NR-38*ylindrical projectile L/d = 2.0, r = 0.000 psec. (b) HULL code impact simulation NR-38*ylindrical projectile L/d = 2.0, t = 12.000 psec. (c) HULL code impact simulation NR-38--cylindrical projectile L/d = 2.0, t = 30.000 psec.

wall perforation. Figures 4-15 show pertinent HULL code output frames that are used for more detailed impact response comparisons.

pressure

RESULTS AND OBSERVATIONS

Single-bumper systems: Spherical us cylindrical projectile impact

A comparison of single-bumper system response to spherical and cylindrical projectile impact clearly demonstrated the effect of projectile geometry on system response. When the projectile trajectory was normal to the bumper plate, it was found that cylindrical projectiles with large L/d ratios (i.e., long rods) were more damaging than equal-mass spherical projectiles (Table 3). In the spherical projectile impacts, the projectile and the bumper plate were completely fragmented and a disperse debris cloud was created (see, e.g., the HULL code output for NR-67 in Figs 4a-c). However, when a long rod impacted the bumper plate, only the front portion of the cylinder was fragmented, leaving the remaining rear section intact. For example, in NR-66 (L/d = 3.0), nearly one-third of the original cylindrical projectile was left undisturbed after the projectile had passed through the bumper plate (Fig. Sb). Eventually, this large projectile fragment perforated

the pressure wall plate (Fig. 5~). Similarly, in NR-68

and NR-38, the portions of the rod which remained intact after passing through the bumper plates had sufficient energy to perforate the pressure wall plates. As the L/d ratio decreased to unity, cylindrical and spherical projectile impacts were observed to inflict similar levels of damage to the pressure wall plates of single-bumper systems. This is in agreement with the results of a previous experimental study of the effects of projectile shape on the hypervelocity impact response of dual-wall structures [29]. For example, in the comparing the results of NR-38, NR-44, and NR-45, as the L/d ratio decreased from 2.0 to 0.31, the damage sustained by the pressure wall plate decreased markedly (Table 3). In fact, in NR-45 (L/d = 0.31), the impact of the cylindrical projectile on the bumper plate resulted in complete fragmentation of the projectile. Subsequently, there was no measurable damage to the pressure wall plate. In this case, the debris cloud created strongly resembled that observed in NR-24, the corresponding spherical projectile impact test. Effect of L/d ratio

It was found that the cylindrical projectiles considered in this study could be divided into three groups depending on their L/d ratios. These groups

W. P.

730

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Fig. 7. (a) HULL code impact simulation NR-44-cylindrical projectile L/d = 1.0, t = 0.000 psec. (b) HULL code impact simulation NR-hl-cylindrical projectile L/d = 1.O, t = 10.000 psec

Parametric study of multi-wall structural response to hypervelocity impact

731

12.6

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240 272

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Fig. 8. (a) HULL code impact simulation NR-45-cylindrical projectile L/d = 0.31,t = 0.000pm. HULL code impact simulation NR-45-cylindrical projectile L/d = 0.31, t = 15.000 Nsec,

(b)

: I Ip I

732 (a)

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P. SCHONBERG

and J. A. PECK

Density

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Fig. 9. (a) HULL code impact simulation NR-42-cylindrical projectile L/d = 0.11, I = 0 psec. (b) HULL code impact simulation NR-42-cylindrical projectile L/d = 0.11, t = 20.000 psec. (c) HULL code impact simulation NR_rl2--cylindrical projectile L/d = 0.1 I, I = 42.360 psec.

(a)

Density

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Fig. 10. (a) HULL code impact simulation NR-O-cylindrical projectile L/d = 0.0277, t = 0 psec. (b) HULL code impact simulation NR-43+ylindrical projectile L/d = 0.0277, t = 36.000 psec. (c) HULL code impact simulation NR-43*ylindrical projectile L/d = 0.0277, f = 65.320 psec.

m : : m 8% m

Parametric study of multi-wall st~ura1 Densit onpbmatY2!0x10~

(4 14.0

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respouse to hyperveiucity impact

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Fig. 11. (a) HULL code impact simulation NR~yIind~~l projectile L/d = 0.1 I, B = 60”, Cp= o“, J, = W, r = 0.000 psec. (b) HULL code impact simulation NR-~ylind~~l projectile L/d = 0.11, 6 = W, I$ = 0”, t,h= 90”, t = t2.000 psec. (c) HULL code impact simulation NR-4Ccylindrical projectile L/d=O.ll, B =60“, 4 =O”, rl/ =90”, t =28.265psec.

