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Composite Structures 77 (2007) 466–474

Ballistic limit prediction using a numerical modelwith progressive damage capability

Simon Chan, Zouheir Fawaz *, Kamran Behdinan, Ramin Amid

Department of Aerospace Engineering, Ryerson University, 350 Victoria Street, Toronto, ON, Canada M5B 2K3

Available online 5 October 2005

Abstract

The ultimate objective of this study is to provide further understanding of the behaviour of laminated composites of varying laminaorientations and stacking sequences, when under high-velocity impact. Emphasis is placed on the determination of ballistic limits of thesecomposites. To this end, an experimental program is carried out and a computational model, with progressive damage modeling capa-bilities, is developed using LS-DYNA. Experiments are performed whereby striking velocities are measured, via high-speed photography,to determine the ballistic limits of carbon fiber-reinforced polymer (CFRP) laminates of various stacking sequences. The results arereproduced closely by a numerical simulation, indicating that the numerical analysis conducted, including the choice of material modeland contact definition, is an accurate means for modeling the high-speed impact characteristics of CFRP laminates. It is found that theuse of static elastic and strength properties to describe the material is reasonable, since strain rate effects are found to be negligible. Thekinetic energy of the projectile, plotted over the simulated impact duration, is used as the prime parameter to compare the experimentaland numerical results. The numerical results accurately predict the experimental ballistic limit for six of the seven tested laminate stackingsequences. Failure due to delamination is found to play a vital role with respect to the energy absorbing ability and lamina stackingsequence of CFRP laminates.� 2005 Elsevier Ltd. All rights reserved.

Keywords: Ballistic limit; Composite laminates; Progressive damage; Delamination; Experimental; Numerical

1. Introduction

Ballistic protection analysis is a concern in many fields,besides the obvious application of protective armour wherethe primary design objective is that of preventing projectilepenetration. Ballistic and high-speed impact research hasthe prospect to lend itself to aircraft and spacecraft analy-sis, where such impact is a potential threat. Naturally, mostinitial research studies on ballistic analysis have been con-ducted for military purposes. However, research geared to-ward civil applications is now being increasinglyundertaken [1–13]. Laminated fiber-reinforced compositesare now regularly considered in the design of thin platesand thin-walled structures, where high-speed impact is a

0263-8223/$ - see front matter � 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.compstruct.2005.08.022

* Corresponding author. Tel.: +1 416 979 5000x4502; fax: +1 416 9795308.

E-mail address: zfawaz@ryerson.ca (Z. Fawaz).

design concern. To harness the many advantages and un-ique properties these composites can offer, it is essentialto fully characterize them and understand their mechanicaland failure properties under the intended loading, that ishigh-speed impact. Unfortunately, experimental work car-ried out to determine the failure characteristics of newmaterials can be costly. An increasingly popular trend toenhance cost efficiency is to reduce destructive testing ofmaterials by predicting performance characteristics viaanalytical modeling and numerical simulation. It is unlikelythat the process of experimental testing can be totally re-placed by analytical modeling and numerical simulation;rather it is more likely that these methods will work handin hand to complement one another.

The main objective of this study is to provide furtherunderstanding of the behaviour of laminated compositesof varying lamina orientations and stacking sequences,when under high-velocity impact. First, experimental tests

Fig. 2. Target support structure.

Fig. 3. Gas gun.

S. Chan et al. / Composite Structures 77 (2007) 466–474 467

are performed whereby striking velocities are measured, viahigh-speed photography, to determine the ballistic limits ofCFRP laminates of various stacking sequences. A numeri-cal model is then presented to simulate the same tests usingLS-DYNA. Ballistic limits and damage characteristics ob-tained from these simulations are compared to the experi-mental observations.

