hypervelocity_impact_damage_in_composites.pdf

R. A. Clegg et al / International Journal of Impact Engineering

Hypervelocity Impact Damage Prediction in Composites Part I - Material Model and Characterisation

R. A. Clegg**, D. M. White*, W. Riedel+, W. Harwick+

*Century Dynamics Ltd, Dynamics House, Hurst Road, Horsham, West Sussex, RH12 2DT, England + FhG - Ernst-Mach-Institut, Eckerstrae 4, D-79104, Freiburg, Germany

Abstract

This paper reports on the development of an extended orthotropic continuum material model and associated material characterisation techniques for the simulation and validation of impacts onto fibre reinforced composite materials. This Part I of the paper focuses on the details of the numerical model and the material characterisation experiments. Part II Experimental Investigation and Simulations [1] provides details of hypervelocity impact damage experiments and simulations performed to assess the capabilities of the developed model. Here a detailed description of the material model [2], as implemented in AUTODYN [3], is provided. The model is an extension of that presented in [4], which allowed the correct thermodynamic response of orthotropic materials to be simulated under shock wave loading. Improved capabilities to allow prediction of the extent of damage and residual strength of fibre composite materials after impact are described along with set of quasi-static and dynamic experiments used to characterise the directional non-linear strength and extent of damage. Application of the model and derived material data is demonstrated through the simulation of a hypervelocity impact event of an aluminium sphere impacting the Columbus module shielding system of the International Space Station (ISS).

Keywords: Hypervelocity, Impact, Material Model, Material Characterisation, Kevlar, CFRP

1. Introduction

The study of impacts on composite materials is a requirement for both manned and unmanned spacecraft structures. On manned spacecraft, such as the ISS, fibre reinforced composite materials are used in the primary shielding system used to mitigate the effects of orbital space debris impacts. On unmanned spacecraft carbon fibre reinforced composite materials are commonly employed for major structural components. Although such components are not designed to mitigate the effects of hypervelocity impact, the consequences in terms of secondary debris after such impacts is of concern in relation to the survivability of on-board equipment. This paper describes an advanced material model, and set of material characterisation experiments, for orthotropic materials that has been developed to

* Corresponding author. Tel.: +44 1403 270066; fax:+44 1403 270099 E-mail address: [email protected]


improve the predictive capabilities of numerical simulations of hypervelocity impacts on a range of composite spacecraft structures/materials [2].

The foundation for the material modelling and characterisation work presented here is described in detail in [4]. This work led to the identification of the following phenomena, which we believe are of primary interest for composite and textile materials subject to high/hypervelocity impact:

material anisotropy shock response anisotropic strength degradation (damage).

The material model [2] developed to address these aspects of composite material simulation under impact loading is now described. The material model development was carried out hand-in-hand with material characterisation experiments which are also described alongside the model features.

2. Basic Orthotropic Stiffness and Shock Response

In anisotropic materials, the traditional independent approach for the solution of the equation of state and constitutive relations in a hydrocode is complicated because these two sub-models are strongly coupled; volumetric strain leads to deviatoric stress, and similarly deviatoric strain leads to spherical stress. A methodology [5] was implemented and further developed in AUTODYN as reported in [4]. Consider a linear elastic orthotropic material for which the total incremental stress, ij, can be related to the total incremental strain, ij, through the orthotropic stiffness matrix, Cij. The coefficients of Cij being functions of the orthotropic elastic material constants, Eii, ij and Gij.

+= vdijijij C 31

(1)

To facilitate the coupling of the deviatoric and volumetric material response the total strain has been decomposed into volumetric, v, and deviatoric, ijd, components. Since the pressure is the average of the three direct stresses, from (1) we can obtain:

( )( ) ( ) ( ) ddd

v

CCCCCCCCC

CCCCCCP

333323132232221211312111

312312332211

31

31

31

22291

++++++

+++++= (2)

For an isotropic Hookean material the first term on the right-hand side of (2) is equivalent to a linear equation of state, whilst the remaining deviatoric strain terms would be zero. Thus for an orthotropic material we can replace the first term with a non-linear Mie-Gruneisen equation of state and the remaining terms act as a correction due to deviatoric strains.

A model based on the above was implemented in AUTODYN [3] and has subsequently been used for simulating high to hypervelocity impacts on a wide range of applications and materials [6], [7], [8], [9], [10]. This experience identified potential weaknesses of the model especially with respect to anisotropic strength degradation. Characterising and modelling these aspects is the main focus of the


current work. The phases of anisotropic strength degradation in a composite material can be categorised into

Nonlinear hardening (maximum stress increases with strain) Nonlinear softening (maximum stress decreases with strain)

The observed material characteristics, and tests to derive them, are now outlined along with the macro-mechanical material modelling features developed to represent the behaviour.

2.1 Non-linear Hardening

Many composite materials exhibit non-linear stress strain behaviour when subject to tensile uniaxial stress loading. The most common example of such behaviour is found when loading a unidirectional fibre reinforced laminate at 45 degrees to the fibre direction (Fig. 1). The observed non-linear response results in a reduction in the tangent material stiffness with strain.

0

50

100

150

200

0 0.02 0.04 0.06 0.08 0.1 0.12

Strain [-]

Stre

ss [M

Pa]

Stepwise LoadingMonotonic Loading

h

t

l

x

ydraulic piston H

Specimen

Load cell

h = 60 mm w = 10 mm l = 230 mml0 = 165 mmt = 20 mm

wl0

Fig. 1. Uniaxial tension test, cyclic stress strain curve for Kevlar-epoxy (0/90) loaded at 45 to the fibre direction [2].

The envelope to the stress strain curves (Fig. 1) clearly shows non-linear hardening behaviour. Cyclic unloading and re-loading also reveals that the non-linear hardening results in irreversible deformation. This terminology is consistent with that used for dislocation plasticity. However, in this case the underlying micro/meso mechanical behaviour may include a number of different mechanisms such as matrix plasticity, fibre re-orientation and matrix/fibre damage. The baseline material model [4] employs a linear elastic orthotropic stiffness matrix under small tensile strains hence is not capable of capturing this type of behaviour.

To enable phenomenological representation of this hardening behaviour, a generalised limit surface [11] has been adopted. This surface is quadratic in stress space and is generally applicable to composite materials. For example, no a priori assumptions are made in respect of the influence of hydrostatic stress on inelastic deformation as in Hills orthotropic yield criteria [12].