are ‘long rods’ (L/d > I), ‘compact rods’ (L/d IT 1) and ‘thin disks’ (L/d c 1). Figures 6-10 demonstrate the changes in debris cloud composition and pressure wall response for single-bumper system impacts as the L/d ratio was decreased from 2.0 to 0.0277 while the mass of the impacting projectile was kept constant. As noted previously, when a long-rod projectile impacted a single-bumper system, complete fragmentation of the projectile upon impact with the bumper failed to occur. For example, in NR-38 (L/d = 2.0), the solid fragment remaining after bumper plate impact went on to perforate the pressure wall plate (see the results for NR-38 in Fig. 6a-c and in Table 4). As the L/d ratio decreased to unity, more complete fragmentation of the projectile occurred, which in turn resulted in an increase in the spread of the debris cloud. As a result, although the crater damage area increased, the perforation threat of the projectile decreased (see, e.g., the results for NR-44 in Table 4 and compare with those for NR-38). In Figs 7(a, b) and 8(a, b), cylindrical projectiles with L/d ratios of 1.0 and 0.31, respectively, are seen to be completely broken up by the bumper plates and cause minimal damage to the pressure wall plates. Finally,

in the thin disk impacts (L/d = 0.11 and 0.0277), intact sections of the bumper plate were ripped away and sent speeding towards the pressure wall plate. In addition, for these L/d ratios, the debris clouds were noticeably ‘spiked’ in appearance (see Figs 9a-c and 1Oa-c). The spiked shape of the debris clouds and the large fragments contained within them eventually resulted in pressure wall perforation and extreme pressure wall deformation to the point of incipient perforation (Figs 9c and lOc, respectively). It is interesting to note that the projectiles in NR-42 and NR-45 appear to be in a transition region between ‘compact rod’ and ‘thin disk’ projectiles. In NR45, the debris cloud produced by the impact of a cylindrical projectile with LJd = 0.31 quickly degraded into very small particles which caused no measurable pressure wall damage. This behavior resembled that observed in NR-44 where L/d = 1.O. On the other hand, in NR-42 where L/d = 0.11, a small disk appeared to be present at the leading edge of the debris cloud as it left the bumper plate immediately after impact. This behavior resembled that observed in NR-43 where L/d = 0.0277. It would appear, therefore, that for the projectile and target materials considered in this study, a transition from a compact

737

Parametric study of multi-wall structuraf response to hypervelocity impact

(4

Density en DloM ot Y = 2.0x10-’

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Figs 12(a) and (b).

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Fig. 12. (aafHULL code impact simulation ~R~8~~lindr~c~ projectile Lfd = 0.11, B = O”, 4, = o’“, E,& = 90”, t = 0 psec. @) HWLL code impact simulation NR~8~~~~nd~ca~ projectile Ljb = 0.11, 0 = O", # = O",$ = !W',t= 12.000 psec. (c)HULL code impact simulation NR-48,ylindrical projectile L/d=O.Il, 8 =o”, $5=O”, $ =90”, r =22.29o/Sec.

rod

to

a thin

L/d = 0.31 and

disk

projectile

occurs

between at

L/d = 0.11 or ap~~oxjmately

L]d = 0.2, Efect of projectile orientation

From Table 5, it can be seen that, of the different projectile orientations investigated, normal and oblique edge-on disk impacts (e.g., NR-48 and NR46, respectively) were more damaging to the pressure wall than normal straight-on (e.g., NR-42) and yawed (e.g., NR-49) impacts. This can be seen by comparing the pressure wall hole diameters for these four tests in Table 5 and the NULL code output in Figs 9 and 1l-13. In tests NR-46 and NR-48 (Figs 1la-c and 12a--c, respectively), the pressure wall was impacted by a large debris cloud containing large bumper plate and projectile fragments. Although the impact of NR-42 created a spiked debris cloud with a high mass concentration at the leading tip of the cloud (see Figs 9a-c), the high degree of projectile fragmentation resulted in a smaller pressure wall plate hole than in NR-46 and NR-48 (compare Figs 9c, 1lc, and UC). The least damaging prajeetile orientation was that of the disk in NR-49, in which the projectile had a yaw angle of 4 = 60”. The normal impact of this yawed

projectile also resulted in a high degree of fragmentation and did not perforate the pressure wall plate (see Figs 13b, cf. The harmlessness of the yawed impact considered in this study can be explained by using a relatively simple model of yawed cylindrical projectile impact [30]. Consider the normal impact at velocity I’ of a cylindrical projectile whose lon~tudi~al axis is yawed an angle # with respect to the trajectory of the projectile (Fig. 14). In Fig. 14, point A is a point of contact between the projectile and the surface of the target, point B is a point along the surface of the projectile facing the target, and point C is the projection of point b onto the surface of the target. We define a ‘critical angle of yaw’ 4, such that if # = +,, then the shock wave generated along the target-facing surface of the projectile will reach point B at exactly the same time that point B will reach the target surface (at point C). Given this definition of #,,, two possibilities arise. First, if 4 < #,$ then the shock wave will reach point B after point B strikes the target surface. In this case, the amplitude and duration of the shock pressures along the projectile/target interface will be essentially the same as that for an impact of the same projectile at the same velocity without

