2010_maalej paper on numerical model.pdf

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Urban Habitat Constructions under Catastrophic Events (Proceedings) Mazzolani (Ed). 2010 Taylor & Francis Group, London, ISBN 978-0-415-60685-1

Numerical study of functionally-graded cementitious panels

subjected to small projectile impact

S.T. Quek, V.W.J. Lin & S.C. Lee

Department of Civil Engineering, National University of Singapore, Singapore

M. MaalejDepartment of Civil and Environmental Engineering, College of Engineering, University of Sharjah, UAE

ABSTRACT: This paper presents a numerical study of a Functionally-Graded (FG) cementitious panel sub-jected to high-velocity small-projectile impact with striking velocity ranging from 300 m/s to 600 m/s. This FGpanel comprised three different materials, namely PE-fibrous ferrocement, calcium bauxite aggregate concreteand conventional mortar, layered at different sections to improve the target impact resistance, depending on the

properties of the material needed at various stages of the projectile penetration. Good agreements in both pro-jectile penetration depths and average inner crater diameters were observed between the numerical simulationsand experimental results. Using the calibrated model, an optimization study of the FG panel (through varyingtarget thickness) to prevent perforation of the projectile with striking velocity of 600 m/s was then illustrated.An overall target thickness of 60 mm would be adequate in preventing projectile perforation.

1 INTRODUCTION

Recent increasedintensity in terroristsevents have ledmany researchers to carry out studies to develop betterand more economical protective structures for militaryapplications, Government facilities as well as civilianinstallations. Until the last two decades, conventional

reinforced concrete (RC) has been widely used in pro-tective structures applications. With the advancementof concrete technology, concrete with higher com-pressive strength, tensile strength, fracture energy andductility has been developed, opening up new dimen-sions for improving performance of RC protectivestructures. These enhanced cementitious compositeshave shown to be effective in reducing fragmentations,spalling and scabbing at the target surfaces, as wellas penetration depth when subjected to high-velocityprojectile impact (Zhang et al. 2005, Maalej et al.2005).

Besides enhancing the targets material properties,performance of these protective structures can alsobe improved by noting the properties of the mate-rial needed at various stages of the projectile impactand penetration, and to layer the section with mate-rials of appropriate properties. The concept of suchfunctionally-graded (FG) cementitious panels againsthigh-velocity projectile impact is a recent develop-ment andhas been experimentally tested by Quek et al.(2010). These FG panels comprise top and bottomouter layers of polyethylene (PE)-fibrous ferroce-mentto mitigatefragmentation,spallingand scabbing.Underlying the top layer is a thin layer of calcined

bauxite aggregates with sufficient hardness to enhancepenetration resistance. The remaining gap betweenthis layer and the bottom outer layer is filled withconventional mortar to provide inertia and resistance.These FG panels were subjected to 13.35 mm diam-eter ogive-nose projectile impact fired at velocitiesranging from 300 m/s to 600 m/s. Excellent impact

resistance with smaller penetration depth and craterdiameter compared to conventional mortar targetswere observed.

The aim of this study is to develop a three-dimensional finite element (FE) model using thecom-mercial package, LS-DYNA, to simulate the responsesof the FG panels subjected to high-velocity small-projectile impact. The FE model results were com-pared with the experimental data obtained by Queket al. (2010) for verification purposes. Using the cali-brated FE model, an optimizationstudy was performedto determine the minimum thickness of the FG panelrequired to prevent perforation of an ogive-nose pro-jectile with 600 m/s striking velocity as an illustrationof economy in design.

2 FINITE ELEMENT MODEL

Based on the FG panels experimentally test by Queket al. (2010), the FE model target comprises threedifferentcementitious composites, namely PE-fibrousferrocement, calcium bauxite concrete and mortar lay-ered at different sections of the target as shown inFigure 1.

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Figure 1. FE model of functionally-graded (FG) panel.

2.1 Material models

All the cementitious composites were modelled usingmaterial 72 release III (MAT72Concrete DamageMaterial Model) in LS-DYNA. The PE-fibrous ferro-cement wasmodelled as two separatecomponents con-sisting of steel wire mesh reinforcements embeddedwithin a PE-fiber reinforced cementitious composite(FRCC) matrix. The steel wire mesh reinforcement

was modelled using material model 3 (MAT3PlasticKinematic) in LS-DYNA. Lastly, the ogive-nose pro-jectile was modelled as a rigid material using materialmodel 20 (MAT20Rigid Material Model) in LS-DYNA, in view of its small deformation comparedto the FG-panels for computational efficiency.