0222

22221266

23155

22344

33111333222322111223333

22222

21111

++++++++=

kaaa

aaaaaaf

(3)

where the stresses ij refer to the principal material directions, and k is a state variable defining the instantaneous value of the limit surface. The nine coefficients, aij define the extent of anisotropy in the


material response and are constants, implying isotropic hardening. It can be shown [11] that these constants are related to the Plastic Poisson Ratio (PPR) in the material via

PPP

P

P

P

P

P

P

aaaaaa

aaaaaa

313313232223212212

13

313311

32

232233

12

212211

,,

,,

======

(4)

The values of the coefficients can thus be obtained from a series of well-instrumented tension and shear experiments. Fig. 2 shows the results of a typical in-plane and through thickness instrumented tension test on an aramid-fibre-epoxy specimen [2]. Note the non-linear characteristics of both the in-plane and out-of-plane Poisson ratio. For the purpose of the numerical model, this data must be linearised into an elastic and inelastic Poisson ratio.

m m

Applied strain gauges on sample side and front surface

Fig. 2. Uniaxial tension test, measurement of elastic and plastic Poissons ratio [2].

= 0.70

= 0.08 In-plane PPR

Out-of-plane-plane PPR

In terms of numerical implementation, an iterative backward-Euler procedure [13] is used to return trial elastic stresses, which lie outside the limit surface, normally back to the limit surface. The associated incremental inelastic strains are defined using the Prandtl-Reuss equations, often called an associated flow rule, and state that the plastic strain increments are proportional to the stress gradient of the yield function. The proportionality constant, d, is known as the plastic strain-rate multiplier. Written out explicitly the inelastic strain increments are given by

d

aaa

aaaaaaaaa

dddddd

p

p

p

p

p

p

++++++

=

1266

3155

2344

333322231113

332322221112

331322121111

12

31

23

33

22

11

444

222222222

(5)

From which an equivalent inelastic strain measure can be derived [2]


( ) 2238 dfd P = (6)

This in turn feeds back into the hardening function, k, of the limit surface. The developed non-linear hardening option, in combination with the baseline model, allows for

much improved simulation of the non-linear in-plane hardening behaviour of fibre composite materials as shown in Fig. 3.

Fig. 3. Aramid-fibre-epoxy uniaxial stress tension tests - experiment and simulation. (a) Loading at 0 to fibre direction;

(b) Loading at 45 to fibre direction.

2.2 Non-linear Softening (Damage)

Considering failure in fibre composite materials, delamination caused by through thickness strain, shear strain causing matrix cracking, and fibre failure are the dominant modes of damage for impact loading. These modes of failure lead to a reduction in load carrying capacity in one or more material directions we shall term this phase of deformation as softening (reduction in capability to hold stress with strain). A key characteristic here is the anisotropic nature of the effects of failure on the residual strength of the material. For example delamination leaves the material with zero tensile strength across the fibres, but significant tensile strength remains in the plane of the fibres.

To understand and quantify this type of phenomena a range of material characterisation tests must be performed to establish; the point at which softening starts to occur, the rate at which the material softens to zero strength in a particular material direction. These features determine the energy absorbed during the damage process.

The modelling approach taken here introduces additional failure initiation criteria and associated limit surfaces in material stress space, to represent specific modes of failure. Modified forms of the well-known Hashin failure criteria [14] have been adopted for both the failure initiation criteria and additional limit surfaces.

ii-plane:: 1)1()1()1(

2

,

2

,

2

,

2

+

+

= ikfailikik

ijfailij

ij

iifailii

iiiif DDD

e

(7)


The above failure initiation criteria are checked at each material integration point each cycle. If one of the failure criteria is exceeded (eiif>1), the orthotropic damage model is activated for that integration point. The damage model has several aspects:

2.2.1 An Updated Elastic Material Stiffness Matrix

( ) ( ) 000),(1),(1 DDMaxCDDMaxCC

cr

( ) ( )( ) ( )

=

66

55

44

33332223331113

33222322221112

33111322111211

000000000000000000),(1),(1000),(1),(1

CC

CCDDMaxCDDMaxC

DDMaxCCDDMaxC

ijC

(8)

2.2.2 Limit Surfaces in Material Stress Space and Damage Law

Additional limit surfaces are defined in material stress space through the failure initiation criteria in each material plane. If a stress point lies outside a limit surface, it is associatively returned to the limit surface using an iterative backward-Euler procedure [13]. Returning a stress point to a softening limit surface results in inelastic crack strain.

The resulting inelastic strain is then used as input to an orthotropic damage evolution law ij

=

ij

crij

fij

ijijij FG

FLD

2

2

(9)

where Fij represents the initial failure stress in the three material directions and shear, Gijf is the fracture energy for each mode of failure and Lij is a local characteristic dimension of the numerical integration point in each direction. This damage equation is formulated such that the work required to extend a crack by a unit length is relatively insensitive to the local element size in each direction and is an extension of the model developed for isotropic materials [15].

2.2.3 Damage Characterisation

The material data requirement for the orthotropic softening model was purposely limited to the direct and shear failure initiation stress (Fij) in each of the material planes, and the associated fracture energy release rates (Gfij) for mode I and II crack growth. A variety of material characterisation experiments were developed and used to populate the parameters of the failure surfaces.

Static Damage Characterisation Tests For the cross woven aramid-fibre-epoxy laminate under consideration (Kevlar/129-epoxy),

transverse isotropy was assumed. In this case the parameters for the failure surfaces in the two material planes perpendicular to the fibres could be derived from the in-plane uniaxial tension tests, as detailed above: The tensile failure initiation stress could be obtained directly from the experiment; the in-plane shear failure stress was derived through numerical simulation and calibration to match the experimental


results for in-plane tension at 45 to the fibres (Fig. 3). The transverse shear failure stress (mode II) was assumed to be equal to the inter-laminar shear

failure stress and derived from a Double Notched Shear test as descried in Fig. 4(a) (performed according to standard proposal ASTM D 3846-79 and optimised according to [16] to compensate for normal stresses). The mode II delamination energy was derived using an End Notch Flexure test as described in Fig. 4(b) (performed in accordance with standard proposal EN 6034). A predefined crack propagates as a result of the specimen bending and associated shear forces at the crack tip in the Mode II loading. The total fracture energy GIIc is calculated from the initial crack length, the critical load to start the crack and the associated piston displacement at onset of crack propagation.