2. Experimental test procedure and apparatus

2.1. Test material and preparation apparatus

A compression mould was used to fabricate the compos-ite laminates. The compression mould was manufacturedfrom two 30.48 cm by 30.48 cm by 1.27 cm plates and four2.54 cm by 1.27 cm by 30.48 cm rods. The plates and rodswere welded together to form an open box. A total of fiveholes, one at the center of the plate and four at equal dis-tances from the center, were made on the top plate of theopen box. The holes were tapped and lead screws were usedto apply a uniform pressure over the entire laminate. Fourcomposite laminates were sandwiched within eight pressureplates and the entire assembly was placed inside the openbox. The mould and assembly are depicted in Fig. 1. Alllaminates were laid using pre-impregnated AS4/3501 car-bon/epoxy, supplied as a continuous unidirectional tape,30.48 cm wide by 6583 cm long. All laminates consistedof 16 layers of various stacking sequences, cured accordingto the manufacturer�s prescribed cure cycle, using theaforementioned mould assembly. To conduct the impacttests, the cured laminates were rigidly clamped betweentwo steel frames. A total of 16 bolts, at the corners andmidsections of the steel frame, were used to clamp the lam-inates between the steel frames. This was done to ensure arigid mount on all four edges of the test specimen. Theresulting target support structure is depicted in Fig. 2.

2.2. Firing apparatus

The machine used to fire the projectiles at various veloc-ities was designed and built in-house. The firing apparatusconsists of: a pressure chamber, a barrel, a nitrogen tank, aburst diaphragm, a pressure relief valve, a pressure trans-ducer, and a nozzle, all shown schematically in Fig. 3.

Fig. 1. Compression mould assembly.

The firing process requires a gas (nitrogen, in this case)to be fed into the pressure chamber located at one end ofthe barrel. A plastic diaphragm is used to restrain the nitro-gen gas until the pressure in the chamber reaches a pre-determined value, at which moment the diaphragm bursts,accelerating a projectile down the barrel to strike the verti-cally supported specimen. The velocity of the projectile wasdetermined just prior to impact using a high-speed camera.

2.3. Test procedure

Testing for each specimen configuration begins with fir-ing a projectile at increasing velocities until the point wherethe projectile barely penetrates the specimen. The proce-dure continues until complete perforation of the specimenoccurs, at which point the ballistic limit velocity is re-corded. Four impact points per sample were chosen as abalance between the fabrication time and cost, and the abil-ity to get results at each point without affecting other areasof the sample, while maintaining consistent boundary con-ditions. The projectile was made from 660 bronze and itsmass stayed constant, meaning there was no mass erosiondue to impact. Full details on the experimental programcan be found in [14].

3. Numerical/finite element modeling

3.1. General approach

In this study LS-DYNA3D was used to create the numer-ical model. LS-DYNA has been determined by numeroussources to be a suitable tool for large deformation analysis.

468 S. Chan et al. / Composite Structures 77 (2007) 466–474

LS-DYNA performs dynamic analysis by seeking a solutionto the momentum equation, which satisfies all boundaryconditions, while integrating the energy equation to be usedas a balance for global energy. Accuracy is attained from theapplication of proper numerical techniques. Such tech-niques in general, however, are computationally demanding[15]. For our particular case, a penalty-based contact isapplied between projectile and composite plate. Thismethod has the effect of placing springs between all pene-trating nodes and the contact surface. Kinematic boundaryconditions are applied while the semi-discrete equations ofmotion and constitutive equations are solved. Time integra-tion is conducted via the central difference method whensolving for accelerations, velocities and displacements. Amixed time integration scheme is used and the time step isdetermined by the smallest element in the entire model.Databases are then written which record history variablessuch as stress, strain and kinetic energy. The velocities arethen updated followed by displacements and geometryreconfiguration. Finally, LS-DYNA updates the currenttime and checks it against the simulation termination time[16].

3.2. Model development

3.2.1. Material type

Zukas [15] states that the description of the materialdeformation and failure behaviour is a major determiningfactor in modeling ballistic impact of CFRP laminates.After experimenting with numerous material models, mate-rial type MAT 161 was chosen to represent the CFRP lam-inates because of its ability to model progressive damage,in addition to its model�s applicability to the inherentthree-dimensional state of stress created in an impact event.Progressive damage modeling is achieved through MAT161�s implementation of the Hashin failure criteria, internaleroding mechanisms, and progressive damage parameters.The Hashin failure criteria allow for fiber tensile and com-pressive failure, fiber crush failure, and matrix failure per-

Table 1Properties of carbon/epoxy (AS4/3501-6) and 660 bronze

AS4 Brass

Density (kg/m3) 1580 8470 LongitudinalLongitudinal

Youngs modulus (GPa) Transverse teE1 138.00 105.00 Transverse coE2 9.65 105.00 Through thicE3 9.65 105.00 Crush streng