739

Parametric study of multi-w~1 structural response to hypervelocity impact

(4

onpheat:Y- Densi%xiO-~

14.0

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(J =

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740 (e)

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Fig. 13. (a) HULL code impact simulation NR-49--cylindrical projectile L/d = 0.11, 0 = O”, 4 = 60”, $ = O”, f = 0 psec. (b) HULL code impact simulation NR-49-xylindrical projectile L/d = 0.11, 0 = O”, 4 = W, (I = o”, t = 15.173~sec. (c) HULL code impact simulation NR-49--cylindrical projectile L/d=O.ll, 0=0”, 4 =60”, $ =O”, t =23.564psec.

yaw (i.e., 4 = 0’). Second if 4 > 4,,, then the shock wave will reach point B before point B strikes the target surface. In this case, the full shock pressure will exist only at the initial point of impact. At other points along the projectile surface facing the target, the projectile material will be shocked and partially released before striking the target surface. As a result, the shock pressures generated upon impact will be lower in magnitude and will have a shorter duration than those generated in a yawed impact where 4 < +,,. To find 4,,, we note that if 4 = r#~,, then BCIV,

= AB/U,,

point B to reach point C (BC/V), where U, is the projectile material shock wave velocity. Rearranging eqn (19) yields Vo/U, = BCjAB

= sin(4,,)

so that f$,, = sin-‘( V/U,).

(21)

Finally, for a like material-like material impact, the shock wave velocity is related to the impact velocity through the relationship

(19) U, = Co + KV/2.

that is, the time required for the shock wave to reach point B (AB/U,) is equal to the time required for

Fig. 14. Critical yaw angle calculation geometry.

(20)

(22)

For the projectile and target materials in NR-49 (both aluminum), C,, N 5.2 km/set and K u 1.38. For V = 6.0 km/set, eqns (21), (22) yield a critical yaw angle of +,, N 40”. Based on the discussion in the preceding paragraph, since the yaw angle of NR-49 exceeds +,, , the projectile in NR-49 has already begun to deteriorate by the time it completely passes through the bumper plate. This explains why the debris cloud is larger in NR-49 than in NR-42 and NR-46 and why the impact is relatively harmless.

Parametric study of m~ti-w~l

(4

741

structural response to hypervelocity impact

Density

14.0

12.6

$1.2

.

9.6

._”

1.a0

1.50 1.80

2.10

Ld

2.10 2 40

2.40 2 72

=:

E.WxlO-' 9.05X1lh" 1.20 1.50 1.80

9.OOxlO~

4.2

2.6

1.4

0.0

fh

4.2 Radius

C.4

i.6

ia

4.2

RdiU~ cm

cm

Time 0.000 s D. B. 1 AND 4 IN. SEP. -%iL46&

c~~“P%twS

!h

2.0039 - L/D=2

Density

09 14.0 12.6

11.2

2.10 2.40

9.8

E u

a.4

l

P +j h .%j r

7.5

5.6

4.2

._a. 2.6

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J

I

. . ’

_

a--.

_

_. .

,

1.4

a.5

Figs 15(a) and (b).

225 t so

180 1.10 2.40 2 75

:

I?: I

;Y

z

Density

11.2

9.00x10-* 1.20 I.50 1.80 2.10 240

9.6

1 20

1.50 I .a0 2.10 2.40 272

4.2

2.6

1.4

0.0

7.0

n

5.6

I

49

I

2.6

t-4

I

5.0

1

t.4

I

2.6

I

4.2

I

5.6

Fig. IS. (a) HULL code impact simulatibn NR-39-cylindrical projectile double-bumper system, L/d = 2.0, t = 0 psec. (b) HULL code impact simulation NR-39-cylindrical projectile double-bumper system, L/d = 2.0, t = 6.000 gsec. (c) HULL code impact simulation NR-3hylindricai projectile double-bum~r system, L/d = 2.0, I = 18.000 psec.