The through thickness (mode I) delamination energy was obtained using a Double Cantilever Beam test arrangement as described in Fig. 4(c) (performed in accordance with the standard proposal EN6033). An initial delamination or pre-crack is introduced at the tip of the specimen with a diamond saw. The pre-cracked specimen is loaded continuously by the loading device until a total propagated crack length of 100 mm is achieved. The mode I fracture energy can be derived from the resulting load displacement curves.

A major challenge for the characterisation and modelling of fibre reinforced composites subject to impact is the through thickness (transverse shear) mode of deformation. Little attention is paid in the literature to this mode of deformation, most composite research being focussed on in-plane and bending response (structural behaviour). In this work a Short Beam Bending test [2] was used to try to characterise the through thickness behaviour (Fig. 4(d)).

h

t

l

x

hydraulic piston

specimen

load cell

h = 10 mm w = 8 mm l = 40 mm l0 = t = 5.7 mm

l0

Piston

Initial crack

Load cell

Specimen

l

a

l = 100 mm w = 25 mm a = 35 mm b = 40 mm t = 5.7 mm

b

t

L = 200 mm w = 25 mm h = 5.7 mm a = 50 mm

w

h

L

a

Force

l=3.35 mm

wt

5.7 mm

loading fork

50 mm

l=3.35 mm

specimen

fixed support

specimen dimensions:

- length: 140 mm - width: b=20.24 mm - thickness: t=5.7 mm

Fig. 4. (a) Double notched shear test; (b) end notched flexure test; (c) double cantilever beam test; (d) short beam bending test.

(a) (b)

(d)(c)

Dynamic Damage Characterisation Tests Planar Plate Impact tests were used here to estimate the spall strength (through thickness tensile

strength) of the material. The tests consisted of a 3mm thick aluminium alloy flyer impacting 5.65mm thick aramid-fibre-epoxy laminate at velocities between 100m/s and 255m/s. A laser interferometer was


used to measure the particle velocity on the rear surface of the target. To derive the through thickness tensile strength at high strain rates a superposition of release waves

is generated in the target plate. Therefore the ratios of plate thicknesses and shock velocities are adapted to superimpose release waves from the target free surface and from the projectile rear side in the sample (target) material. Fig. 6 shows the velocity signals recorded at the target free surface of the aramid-fibre-epoxy composite. Note that in comparing experiment with numerical simulations of the configurations using accurate shock data for the material [4], mismatches are observed with respect to rise time and the shock plateau level. So far, shock dispersion in the composite sample is assumed to be the reason for this unexpected experimental behaviour. Although spallation measurements with the aramid-fibre-epoxy composite are not as successful as for metals, estimates for input to the material model could be obtained.

2.3 Final Material Model, Data and Required Material Characterisation

The full set of capabilities of the developed model for fibre composite materials can be summarised Orthotropic elastic stiffness Non-linear and energy dependent volumetric response for high compressions Non-linear orthotropic strength with isotropic hardening Stress based failure initiation on each material plane Orthotropic damage based on fracture energy

The required input parameters and the matrix of material characterisation tests used to derive each parameter is presented in Table 1. Data derived for the aramid-fibre-epoxy laminate considered here is also provided.

Table 1. Model input data and derived material constants for Kevlar-epoxy

EQUATION OF STATE : Orthotropic STRENGTH MODEL : Orthotropic Yield (non-linear hardening) Parameter Source Parameter Source

= 1.65000E+00 g/cm3 Direct Measurement a11 = 1.50000E+00 0o tension test E11 = 1.94800E+06 kPa Uniaxial tension tests* a22 = 1.00000E+00 0o tension test E22 = 1.79898E+07 kPa 0o tension test a33 = 1.00000E+00 0o tension test E33 = 1.79898E+07 kPa 0o tension test a12 = -6.80000E-01 0o tension test

12 = 7.56000E-02 0o tension test a13 = -6.80000E-01 0o tension test 23 = 7.56000E-02 0o tension test a23 = -2.60000E-01 0o tension test 31 = 6.98000E-01 Confined compression test [4] a44= a55=a66 = 4.00000E+00 45o tension test

G12 = 2.23500E+05 kPa G23 = 1.85701E+06 kPa G31 = 2.23500E +05 kPa

45o tension test Short beam shear test Short beam shear test

Plastic Strain = 0.0, 9.0e-6, 6.2e-4, 1.9e-3, 2.5e-3, 5.0e-3, 8.8e-3, 1.2e-2,

2.6e-2

0o tension test

Tref = 3.00000E+02 K Cv = 1.42000E+03 J/kgK)

- Literature

Effective stress = 1.55e5, 1.55e5, 1.67e5, 1.78e5, 1.87e5, 1.93e5,

2.10e5, 2.35e5, 2.52e5, 3.16e5 kPa

0o tension test

Sub Equation of State:: Polynomial FAILURE MODEL : Orthotropic Damage (non-linear softening)

A1 = 5.89499E+06 kPa Planar plate impact tests Parameter Source A2 = 5.00000E+07 kPa Planar plate impact tests fail 11 = 4.50000E+04 kPa Calibration to match PPI Spall and DCB tests T1 = 5.89500E+06 kPa Assumed equal to A1 fail 22 = 2.45000E+05 kPa

fail 33 = 2.45000E+05 kPa 0o tension test fail 12 = 1.40000E+04 kPa Interlamina shear test fail 23 = 2.00000E+04 kPa Calibration to match 45o tension test fail 31 = 1.40000E+04 kPa Interlamina shear test Gf11 = 5.44710E+02 J/m2 Double cantilever beam test Gf 22 = 3.00000E+01 J/m2 Calibrated to 0o tension test Gf12=Gf23=Gf31=1.46130E+03 J/m2 End notched flexure test


3. Validation

Initial validation and assessment of the developed material model and derived input was performed using dynamic planar plate impact experiments [2]. Here we shall discuss two examples of this type of test. Further examples are described in Part II of the paper [1] along with hypervelocity impact validation.

3.1 Inverse Plate Impact

During development of the baseline model [4] inverse plate impact experiments were reported from which the uniaxial compression behaviour at strain rates up to 104 /s was studied for aramid-fibre-epoxy composites. In these sets of experiments a 50mm diameter projectile composed of aramid-fibre-epoxy with a C45-steel backing plate impacts a stationary witness plate also made of C45-steel. A VISAR laser interferometer system recorded the velocity trace of the witness plate during the impact. Simulations of these experiments are repeated here using the enhanced material model and data to ensure that the addition of the non-linear strength and damage aspects of the model did not prejudice the models ability to reproduce the transient shock wave propagation phenomena. The simulations were performed using the Lagrange solver of AUTODYN [3] in a uniaxial strain configuration with element size 0.1mm. Fig. 5 demonstrates the ability of the model to reproduce experimental VISAR signals at three velocities.