2.2 Material erosion algorithm

To simulate the cratering process of the target by theprojectile upon impact, it is necessary to introducea material erosion algorithm to capture the removalof failed elements as the projectile penetrated intothe target. As MAT72 is not incorporated with sucherosion algorithm, MAT_ADD_EROSION was uti-lized for the removal of failed elements in the FE

model. This MAT_ADD_EROSION option in LS-DYNA is currently applicable for two-dimensionaland three-dimensional solid elements with one pointintegration.

In thisstudy, two erosion criteria, namely maximumand minimum principal strains, were used for remov-ing the failed elements from the FE model. Thesefailure criteria were determined through a trial anderror approach in which one series of the experimen-tal data were used to match the local damages inducedby the projectile impact in the FE model. The fail-ure values obtained were then adopted for all the FEsimulations and they are summarized in Table 1.

2.3 Strain rate effects

It is well-known that many materials behave dif-ferently under short-duration rapid loading such ashigh-velocity projectile impact compared to quasi-static loading. Under impact loading, large amount ofenergy is suddenly transferred to the target, causingthe target material to undergo continuously varyingstrength, stiffness, energy-absorption and dissipationproperties (Lee, 2006). This phenomenon, which canbe somewhat characterized by the strain-rate, causes

Table 1. Summary of Erosion Criteria Failure Values.

Compressive Strain Tensile StrainMaterial % %

PE-FRCC 70 20C. Bauxite Concrete 70 16Mortar 70 11

the materials to experience strength enhancement andcan be quantified through the Dynamic Increase Fac-tor (DIF), defined as the ratio of dynamic to staticultimate strength.

To accurately simulate the responses of the FG pan-elssubjected to theprojectile impact,strain-rate effectswere also incorporated into the FE model. The loadcurveoption in MAT72releaseIII was used tocapturethe materials strain-rate effect, in which the abscissavalues of the load curve represent the strain-rateswhile the ordinate values represent the DIF values.Thestrain-rate effect of the steel wire mesh reinforcementwas incorporated into the FE Model using the Cowperand Symonds model built in MAT3.

The dynamic behavior of PE-FRCC (tensile) andsteel wire mesh were modelled based on the exper-imental data obtained by Lin (2008), while those ofPE-FRCC (compressive), concrete and mortar weremodelled based on the DIF-strain-rate relationshipsproposed by CEB model (1993) and Malvar and Ross(1998).

2.4 Numerical simulation

Similar to the experimental study conducted by Queket al. (2010), three different configurations of four-layer FG-panel, namely, FGP-1:1:7:1, FGP-2:1:6:1andFGP-1:2:6:1, were numerically simulated. The set of

numbers following the acronym FGP correspondedto the ratio of the thickness of each layer to the overallthickness of the panel. For example, for FGP-1:2:6:1with an overall thickness of 100 mm, the first num-ber 1 implies that the thickness of the first layer is10 mm, while the thicknesses of the remaining layersare 20 mm, 60 mm and 10 mm, respectively. As thepanel layers were cast one on top of the other beforesetting, perfect interfacial bonding between layers wasassumed for simplicity.

In view of symmetry and computational efficiency,only onequarter of thepanelwith theprojectileimpactwas modelled as shown in Figure 1. As in the experi-ment, the specimen wasmodelledas simply-supportedalong one side using the BOUNDARY_SPC option torestrict the specimen movement.

The panel and projectile were modelled as eightnodes solid elements using one-point integrationwith Flanagan-Belytschko stiffness hourglass control,while the steel wire mesh reinforcements were mod-elled as two nodes truss element. Each solid elementhad dimensions of 2.5 2.5 2.5mm whilethatof thesteel wire mesh reinforcements had length of 2.5 mm.These mesh sizes were selected based on a meshconvergence study.

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It is worth to mention here that when using consti-tutive equations with strain softening in FE analysis, itis expected that the strains tend to localize randomlywithmesh sizerefinementleading to non-convergencein the numerical results (Baant, 1976). In LS-DYNA,this mesh size sensitivity can be reduce through the

use of the MAT_NONLOCAL option, which is basedon the concept of non-localization by Pijaudier-Cabot& Baant (1987), that averages the rate of increase ofdamage in a particular element with its neighboringelements whose centroid lie within a specific radialdistance.

The impact velocity of the projectile was mod-elled by prescribing an initial velocity for theprojectile through using the INITIAL_VELOCITY_RIGID_BODY option in LS-DYNA. Similar to theexperimental tests, impact velocities of the pro-jectile were varied between 300 m/s and 600 m/sfor all specimen configurations. Lastly, the contactbetween the projectile and target was modelled usingCONTACT_ERODING_ SURFACE_TO_SURFACE

option in LS-DYNA to allow removal of failed ele-ments in contact with the penetrating projectile.