(a) 14.0

Clensitv

12.6

11.2

2 IO 2 w

9.8

5

6.4

? j/ 9 r

7.0

5.6

4.2

2.0

1.4

0.0

516

I

4.2

I

2.8

I

1.4

i

0.0

I

1.4

I

2.8

742

I

4.2

5.6

240 272

Density

@I 14.0

Color

VOlUeO

L&m-~m’cm’ 6.00x10-’ s.mx o-1 lo-’ EY”3.ooxlo-’

I

150 1.80 2.10 2 40

9.00x 120 1.50

1.80

2.10 240 2 76

4.2

._

_.

2.8

_’

1

7.0

5.6

I

4.2

1

‘.

I

I

2.8

1

0.0

1.4

1.4

Radius cm

I

2.8

0

4.2

I

5.6

Radiue cm

Densitv

12.6

I.ooxlo-~m’c”3.00x10-’

3.00x I 0“

8.00X10-'

~.~‘“-’

1.50 1.80 2.10 240

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120 1.50 1.80 2.10 2.40 272

. . ‘.

--

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. .

. .-.

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i .* ” +

cf

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-I

.

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Radium cm

Time DB

-

1 A,‘o9~:‘hd’%P.

Radii

Cycle 4796 - D=l.44CM

cm

CYLP;;Tjb$?&/S

-‘pD~.O28 P

Fig. 16. (a) HULL code impact simulation NR47-cylindrical projectile double-bumper system, L/d = 0.0277, t = 0.000 psec.(b)HULL code impact simulation NR-47-cylindrical projectile doublebumper system, L/d = 0.0277, r = 24.000 psec.(c)HULL code impact simulation NR-47-cylindrical projectile double-bumper system, L/d = 0.0277, t = 79.641 pet. CAS 49,4-L

743

I

I I : E-l :

W. P.

144 Single

us double-bumper

system

SCHONBERGand J. A. PECK

impact

As expected, it was found that double bumper systems offered more pressure wall protection against perforation by cylindrical projectiles with large L/d ratios than did equal-weight single bumper systems. The most dramatic illustration of this can be seen by comparing the results for NR-39 in which a long rod impacted a double-bumper system with those for NR-38 in which the same long rod impacted an equal-weight single-bumper system (Table 6). While a large section of the long rod projectile remained intact after impact with the single bumper in NR-38 (Fig. 6b) and the first bumper in NR-39 (Fig. 15b), the second bumper in NR-39 caused additional projectile fragmentation. As a result, the pressure wall of NR-39 was not perforated and suffered only minor damage (Fig. 15~) while that of NR-38 was completely perforated (Fig. 6~). In case of thin disk impact (NR-47 and NR-43 in Table 6), the impact of the disk on the single bumper of NR-43 and the first bumper of NR-47 caused intact sections of the bumper plates to rip away and travel towards either the pressure wall in the singlebumper system or the inner bumper of the doublebumper system (Fig. lob and 16b, respectively). Although neither system was perforated, in the double-bumper system the impact of the outer bumper and projectile fragments on the inner bumper caused more complete fragmentation to occur than that which was observed in the singlebumper system (compare Figs 1Oc and 16~). Therefore, it would appear that the pressure walls of single-bumper configurations would also be at a greater risk of perforation by thin disk projectiles than the pressure walls of equal-weight doublebumper systems.

SUMMARY

AND CONCLUSIONS

A numerical parametric study of hypervelocity impact response using the HULL hydrodynamic computer code was revealed several interesting response characteristics of single- and double-bumper systems under cylindrical projectile impact. For single-bumper systems, long rod impacts were found to be more damaging than equal-weight spherical projectiles because the trailing end of the rods survived the initial bumper plate impacts relatively intact. The damage caused by compact rod impacts was similar to that caused by spherical projectile impacts. Thin disk impacts caused a relatively intact section of the bumper plate to rip away and impact the pressure wall. Finally, edge-on disk impacts, whether normal or oblique, were more damaging than straight-on impacts. In the case of long rod and thin disk impacts, double-bumper systems were found to offer more protection to the pressure wall against perforation than equal-weight singlebumper systems because the inner bumpers caused

additional ticles.

fragmentation

of the debris

cloud

par-

Acknowledgements-The authors are grateful for support from NASA/Marshall Space Flight Center contract (NASS36955/D.0.74) with Miria Finckenor serving as Technical Monitor. The authors would like to express their appreciation to John Tipton of the U.S. Army Corps of Engineers, Huntsville Division, for performing the HULL code calculations under separate contract to the NASA/MSFC Structures Division that made this investigation possible and to John Osborn of Orlando Technologies, Inc. for his assistance with questions regarding the HULL code. The authors also wish to acknowledge the assistance of Benjamin Hardof the manuscript ing in the preparation REFERENCES

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