5.7mm2.0mm

C45 Steel

Kevlar-Epoxy

2.0mm

C45 Steel

Stationary witnesplate

s

Projectile

5.7mm2.0mm

C45 Steel

Kevlar-Epoxy

2.0mm

C45 Steel

Stationary witnesplate

s

Projectile

Fig. 5. Aramid-fibre-epoxy inverse flyer plate experiments and simulation comparisons (572m/s, 788m/s, 1055m/s).

3.2 Plate Impact Damage

Both direct and symmetric planar plate impact tests were performed at different velocities to provide a basis for validating the ability of the numerical model to predict damage levels for given impact conditions [2]. 2D axisymmetric simulations of these tests were conducted using the Lagrange solver of AUTODYN [3] and the material model and data as described in [2]. Elements of side 0.1mm were used throughout. The results are presented and compared with the experiment, and results using the baseline material model and data [4] (Fig. 6).


(Expt.) 117m/s (Simulation)

(Expt.) 150m/s (Simulation) Fig. 6. Planar plate impact test. (a) target rear surface velocity; (b) recovered samples and simulated delamination.

The key item to correlate between simulation and experiment is the magnitude of the pull-back spall signal observed in the tests. For the higher velocity, the experiment shows a pull-back spall signal of 62 m/s. The simulation with the original baseline model and data does not show any velocity reduction after the peak velocity. The new extended model and data gives a reduction of 58m/s by release waves, which is similar to the observed signal.

The samples recovered from the experimental tests all showed extensive delamination, illustrating that the spall strength was exceeded in all tests. Contours of simulated through thickness damage are consistent with experimental observations (Fig. 6).

The results of simulations of a symmetric planar plate impact test with the enhanced model and data show a more marked improvement in the prediction levels of damage levels over the original base model. This configuration is further discussed in detail in Part II [1].

4. HVI Simulation Columbus module shielding

Hypervelocity impact simulations on the Columbus shielding configuration using the baseline material model have previously been conducted and reported in [4]. These 2D axisymmetric simulations have been repeated here using the enhanced material model and data. Comparisons with the previous simulation work and experiments [2] are discussed. The case of a 15mm diameter Al2007 sphere impacting the shielding configuration at 6500m/s (Test case A8611, [4]), is described here.

The projectile, first bumper (aluminium) and the second bumper (Nextel and Kevlar-epoxy) are represented using the SPH solver with smoothing length of 0.25mm. The rear wall is represented using the Lagrange solver with element edge size of 0.25mm out to a radius of 60mm. Gradual transition to larger elements is then made to a final radius of 200mm for efficiency purposes.

Fig. 7 highlights the through thickness damage (delamination) predicted. It can be seen that during the impact extensive delamination/damage occurs in the immediate vicinity of the impact (Light grey regions Fig. 7). However the lateral growth in delamination is significantly less for the latest model and data. This correlates better with experimental observations compared with previous simulations [4]. As observed in experiment, the new simulation predicts cratering of the backwall with no. This represents a


refined prediction of rear-wall damage over equivalent simulations performed using the baseline material model and data [4], as quantified in Table 2.

(a) Final damage, old model and data[4] (b) Final damage, new model and data[4]

Fig. 7. 2D Axisymmetric simulation of Alenia/EMI test A8611 [2].

No perforation of backwall

Table 2. Columbus shield HVI simulations, quantitative damage comparison

Kevlar/Epoxy Back wall Test / Ident Bumper Hole

Nextel Hole Front Back Hole Crater Pl. Def.

Experiment 26.55 95 68 52 N/A 1.2 227.5 Original

Simulation [4] 29 96 94 46 6 N/A 174

New Simulation [2] 30 88 77 75 N/A 1.5 180

5. Conclusions

An improved continuum material model suitable for modelling impact on composite materials under low to hypervelocity impact conditions has been developed and implemented in AUTODYN [3]. The model is now capable of representing: orthotropic elastic stiffness, non-linear shock effects, orthotropic non-linear hardening, orthotropic non-linear damage. The features of the model can be turned on/off as required for the material being simulated and the available input data. The model is designed to be applicable to a wide range of orthotropic materials under low to hypervelocity impact conditions.

An extensive experimental programme covering a wide range of static and dynamic tests was conducted hand-in-hand with the numerical modelling work. This included both material characterisation experiments for; directional strength and failure, delamination energy, equation of state measurement. Additionally new impact experiment configurations were developed to allow quantitative assessment of the extent of damage development in composite materials under different loading


conditions. Throughout the model development and experimental programme, an extensive simulation

programme was used to support the model development and assess and validate the improved composite material model. This included; simulation of material characterisation tests to verify that the model could reproduce the underlying material response observed in experiments, simulation of impact damage experiments to assess the evolving material model and supplied input data, simulation of hypervelocity impact events on simplified and representative shielding configurations to assess the performance of the new model and data on the target application.

Further application and validation of the final model and input data is described in Part II of this paper [1]. Acknowledgements

This work was funded by ESA/ESTEC under contract No.12400/97/NL/PA(SC), CCN No. 2. The

authors gratefully acknowledge the direction and advice provided by Michel Lambert of ESTEC.

References

[1] Riedel W, Nahme H, White DM, Clegg RA, Hypervelocity Impact Damage Prediction in Composites, Part II Experimental Investigation and Simulations, paper submitted to Int. J. Impact. Engng. 2005.

[2] Riedel W, Harwick W, White DM, Clegg RA, Advanced Material Damage Models for Numerical Simulation Codes, Fhg-EMI report no. I 75/03, ESA CR(P) 4397, 2003.