3 SIMULATION RESULTS AND DISCUSSION

The numerical results obtained from FE analysis wereverified withexperimental databy comparing the localdamages in terms of penetration depth, average innerand outer crater diameters at the target impact surface.

3.1 Penetration depth

The penetration depth of the projectile was measuredfromthe maximum displacementof theprojectile tipintheFE model upon entering the target. The plots of themaximum penetration depth versus projectile impactvelocity for all FG panel configurations are shown inFigure 2. Good agreements between the FE predictedpenetration depth and experimental test results wereobserved.

3.2 Average inner crater diameter

The average inner crater diameters of the FG-cementitious panel were determined by averagingthe orthogonal and diagonal distances of the crater(defined as the region where an opening was formedat the target impact face in the numerical model) cen-tered at the projectile point of entry of the quarterpanel, multiplied by two for the full panel. Figure 3

shows the average inner crater diameter versus projec-tile impact velocity for all FG panel configurations.Reasonably good agreements between the FE aver-age inner crater diameters and experimentaltest resultswere also observed.

3.3 Average outer crater diameter

Besides the average inner crater diameter presentedin most of the projectile impact studies, an additional

damage criterion identified as the average outer craterdiameter was used to assess the target impact damage(Quek et al., 2010). This average outer crater diame-ter is defined as the average diameter of the bulgedboundary on the impact surface due to the membraneaction of the PE-fibrous ferrocement layer. This bulge

could be causedby delaminationof thePE-fibrousfer-rocement layer from the tough concrete layer and/ordisplacement of material beneath the impact face.

The average outer crater diameter was taken as theaverage of the orthogonal and diagonal distances ofthe bulge region (relative to the original target sur-face) centered at the projectile point of entry of thequarter panel, multiplied by two for the full panel.Figure 4 shows the average outer crater diameterversus projectile impact velocity for all FG-panelconfigurations.

The FE model consistently under-estimated theaverageoutercrater diameters of allFG-configurationsfor the range of impact velocities investigated. Thismay be due, firstly, to the fact that delamination was

not incorporated in the model and secondly to thesimplistic smeared material model used to describethe cement paste and calcined bauxite aggregates. Thelatter resulted in the removal of concrete material ele-ment once it violated the erosion criterion, whereas inthe actual experiment, the calcined bauxite aggregateswere not fully eroded but displaced sideways to causethe bulge at the impact face. As the projectile velocityincreases, more aggregates are displaced sideways tocause the bulge at the impact face leading to largerdifferences between the numerical and experimentalresults observed in Figure 4.

Nevertheless, the FE model is capable of estimat-ing the maximum penetration depth and average innercrater diameter of the FG-cementitious panel (whichare the more important damage parameters definedin most penetration studies) with reasonably goodaccuracy.

4 OPTIMIZATION STUDY

Using the calibrated FE model, an optimization studyof the FG panel was conducted to determine theminimum overall thickness of the FG panel to pre-vent perforation of a 13.35 mm diameter ogive-noseprojectile impact fired at striking velocity of 600 m/s.

From both the experimental and numerical studies,FGP-1:2:6:1 specimens demonstrated the best per-formance against projectile penetration. As such, thethicknesses of the PE-fibrous ferrocement protectivelayers at both the impact and distal faces were fixedat 10 mm while that of the calcined bauxite aggregateconcrete layer were fixed at 20 mm in theoptimizationof the targets overall thickness. The thickness of themortar core was varied from 10 mm to 60 mm (cor-responding to the target overall thickness of 50 mmto 100 mm respectively) at 10 mm intervals. TheseFG panels were subjected to projectile impact withstriking velocity of 600 m/s. Figure 5 shows the target

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Figure 2. Penetration depth versus projectile impact velocity.

Figure 3. Inner crater diameter versus projectile impact velocity.

Figure 4. Outer crater diameter versus projectile impact velocity.

Figure 5. Inner crater diameter versus projectile impact velocity.

damage at the end of the numerical simulations (ter-minated at t=600s). The numerical values, in termsof penetration depth and average inner crater diameterare shown in Figure 6.

As observed in Figures 5 and 6, the impact damageon the FG panels with overall thickness greater than80 mm were similar. The penetrations of the projectilewere deeper and more severe damage on the mortar

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Figure 6. (a) Penetration depth (b) Average inner crater diameter versus FG-cementitious panel overall thickness.

Figure 7. (a) 60 mm (b) 50mm thick FG panel damage at t= 600s.

core was observed for panels thinner than 80 mm. Atan overall target thickness of 60mm, the penetration

depth was observed to be 60.81 mm (which is greaterthan the target thickness). This is only possible whenthe material of the layer at the distal face is ductile,facilitating membrane action to further dissipate theprojectiles remaining energy. Full perforation of thetarget was observed when the target thickness wasreduced to 50 mm.