Fiber mode sShear modulus (GPa) Yield strengt

G12 5.24 –G23 2.24 – Matrix modeG31 5.24 – 1–2 plane

2–3 planePoisson�s ratio 3–1 plane

m21 0.021 0.300m31 0.021 0.300 Coulomb fricm32 0.490 0.300 Limit damag

pendicular and parallel to the laminate layering [17–20].These criteria evaluate the stress state with correspondingfailure strengths to determine the mode of failure. A moredetailed description of these failure criteria and elementpost failure behaviour can be found in Ref. [17]. The inter-nal eroding mechanisms are modeled for orthotropic mate-rials to aid in the deletion of highly strained elements.Progressive damage parameters are utilized to describematerial behaviour after local failure has occurred.

3.2.2. Contact definition

Numerical modeling of high-speed impact requires care-ful definition of the contact between projectile and target.There are three ways in which LS-DYNA treats contact be-tween bodies: the Kinematic Constraint method, the Pen-alty method and the Distributed Parameter method. ThePenalty method algorithm is used to define the contact be-tween projectile and composite plate. It has the effect ofplacing normal interface springs between penetrating nodesand their respective surfaces. A unique modulus is com-puted for each element in which a spring resides and theinterface stiffness is based on the stiffness of the elementnormal to that interface. This method excites very littlemesh hourglassing due to the symmetry of the approach,since the momentum equation is exactly conserved andno special treatment is given to intersecting interfaces.Also, the computed time step is not affected by the exis-tence of the interfaces, but large interface pressure mayproduce unacceptable penetration. This problem can beremedied by scaling up the stiffness or scaling down thetime step at the cost of increasing solution time [16].

Kinematic contacts were tested to aid in progressivedamage simulation of CFRP laminates. These contactswere applied at coincident nodes of shell elements to allowfor perforation of certain material models, and were alsotried as contact definitions between the lamina of theCFRP laminate. To no avail, the kinematic contact defini-tions did not enhance the performance of the model. Thus,a penalty-based contact with erosion criteria is the only

AS4 Brass

tensile strength (MPa) 2280 –compressive strength (MPa) 1440 –nsile strength (MPa) 57 –mpressive strength (MPa) 228 –

kness tensile strength (MPa) 57 –th (GPa) 10 –hear strength (GPa) 10 –h (MPa) – 483

shear strengths (MPa)71 –71 –71 –

tion angle 30 –e parameter for elastic modulus reduction 0.99 –

Table 2Dimensions of 1/4 plate and 1/4 projectile of numerical model

1/4 plate 1/4 projectile

Length (cm) 10.0 Radius (mm) 6.35Width (cm) 10.0 Length (cm) 5.08Thickness (mm) 2.4

S. Chan et al. / Composite Structures 77 (2007) 466–474 469

contact algorithm used by the numerical model to definethe contact between target and projectile.

3.3. The finite element model

The model consists of a projectile with an initial velocityand target 16 layer composite laminate, with clampedboundary conditions. The model was meshed using Hyper-mesh version 5.1. The projectile, which is cylindrical inshape having a spherical end, is meshed with 1190 brick ele-ments and assigned an initial velocity that is unique to eachimpact event. The CFRP composite plate is modeled using16 layers of 2500 brick elements per lamina. Each layer rep-resents an individual unidirectional fiber ply. Solid brickelements are used, since a 3D analysis of the stresses devel-oped during a high-speed impact event is required for thepresent work.

Table 1 gives the elastic and strength properties of theunidirectional laminae in the CFRP plate and the projec-tile, while Table 2 gives the dimensions of the projectileand composite plate. To reduce the time of simulation,the projectile is situated only a fraction of a millimeteraway from the target plate, so that minimal computationtime is spent before the projectile impacts the plate. Also,only a 1/4 of both the plate and projectile are modeled withappropriately applied symmetry boundary conditions.

4. Results and discussion

4.1. Experimental results

The ballistic limit testing conducted involves determin-ing the velocity at which there is a 50% probability of spec-

Fig. 4. Laminated pla

imen penetration. Accordingly, a certain number of shotsare taken where the projectile penetrates the specimen,and the same number of shots are taken where no penetra-tion occurs. The ballistic limit is calculated from the aver-age of these measurements. Fig. 4 depicts the impact pointsand the deformed shape at the back of two test laminates,and Table 3 lists the laminates and summarizes the exper-imental results in terms of the ballistic limit velocities andgeometrical damage characteristics.