[3] Century Dynamics, AUTODYN Theory Manual, 2005. [4] Hiermaier SJ, Riedel W, Hayhurst CJ, Clegg RA, Wentzel CM, Advanced Material Models for

Hypervelocity Impact Simulations, EMI report no. E43/99, ESA CR(P) 4305, 1999. [5] Anderson CE, Cox PA, Johnson GR, Maudlin PJ, A Constitutive Formulation for Anisotropic Materials

Suitable for Wave Propagation Computer program-II, Comp. Mech. 1994; 15: 201-223. [6] Hayhurst CJ, Livingstone IH, Clegg RA, Destefanis R, Faraud M, Ballistic Limit Evaluation of Advanced

Shielding using Numerical Simulations, Int. J. Impact Engng. 2001; 26: 309-320. [7] Clegg RA, Hayhurst CJ, Nahme H, Validation of an Advanced Material Model for Simulating the Impact

and Shock response of Composite Materials, APS SCCM 2001. [8] White DM, Taylor EA, Clegg RA, Numerical Simulation and Experimental Characterisation of Direct

Hypervelocity Impact on a Spacecraft Hybrid Carbon Fibre/Kevlar Composite Structure, Int. J. Impact Engng., 2003; 29 : 779-790.

[9] Silva MAG, Cismasiu C, Chiorean CG, Numerical Simulation of Ballistic Impact on Composite Laminates, Int. J. Impact Engng. 2004.

[10] Riedel W, Thoma K et al, Vulnerability of composite aircraft components to fragmenting warheads experimental analysis, material modeling, numerical studies, 20th Int. Symp. Ballistics, 2002.

[11] Chen JK, Allahdadi FA, Sun CT, J. Comp. Mat., 19997; 31: 788-811. [12] Hill R., Proc. Royal Society, London A, 1948; 193: 281-297. [13] Crisfield MA, Non-linear Finite Element Analysis of Solids and Structures, John Wiley, 1997. [14] Hou JP, Petrinic N, Ruiz C, Prediction of impact damage in composite plates, Comp. In Sc. and Tech., 2000;

60: 273-281. [15] Clegg RA, Hayhurst CJ, Numerical modelling of the compressive and tensile response of brittle materials

under high pressure dynamic loading, Shock Compression of Condensed Matter, AIP press, 1999. [16] Thielicke B, Mechanical properties of C/C composites, Key Engineering Materials, 164-165: 145-160.

W. Riedel et al. / International Journal of Impact Engineering

Hypervelocity Impact Damage Prediction in Composites Part II - Experimental Investigations and Simulations

Werner Riedel*+, Hartwig Nahme+, Darren M. White**, Richard A. Clegg**

+FhG - Ernst-Mach-Institut, Eckerstrae 4, D-79104, Freiburg, Germany **Century Dynamics Ltd., Dynamics House, Hurst Road, Horsham, West Sussex, RH12 2DT, England

Abstract

The extension of damage in composites during hypervelocity impact (HVI) of space debris is controlled by failure thresholds and subsequent energy consumption during damage growth. Characterisation and modelling of the material under partially and fully damaged states is essential for the prediction of HVI effects on fibre-composite structures. Improved experimental and numerical analysis techniques have been developed [5] and are summarised in paper part I [1]. The present part II deals with the establishment of two precise damage experiments under hypervelocity impact conditions as a validation basis for numerical simulations: The first type consists of space debris impact configurations optimised for damage evaluation, the second experiments reproduce HVI strain rates and compressions in plate impact. Coupling of experimental damage analysis techniques (visual, ultrasonic, residual strength) to quantify different aspects of failure has been achieved. Numerical simulations using the commercial hydrocode AUTODYN [4] in mesh-based and SPH formulations are presented using the material model and data described in part I [1]

Keywords: Delamination, Composite, Damage Modelling, Residual Strength, Plate Impact, ISS

1. Introduction

Model approaches for dynamic behaviour and damage in composite structures caused by hypervelocity transverse shock loading need to replicate several key aspects of mechanical behaviour: Non-linear equation of state properties must describe the shock impedances for accurate prediction of compression and release states with phase changes and spallation [1]. Orthotropic strength is a key aspect of composite in-plane behaviour to be coupled to equation of state properties. Characterisation and modelling methods coupling these aspects of directional non-linear mechanical properties have been developed recently [5] and are described in paper part I Material Model and Characterisation [1].

In part I, application of the numerical technique is demonstrated on the examples of the space debris protection shield of the International Space Station (ISS) Columbus module involving aramid-

*Corresponding author. Tel.: +49 761 2714 335; fax: +49 761 2714 316. E-mail address: [email protected]


fibre reinforced plastics (AFRP) as an intermediate bumper. The aim of the present study was to enlarge the validation basis by adding controlled damage experiments and loading conditions relevant for hypervelocity impact applications. Combinations of non-destructive and destructive testing of the damaged samples should enable in-depth analysis of the aspects of damage and couple different evaluation techniques. Two types of HVI damage experiments have been developed and used for validation of the new model approach:

Table 1. Overview and damage experiment types

Damage generated by Discussion (+ advantages, - limitations)

HVI debris cloud + very close to applications + damage gradient adapted for validation - locally statistical impact conditions

Plate impact + precise and recorded impact conditions + relevant strain rates and pressures - mainly plane compression and release waves

All tested composite material consisted of 18 layers of 0/90 woven Kevlar 129/812 fabric

(aramid) with 38% mass content of epoxy resin Ciba 914 (Hexcel prepreg: 914/38%/812). The slightly cylindrical panels, curved to an external radius of 2163.2 mm correspond to the intermediate composite bumper configuration of the European Columbus module of ISS.

2. Debris Cloud Damage

2.1 Impact Conditions

Whipple shield configurations consisting of an aluminium bumper layer and a composite plate impacted by an aluminium projectile have been optimised in view of validation of computational damage models. Experimental knowledge in hypervelocity impact testing and predictive simulations were used (see Fig. 1) for pre-test optimisation of the design with respect to:

Ballistic limit: Only a small central perforation should occur. Shatter region: Smooth transition of hit densities from the central impact region to the

outer damage area should be reached by avoiding a large central fragment. Cloud extension: By maximising this parameter a large damage transition area should be

produced but fully contained in intact surroundings of the sample plate.

Table 2. Impact conditions for debris cloud damage experiments

Experiment No. 4354 4355 4356 Projectile - material Al 99.98%

AlMg3 (Al5754 H34/ hard)

AlMg3 (Al5754 H34/ hard)

- density 2.70 g/cm3 2.70 g/cm3 2.70 g/cm3 - diameter 7.00 mm 8.20 mm 7.0 mm - mass (weighed) 474.44 mg 770.88 mg 474.86 mg - impact velocity 4.75 km/s 4.68 km/s 4.81 km/s - impact angle 0 0 0


The resulting three configurations consisted of an aluminium sphere (diameter 7.0 to 8.2 mm) fragmented during perforation of a 2 mm aluminium plate at 4.7 km/s (Table 2). A clear distance of 150 mm to the 5.7 mm composite plate permitted the fragment cloud to expand to a lateral extension of about 360 mm diameter. High speed shadowgraphs (exposure time 100ns) are shown in Fig. 1, right. It can be seen that only a small central area is fully perforated, the rest of the plate is impacted and damaged by a wide range of fragment densities.