The above observations indicate that a minimumoverall targetthickness of 80 mm would be required toprevent or minimize damage to the mortar core whensubjected to projectile impact of 600 m/s. Depend-ing on the design requirement, if the objective of thisFG-cementitious panel is only to prevent perforation,a minimum overall target thickness of 60 mm wouldsuffice.

However, when the thickness of the mortar corebecomes too thin, it may be more economical toconstruct a PE-fibrous ferrocement sandwich panelinfilled with calcined bauxite aggregate concrete.Using 10 mm thick PE-fibrous ferrocement protectivelayers, two additional numerical simulations of 50 mmand 60 mm thick (having 30 mm and 40 mm of cal-cined bauxite concrete infill respectively) PE-fibrousferrocement sandwich panel subjected to 600 m/s pro-jectile impact were performed. Figure 7 shows the

target damage at the end of the numerical simula-tions (t= 600s). The sandwich panel with overall

thickness of 60 mm was able to prevent perforation ofthe projectile. The penetration depth was 52.71 mm.For the 50 mm thick PE-fibrous ferrocement sand-wich panel, the velocity of the projectile was 94 m/sat ejection, which is approximately the same as the92 m/s observed for the FG panel. Thus, the penetra-tion resistance in the rear crater may not be sensitiveto the material unconfined compressive strength asillustrated by Hanchak et al. (1992).

5 SUMMARY AND CONCLUSION

In this study, a finite element model of the FG panelsubjected to high-velocity small ogive-nose projec-tile was successfully developed using the commercialLS-DYNA FE package. By incorporating the materialstrain-rate effects and using the erosion algorithm, thepenetration depths and average crater diameters of theFG panels subjected to projectile impact with impactvelocities ranging from 300 m/s to 600m/s were simu-lated. The numerical predictions were then comparedvis--vis experimental impact test results in whichreasonably good agreement were observed in the pen-etration depths and average inner crater diameters, but

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not in the average outer crater diameters. It seems thatthe application of a smeared material model for cal-cined bauxite aggregateconcrete wasunableto capturethe average outer crater diameter of the FG panel asit resulted in the removal of tough concrete materialelement once it violated the erosion criteria. Never-

theless, in most projectile penetration studies, only thepenetration depth and inner crater diameterare definedas the parameter of interests and thus, the FE modelmay be adequate for design purpose.

Using the calibrated FE model, an optimizationstudy on overall thickness of the FG panels to preventperforation of an ogive-nose projectile with strik-ing velocity of 600 m/s was performed. It was foundthat an overall target thickness of 80 mm is suffi-cient to prevent or minimize damage to the mortarcore layer, while a minimum overall target thicknessof 60 mm would be adequate to prevent perforationwhen the target is subjected to projectile impact at600 m/s. Such optimization study can serve as a valu-able tool to arrive at more economical protective

structuraldesign and minimizethe needfor conductingexpensive experimental tests.

ACKNOWLEDGEMENTS

The authors would like to acknowledge the DefenceScience and Technology Agency of Singapore(DSTA), through the Centre for Protective Technol-ogy, National University of Singapore, for supportingthis research workunder the project grant (R-379-000-014-232).

REFERENCES

Baant, Z.P. 1976. Instability Ductility and Size Effect in

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CEB, Comit Euro-International du Bton. 1993. CEB ModelCode 1990. Trowbridge, Wiltshire, UK: Redwood Books.

Hanchak, S.J., Forrestal, M.J., Young, E.R. & Ehrgott, J.Q.1992. Perforation of Concrete Slabs with 48MPa (7ksi)and 140MPa (20ksi) Unconfined Compressive Strengths.

International Journal of Impact Engineeri ng 12(1): 17.Lee, S.C. 2006. Finite Element Modeling of Hybrid Fiber

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Maalej, M.,Quek, S.T. & Zhang, J.2005.Behavior of Hybrid-Fiber Engineered Cementitious Composites Subjected toDynamic Tensile Loading and Projectile Impact. ASCE

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Effects for Concrete in Tension. ACI Material Journal95(6): 735739.

Pijaudier-Cabot, G. & Baant, Z.P. 1987. Nonlocal Dam-age Theory. ASCE Journal of Engineering Mechanics113(10): 15121533.

Quek, S.T., Lin, V.W.J. & Maalej, M. 2010. Developmentof Functionally-GradedCementitious Panelagainst High-VelocitySmall Projectile Impact.International Journal of

Impact Engineeri ng: Article in press.Zhang, M.H., Shim,V.P.W., Lu, G. & Chew, C.W. 2005. Resis-

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