4.2. Simulation results

Figs. 5–10 are the kinetic energy plots for the [(0,90,0,90)2]S, [(45,�45,45,�45)2]S, [(45,�45,0,0)2]S, [(0,0,45,�45)2]S, [(0,�45,45,0)2]S, and [(45,�45,90,0)2]S compositelaminates, respectively. Initial velocities were given to theprojectile corresponding to impact events that producedperforation (all figures labeled �b�) and to impact events justprior to perforation (all figures labeled �a�). The initial ki-netic energy (KE) of the projectile is easily calculated giventhe mass and velocity. The KE of the projectile was thenplotted versus time, and it is this KE history that is usedto corroborate the experimental ballistic limits. The simula-tion time is set sufficiently long (400 ls) to allow for com-plete perforation of the composite plate or total stoppageof the projectile.

4.3. Discussion of the experimental and simulation

results

The numerical model was successful in corroboratingthe ballistic limits for six of seven experimentally testedCFRP plates. By comparing the KE absorbed by laminateswith a given stacking sequence to their respective projectilevelocities, i.e. those that produced perforation and thosejust prior to perforation, one can note the accuracy ofthe model for ballistic limit prediction. Inconclusive resultswere obtained when trying to match the experimental andnumerical results pertaining to the damaged area and finalmid-plane deflection.

tes after impact.

Table 3Experimental results

Averagevelocity (m/s)

Majoraxis (m)

Minoraxis (m)

Mid-planedeflection (m)

Impactenergy (J)

Numerical delaminationscale factor

[(45,�45,0,0)2]S 41.60 0.102063 0.026400 0.001347 34.69 148.13 0.118625 0.027520 Perforated 46.46

[(0,0,45,�45)2]S 42.12 0.137655 0.031358 0.001422 35.62 148.12 0.139864 0.032247 Perforated 46.50

[(0,45,�45,0)2]S 41.65 0.119959 0.029924 0.001393 34.83 148.19 0.124730 0.030678 Perforated 46.61

[(45,�45,0,90)2]S 48.29 0.124449 0.039716 0.001522 48.09 –58.88 0.125419 0.040028 Perforated 69.68

[(45,�45,90,0)2]S 41.48 0.104573 0.038986 0.001490 34.51 0.548.27 0.112790 0.039645 Perforated 46.78

[(0,90,0,90)2]S 34.52 0.075005 0.019668 0.000899 23.92 0.841.55 0.081325 0.022765 Perforated 34.68

[(45,�45,45,�45)2]S 48.95 0.090167 0.043412 0.001854 48.05 3.559.22 0.112538 0.044318 Perforated 70.33

Fig. 5. Projectile kinetic energy history for impact against [(0,90,0,90)2]S composite. (a) Non-perforated case, i.e. Vi = 34.52 (m/s). (b) Perforated case,i.e., Vi = 41.55 (m/s).

Fig. 6. Projectile kinetic energy history for impact against [(45,�45,45,�45)2]S composite (a) Non-perforated case, i.e. Vi = 48.95 (m/s). (b) Perforatedcase, i.e., Vi = 59.22 (m/s).

470 S. Chan et al. / Composite Structures 77 (2007) 466–474

MAT 161 enforces several failure criteria to simulateprogressive failure of composite materials. Eq. (4.1) is thedelamination failure criterion used by MAT 161. Thisparticular criterion features a scale factor denoted by �Sd�[17].

f5 ¼ Sd

hrciSbT

� �2

þ sbc

S0bc

� �2

þ sca

Sca

� �2( )

� 1 ¼ 0 ð4:1Þ

where SbT, S0bc and Sca are the failure strengths correspond-ing to the stress state rc, sbc and sca. The greater the value

Fig. 7. Projectile kinetic energy history for impact against [(45,�45,0,0)2]S composite. (a) Non-perforated case, i.e. Vi = 41.6 (m/s). (b) Perforated case,i.e., Vi = 48.13 (m/s).