Fig. 1. Left: Predictive simulation using base line model [3].

Right: High speed shadowgraphs (28 s, 55s; exposure 100ns) of fragment cloud impact onto composite plate (exp. 4355).

2.2 Visual Damage Inspection

Visual inspection of the samples proved good pre-test prediction: all three fragment clouds loaded the composite plates slightly above the ballistic limit in the very centre of the impact cloud. The impacted faces of the plates are shown in Fig. 6. Fig. 2 gives additional views of plate 4355.

Table 3. Visible composite damage after debris cloud impact; damage measure defined in Fig. 2 (right)

No. Front Rear Primary damage Secondary damage d1,f d2,f D1,f D2,f d1,r

d2,r

D1,PS,r

D2,r

[mm] [mm] [mm] [mm] [mm] [mm] [mm] [mm] 4354 110 110 360 345 75 125 100 130 4355 110 135 130 390 390 110 230 10 4356 110 105 365 360 125 75 132 130

Perforation in Composite / Effect on Witness Plate 4354 some composite layers completely destroyed, no clear hole / few scratches on witness panel

4355 clear perforation hole visible / two bulges; distance from centre and several small bulges in the middle; cratered area about 100 x 90 mm. 4356 some composite layers completely destroyed, no clear hole / few scratches on witness panel

Notation: di,PS diameter of damaged composite layers; Index: f front, r rear, 1 vertical, 2 horizontal In experiments 4354 and 4356 with 7 mm spheres no clear hole was noticed but scratches on

witness plates behind the composite indicated composite fibres ejected from the rear surface. Loading with an 8.2 mm sphere produced a small but clear hole in the composite.


In all cases, damage can be categorised into two zones: Primary damage in the central area with high hit densities and clearly visible surface

delaminations on the front face. The adjacent area of secondary damage shows isolated, local impacts without obvious

coalescence of damage or delamination on the surface. The observed damage patterns are summarised in Table 3.

front:drear

1,PS,f

:d1,PS,r

D1

D2,PS

,PS

front:drear

2,PS,f

:d2,PS,r

Fig. 2. Visible damage on impact and rear face. Definition of damage measures.

2.3 Non-destructive Damage Characterisation

Through thickness failure was analysed by ultrasonic measurements before sectioning of the target for further evaluations described below. The composite panels and the ultrasonic detector were placed in water for transmission of longitudinal waves from the source into the test object and back. The pulse travels through the water and is partially reflected at every impedance boundary such as the front side, discontinuities in the material or the rear surface of the sample.

0 mm

d2

d1=1,568mm; d2=5,91mm d1=1,86mm; d2=5,91mm

d1

100 mm

0%

100%

100 mmd3=19% d3=16%

d3

Fig. 3. Left pair: Depth of delamination measured from impact and rear side: cone shaped delamination shape.

Right pair: Intensity of reflection from impact and rear side.

The scanning area captured 320 x 320 mm with a scanning step of 0.2 mm. An analysis gate defined the range d1 to d2 through thickness between the front side and back wall echo in order to avoid misinterpretation of the plate free surfaces. The values refer to front side, the position of which is following the curvature of the composite panels. The location of the intermediate echo, caused by


delamination, correlates with the depth of the defect. A lower sensitivity threshold value d3 of 16-19% intensity was used to suppress background noise (see Fig. 3).

Fig. 6 shows scan results of the three panels from the impact side. Fig. 3 gives additionally the rear view, as only the depth of the first delamination detected in the analysis gate can be displayed in any scan. The gray scaling of the plate refers to the delamination depth measured between the specified limits d1 and d2. The following observations could be stated:

Large areas of delamination are shown also in the outer zones where only isolated impacts occurred. The delaminated areas clearly exceed the visible ranges of heavy damage di,f.

Beginning from a central region of delamination through the complete thickness, the damage in the secondary region is cone shaped toward the rear surface.

The damage patterns are mostly circular, slightly flattened normal to the laminate axis. The large sphere (8.2 mm, No. 4355) creates a bigger central damage zone especially on

the rear surface compared to the smaller projectile of equal strength (7.0 mm, no. 4354). But the total area around the outer zones of damage is of the same size.

Comparing effects created by the small spheres (No. 4354, 4356), the harder alloy (No. 4356) provides a smaller extent of damage with a sharper transition zone. The delamination cone is steeper through thickness.

2.4 Destructive Testing: Visible Inspections and Residual Strength

Sectioning in strips of 20 mm width, visual inspection and residual strength testing provided deepened insight to the amount of damage. Hydrocutting was used to minimise additional damage. Visual inspection of all sections, as exemplarily shown in Fig. 4 showed very fine delaminations in the zone of secondary damage, proving high sensitivity of ultrasonic scanning.

total failure delamination delamination

15 18 21 24 27 1296 3 0 30

Fig. 4. Visual inspection of in-depth damage after sectioning: example central section 4355_8 (out of 16).

Positions of transverse shear testing 0, 3, 6, , 30 of each section.

Advanced damage measures in constitutive models not only describe the areal extension but also the quantitative effects in terms of strength or stiffness loss. In order to establish the link between observed damage and its strength effects, local shearing was applied to every section as shown in Fig. 5. Testing every 30 mm (see scale above Fig. 4) provided a strength analysis grid with 20 mm x 30 mm resolution in the central area of 300 x 300 mm of each composite panel. A surface plot of damage in terms of shear strength degradation is shown in Fig. 5, right.


0

500

1000

1500

2000

2500

3000

0 1 2 3 4 5 6 7 8distance [mm]

Forc

e [N

]

4355_8_04355_8_34355_8_64355_8_94355_8_124355_8_154355_8_184355_8_214355_8_244355_8_274355_8_30

0

3

6

9

12

1518

21

24

27

30

stiffnessstrength

0

0.2

0.4

0.6

0.8

1Damage [-]

2 4 6 8 10 12 14 16 18 20 22 24 26 28 300

36

912

1518

2124

2730

width [cm] (sections)

lengt

h [cm

]

0.8-10.6-0.80.4-0.60.2-0.40-0.2

Fig. 5. Left: shear test curves of section 4355_8. Right: Damage distribution (shear strength ratio) in plate 4355.

2 6 10 14 18 22 260

6

12

18

24

30

3000-35002500-30002000-25001500-20001000-1500500-10000-500

2 6 10 14 18 22 26

0

6

12

18

24

30

2500-30002000-25001500-20001000-1500500-10000-500

18 22 26 30

0

6

12

18

24

30

2000-25001500-20001000-1500500-10000-500

Fig. 6. Coupling evaluation techniques: left: visible damage, centre: ultrasonic scan of depth of defects, right: shear strength.


Fig. 6 correlates visual surface damage, depth of delaminations and strength reduction for all three plates. Quantitative comparison of all three techniques provides:

Secondary damage by isolated cloud fragments causes substantial delamination around the primary damage zone.

Although hardy visible in sections, delamination in the secondary damage zone reduces the shear strength by 10% to 30%.

Ultrasonic scanning can detect secondary damage with high resolution. Primary damage results in strength and stiffness losses from 60% to 100%.

2.5 Simulation of HVI Damage Experiments

The axisymmetric simulation model of test 4355 was established using Smooth Particle Hydrodynamics discretisation (AUTODYN [4], Fig. 7). A smoothing length of 0.2 mm throughout allowed to resolve the composite panel with 29 particles through thickness. The Al2017A bumper shield of thickness 2.0 mm was modelled to a radial extent of 75 mm (3750 particles), the nominally 5.7 mm thick Kevlar-epoxy target to 200 mm (29725 particles).

a) impacting fragment cloud b) new model [1],[5]

c) sample

d) details damage, plastic strainFig. 7. (a) Simulated debris cloud impact , (b) delamination extension and central hole after HVI impact damage; (c)

comparison to experiment; (d) details of damage (D=0-1) and plastic hoop strain (0-20%).

More realistic simulations of the outer area with loading by isolated fragment impacts were achieved by additional 3D models. However, meshing with 0.6 mm diameters or only three particles through composite thickness already resulted in a total of 590 000 particles. Details on composite material model and data for both approaches are given in part I [1]. Analysis of the simulation allows the following conclusions:

The central perforation hole is very accurately predicted by the modelling approach. Earlier

0

1

0

0.5 1

0

1 0.5

0%

10%

20%

15%


model approaches [6] with shock and orthotropic strength descriptions but simpler failure models provided too large perforation holes (Fig. 1, left).

Extents of surface damage on front and rear face are well captured. In-depth delamination is correctly modelled in the primary damage zone. Coalescence in

the secondary zone is partly replicated as damage and plastic strain in the fine axisymmetric model with tendency to underpredict the extent.

The implementation of the model in 3D SPH discretisation provides in the coarse model qualitatively good results. Higher mesh refinement with the associated computational effort would be required to validate in detail the extent of delamination.

Fig. 8. Coarse 3D model with three nodes through thickness; left to right: mode I delamination damage (0-1) on front face, at

2.5mm depths and on rear face; representation in plate sections.

3. Plate Impact Damage

Locally varying loading conditions are an inconvenience of the above described debris cloud damage experiments. Statistics become more important for the smaller damage amounts in the secondary zone, making validation of limited degradation more difficult.

Therefore, small amounts of damage at relevant stresses and strain rates for hypervelocity impact applications have been generated in additional experiments of uniaxial strain loading. Two types of plate impact damage experiments have been performed on the basis of established flyer plate methods. The first type of axial compression and subsequent axial tension (spallation) is described and validated in paper I [1]. The following description will focus on the second type of multiple dynamic compression and later radial extension.

A symmetric configuration of composite and aluminium plates was used to prevent heavy delamination caused by superposition of release waves. In this way pre-damaged but solid, monolithic plates could be produced to perform residual strength tests. Properties of plates and impact velocities for all tests are summarised in Table 4.

Table 4. Impact conditions for plate impact damage experiments (plate diameters 50 mm)

Test No. 2606 2607 2608 2609 2610 Projectile thickness

(Al+comp.) 10.00 mm + 5.63 mm

9.96 mm + 5.63 mm

10.01 mm + 5.64 mm

10.00 mm + 5.56 mm

9.96 mm + 5.52 mm

Target thickness (comp.+Al)

5.63 mm + 10.00 mm

5.56 mm + 9.95 mm

5.57 mm + 10.01 mm

5.58 mm + 10.00 mm

5.52 mm + 10.00 mm

Impact velocity 124.4 m/s 206.6 m/s 276.1 m/s 255.6 m/s 241.7 m/s

0

1

0.5

0.8

0.4

0


Due to the symmetric impact conditions half of the projectile momentum is transferred to the target. Considering the different impedances of composite (AFRP) and aluminium (Al) the up and the X-t diagram can be derived according to Fig. 9. Pressure in the composite samples increases stepwise up to the state (3,III) before release waves (5) and (V) from the backing and target free surface arrive inside the composite plates. Subsequently the compressive stress is iteratively decreased by complex wave superposition, but no tensile loading in through thickness direction occurs during the whole process. However, tensile loading and complex stress-strain states occur when lateral release waves arrive from the circumference. At these late stages, no one-dimensional analysis of stress and strain states is possible, but the loading history can be numerically simulated in two dimensions, e.g. using axisymmetric modelling approaches.

particle velocity up

stress Projectile (Al) compression Projectile (Al) release Projectile (AFRP) compression Projectile (AFRP) release Target (Al) compression Target (Al) release Target (AFRP) compression Target (AFRP) release

0,A

6,E

C 0,

2,

V 5 II,

VI,

1,I

3,III

v0

IV, D,4

v0 F

A

B

C

0

1

2

0

I

II

III3 4

location x

time

IV D

E F V 5

VI 6

0

50

100

150

200

250

300

350

0 5000 10000 15000 20000

Time [ns]Fr

ee S

urfa

ce V

eloc

ity [m

/s]

V2606 124m/s

V2608 276m/s

AUTODYN - ADAMMO

AUTODYN - ORIG. AMMHIS DATA

Fig. 9. Lagrange and X-t-diagrams of symmetric uniaxial strain damage experiment. Right: Measured and simulated free

surface velocities. Similar stress wave levels occur for baseline model AMMHIS [3] and new ADAMMO approach [1].