Fig. 8. Projectile kinetic energy history for impact against [(0,0,45,�45)2]S composite. (a) Non-perforated case, i.e. Vi = 42.12 (m/s). (b) Perforated case,i.e., Vi = 48.12 (m/s).

Fig. 9. Projectile kinetic energy history for impact against [(0,45,�45,0)2]S composite. (a) Non-perforated case, i.e. Vi = 41.65 (m/s). (b) Perforated case,i.e., Vi = 48.19 (m/s).

S. Chan et al. / Composite Structures 77 (2007) 466–474 471

of �Sd�, the more susceptible that particular laminate stack-ing sequence has to failure by delamination. It was foundthat this scale factor played a vital role in correlating thenumerical results with the experimentally obtained ballisticlimits. Adjusting this scale factor allowed for accurate cor-relation of the experimental results with the numerical sim-ulations. Table 3, in addition to displaying theexperimental results also includes the scale factor, Sd thatwas used in Eq. (4.1) to best predict the ballistic limitsvia the numerical model. It has been found that the familyof composite laminates containing 0, 45, and �45 laminaorientations has identical delamination scale factors.

Only six of seven ballistic limits could be verified by thenumerical simulation using the kinetic energy of the projec-tile as the prime identifier. The ballistic limit of the[(45,�45,0,90)2]S laminate, which was determined experi-mentally as 58.88 m/s, could not be verified with thenumerical model, irrespective of the value used for Sd.On the other hand, the [(45,�45,90,0)2]S, laminate withan experimentally determined ballistic limit of 48.27 m/swas verified by the present numerical model. The large dif-ference between these two values is suspicious and moretests may be required to confirm the results. Indeed, theClassical Lamination Theory (CLT) shows that the above

Fig. 10. Projectile kinetic energy history for impact against [(45,�45,90,0)2]S composite. (a) Non-perforated case, i.e. Vi = 48.27 (m/s). (b) Perforatedcase, i.e., Vi = 41.48 (m/s).

472 S. Chan et al. / Composite Structures 77 (2007) 466–474

two laminates have identical extensional stiffness matrices,[A], and all coupling stiffness matrix components, Bij, equalto zero. Differences in laminate behaviour, if any, may thenbe attributed to the bending or flexural stiffness responsedescribed by the [D] matrix [21]. The bending/flexural stiff-ness matrices for the [(45,�45,0,90)2]S, and [(45,�45,90,0)2]S laminates are shown in Eqs. (4.2) and (4.3), respec-tively. As can be seen, the only difference between the twomatrices is the swap of the D11 and D22 components, whichrepresent the longitudinal and transverse normal bendingstiffness parameters of the laminates.

½ð45;�45; 0; 90Þ2�S laminate ½D�

¼68:1427 25:7889 5:0102

25:7889 57:6896 5:0102

5:0102 5:0102 30:8865

264

375GPa ð4:2Þ

½ð45;�45; 90; 0Þ2�S laminate ½D�

¼57:6896 25:7889 5:0102

25:7889 68:1427 5:0102

5:0102 5:0102 30:8865

264

375GPa ð4:3Þ

Observation of the two laminates under identical impactconditions for the first 50 ls of the numerical simulationsshows almost identical stress responses mirrored aboutthe contact point. The only exceptions occur at 30 and35 ls, where the maximum stress does not develop at mir-rored locations in the laminates. The magnitude of themaximum and minimum stresses over the 50 ls have amaximum difference of 33% and 8% respectively, howeverthe average difference is only 6.9% for the maximum stressmagnitudes, and 3.1% for the minimum stress magnitudes.

Impact problems may require consideration of inertiaeffects and possibly stress wave propagation, which leadsto the concern of material behaviour at high rates of load-ing. However, static stiffness and strength values may beused by the model if strain rate effects can be assumed neg-ligible [13]. The material model incorporates the effect ofstrain rates by modifying the appropriate strength param-eters during impact. Strength values are modified by a mul-tiplication factor SRT, given by the following expression:

SRT ¼ 1þ Crate ln_�e_eo

� �ð4:4Þ

where _�e is the effective strain rate for _eo ¼ 1s�1 [17]. Strainrates are computed internally while the user may vary theCrate parameter to magnify or reduce the effects of strainrate. Sensitivity tests of the Crate parameter showed negligi-ble changes in the results when varying the range from 0.1to 20. Co-developer of the material model, MSC, recom-mended a value of 2 for this parameter, which is the valueused in this final model. Thus, strain rate effects were deter-mined to be insignificant, which permits the use of staticstiffness and strength properties.

A limited mesh sensitivity study was performed usingthree different sizes of the mesh grid for the plate. Hyper-mesh version 5.1 checks element aspect ratios against a de-fault value of 5. The minimum number of grid elementsthat must be used to achieve an aspect ratio (AR) of 5 orless is 68 · 68, which results in an AR of only 4.9.Fig. 11 shows a kinetic energy comparison of the non-per-foration case of the [(0,0,45,�45)2]S composite laminateusing a 68 · 68 element grid vs. a 50 · 50 element grid (ele-ment AR of 6.67), respectively. Fig. 11(b) clearly shows aslightly stiffer response, with the projectile�s kinetic energyand hence velocity reaching zero at approximately 350 ls,whereas Fig. 11(a) shows the zero kinetic energy mark ata time of approximately 380 ls. This is only a 7.9% differ-ence in the time at which the projectile is stopped by thecomposite plate, yet the simulation time is increased by58% escalating from 24 h to 38 h. A coarser grid of35 · 35 elements corresponds to an AR of 9.52 and a sim-ulation time of 16 h. The plate tends to act excessively stiff,however, as indicated by the projectile attaining zero veloc-ity at approximately 310 ls. This is 18.4% off the stoppagetime found by the grid of 68 · 68 elements. A compromisewas ultimately made by using the relatively coarser mesh of50 · 50.

Observation of the numerical simulations showed thatthe entire plate responds to the impact indicating stresseswill be felt at the boundaries, and suggests that edge effectsmay not be negligible. Fig. 4 shows an experimentallytested composite laminate with wide spread damage, com-

Fig. 11. Kinetic energy comparison of the non-perforation case of the [(0,0,45,�45)2]S composite laminate using a 68 · 68 element grid (a) vs. a 50 · 50element grid (b).

S. Chan et al. / Composite Structures 77 (2007) 466–474 473

ing close to the boundary of the clamped edge. It also sup-ports visual observations made from the numerical modelsimulation. On the other hand, Cantwell and Morton [4]found that high-velocity impact test results (of compositebeams) tended to have very localized damage and the per-foration threshold was invariant to the distance betweenpoint of impact and boundary.

5. Conclusion

This paper presented experimental results related to thehigh-speed impact characteristics of carbon–fiber-rein-forced plastic (CFRP) laminates and a numerical modelwhich simulates the same problem. The ultimate objectiveof the underlying study was to provide further understand-ing of the behaviour of laminated composites of varyinglamina orientations and stacking sequences, when underhigh-velocity impact. Emphasis was placed on the determi-nation of ballistic limits of those composites. Experimentaltests determined the ballistic characteristics for seven CFRPplates of various stacking sequences and lamina orienta-tions. The projectile�s velocity, and hence kinetic energy,was measured and used to determine these ballistic limits.

It was found that a suitable numerical model to performhigh-speed impact analysis on CFRP laminates requiresaccurate description of the material response and definitionof the contact between target and projectile. An appropri-ate orthotropic material model with progressive failurecharacteristics is thus required. The LS-DYNA materialmodel MAT161, which incorporates Hashin failure criteriaalong with various material parameters and eroding mech-anisms, was adopted. Furthermore, an eroding contactalgorithm was used in order to delete highly distorted ele-ments caused by extreme stresses and pressures. This pro-vided a numerical model capable of progressive damagefailure for use in ballistic impact analysis.

Strain rate effects were determined to be negligible forthese impact simulations, thus validating the use of staticelastic constants and strength values. It was, however,determined that delamination failure drastically affectedthe energy absorbing ability of the CFRP composite lami-

nates. Adjusting the scale factor employed by the delami-nation failure criterion allowed the prediction of theballistic limit for six of the seven composite laminatestested experimentally.

Acknowledgements

The authors gratefully acknowledge the financial sup-port provided by the Natural Science and Engineering Re-search Council (NSERC) of Canada and Materials andManufacturing Ontario (MMO). The technical supportprovided by Materials Sciences Corporation (MSC) is alsogratefully acknowledged.

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