The free surface velocity measured with the VISAR during early stages of the plate impact damage experiments is shown in Fig. 9, right. They were not used to derive directly constitutive data, but to validate simulated free surface velocities of the early arriving stress waves. For the lowest impact velocity of 124.4 m/s (No. 2606), almost no damage is apparent on the recovered samples. With increasing impact velocity more stiffness loss can be assumed from visible inspection. For intermediate to fast impacts up to 276 m/s delamination of the discs is observed.

V2608visible delaminations

V2606no visible delaminations

0

500

1000

1500

2000

2500

0 50 100 150 200 250 300velocity [m/sec]

stiff

ness

[N/m

m]

.

0

500

1000

1500

2000

2500

3000

Fm

ax [N]

124.4 m/sec stiffness206.6 m/sec stiffness241.7 m/sec stiffness255.6 m/sec stiffness276.1 m/sec stiffnessintact stiffnessaverage stiffness124.4 m/sec Fmax206.6 m/sec Fmax241.7 m/sec Fmax255.6 m/sec Fmax276.1 m/sec Fmaxintact Fmaxaverage Fmax

Fig. 10. Left: Plate impact damage samples recovered and sectioned after loading with 124.4 m/s and 276 m/s.

Right: Strength degradation in terms of stiffness and maximum shear loading.

124 m/s

276 m/s


In the same manner as the debris cloud damage panels, the preloaded plate impact samples were sectioned to 20 mm strips and shear tested. Fig. 10 shows the measured shear stiffness and strength decrease. Already 124 m/s impact loading caused strength and stiffness decreases by 25 to 30%. Above 220 m/s, the plates are mostly damaged with a residual strength of about 20%. Again, delaminations hardly observable in sections have major effects on the residual strength.

The experiments were simulated using the composite model approach [1]. 0.125mm square Lagrangian cells were used to model the thickness of the composite plates in axial symmetry. Fig. 15 shows the comparison of simulated free surface velocities of the aluminium target plate. Differences were observed on details of shock amplitudes and deceleration by release waves. But the overall match of acceleration during the first 20 s proved good replication of the momentum balance between projectile and target plates. Interestingly, the earlier model approach [3] describing non-linear equation of state with linear-orthotropic strength and instantaneous failure simulates very similar free surface velocities. Obviously, the uniaxial strain compression properties are not strongly influenced by additional dissipation from non-linear inelastic deformations as modelled in the new approach.

Exp. Model [1] ,[5]: Through thickness damage D11=0-1

Model [1],[5]: Plastic strain 0-10%

Model [3]: Material status

2606

124.4 m/s

2608

276.1 m/s

Fig. 11. Simulated plate impact damage tests: negigible damage, permanent strains below 3% for 124 m/s impact; strains up to

10% for 276 m/s impact, no delaminations simulated. Overpredicted failure simulation with earlier model status [3].

failure 11

elastic

failure 11

multiple failure modes

0%

1.8%

2.7%

5%

7%

0

0.25

0


Detailed consideration of simulated deformation and damage contours (Fig. 11) shows that the new damage model replicates the intact composite samples. Delamination damage is not directly predicted (as ORT DAM 11). But the slowest impact velocities cause plastic deformations up to 3% and up to 10% local deformation are reached in the samples impacted at 276 m/s. Compared to the previous model approach with linear-orthotropic strength up to failure, much improved prediction of material states is observed. With the earlier model, both loading types caused complete through thickness delamination, which was not observed experimentally.

4. Summary and Outlook

Delamination damage in the aramid-weave-epoxy composite panels impacted by space debris clouds extends far beyond the area of primary damage into areas, where only isolated impacts are visible on the surface. In the secondary zone of the debris cloud damage test ultrasonic testing detected very fine areal delaminations, which were hardly visible in sections of samples.

However, subsequent destructive shear testing across the samples showed the important mechanical effects of small delaminations on shear stiffness and strength. The following damage quantities could be identified:

The zone of primary damage with high densities of impacting debris resulting in obvious surface delamination correlated with strength and stiffness losses from 100% to 70%.

In the zone of secondary damage with low hit densities and isolated impacts, delaminations extended almost to the external limit of debris impacts. They caused strength and stiffness losses from 20% to 60%.

Loading by hypervelocity debris clouds results in strong local variations, especially in the secondary zone of the debris cloud damage experiments. These variations make validation of numerical methods in the area of limited degradation more difficult. Therefore, plate impact damage experiments were designed to create smaller damage amounts under well defined loading conditions at relevant strain rates. A number of samples ranging from weak damage (


Fig. 12. Preliminary application of new composite model approach [5] to a CFRP-aluminium honeycomb structure

(ENVISAT). Analysis of hit point influence on debris cloud dispersion [7].

Acknowledgements

The authors gratefully acknowledge the important technical contributions of Frank Schfer, Holger Voss and Jochen Peter. We would like to express our thanks to Michel Lambert from ESA/ESTEC for funding and directing the described research.

References

[1] Clegg RA, White DM, Riedel W, Harwick W. Hypervelocity Impact Damage Prediction in Composites, Part I Material Model and Characterisation, submitted to Jn. Impact Engn. 2005

[2] Clegg RA, White DM, Hayhurst CJ, Riedel W, Harwick W, Hiermaier S, Advanced Material Models and Material Characterisation Techniques for Composite Materials subjected to Impact and Shock Wave Loading, Journal de Physique IV 2003, 110: 311-316

[3] Hiermaier SJ, Riedel W, Hayhurst CJ, Clegg RA, Wentzel CM, Advanced Material Models for Hypervelocity Impact Simulations, EMI report no. E43/99, ESA CR(P) 4305, 1999.

[4] N.N., AUTODYN, Theory Manual, Century Dynamics Ltd. Horsham, UK, 2003 [5] Riedel W, Harwick W, White DM, Clegg RA. ADAMMO Advanced Material Damage Models for

Numerical Simulation, ESA CR(P) 4397, EMI report I 75/03, Freiburg October 31, 2003 [6] Soden P, Hinton M., Kaddour A. Failure criteria in fibre reinforced polymer composites, Composites

Science and Technology 1998, 58, Special Issue. [7] Ryan S, Riedel W, Schfer F. Numerical Study of Hypervelocity Space Debris Impacts on CFRP/AL

Honeycomb Spacecraft Structures, International Astronautical Congress, Vancouver, 2004

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