DTIC ADA622799: Finite Element Analysis of Functionally Graded Material to Reduce Crazing in Transparent Armor

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AD-E403 681

Technical Report ARMET-TR-14042

FINITE ELEMENT ANALYSIS OF FUNCTIONALLY GRADED MATERIAL TO
REDUCE CRAZING IN TRANSPARENT ARMOR

Lyonel Reinhardt
Aisha Haynes
Stephen Recchia
Michael Miller

September 2015

U.S. ARMY ARMAMENT RESEARCH, DEVELOPMENT AND

til),,

ENGINEERING CENTER

il 1 1 If

Munitions Engineering Technology Center

Picatinny Arsenal, New Jersey

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September 2012 to April 2013

4. TITLE AND SUBTITLE

FINITE ELEMENT ANALYSIS OF FUNCTIONALLY GRADED
MATERIAL TO REDUCE CRAZING IN TRANSPARENT ARMOR

5a. CONTRACT NUMBER

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHORS

Lyonel Reinhardt, Aisha Haynes, Stephen Recchia, and Michael
Miller

5d. PROJECT NUMBER

5e. TASK NUMBER

5f. WORK UNIT NUMBER

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

U.S. Army ARDEC, METC

Fuze & Precision Armaments Technology Directorate
(RDAR-MEF-E)

Picatinny Arsenal, NJ 07806-5000

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REPORT NUMBER

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U.S. Army ARDEC, ESIC

Knowledge & Process Management (RDAR-EIK)

Picatinny Arsenal, NJ 07806-5000

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Technical Report ARMET-TR-14042

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13. SUPPLEMENTARY NOTES

14. ABSTRACT

The overall goal of this particular study was to provide proof of concept through modeling and simulation to
predict the impact of a functionally graded material (FGM)-based target on the shockwaves generated from an
impactor. Most armor systems are comprised of a single material or a composite layup of several materials.
The intent of this study was to provide insight into the effectiveness of morphed microstructure consisting of a
glass and transparent ceramic FGM.

15. SUBJECT TERMS

Functionally graded material

Finite element ABAQUS

16. SECURITY CLASSIFICATION OF:

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ABSTRACT

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OF

19a. NAME OF RESPONSIBLE PERSON
Michael Miller

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CONTENTS

Page

Introduction 1

Goals, Scope, Status, and Prior Work 1

Brief Conclusions 1

Method 2

Model Information, Procedures, and Possible Errors

Assumptions

Parts and Instances

Material Properties

Interactions and Constraints

Results 4

Tensile Pressure (psi) 4

Conclusions and Path Forward 5

References 7

Distribution List 9

FIGURES

1 Pressure plot 1

2 3D Digimat unit cell and 2D plane strain model for ABAQUS 2

3 Control and FGM models 3

4 Boundary conditions 4

5 Pressure results (time = 23.47 ps) 4

6 Pressure results 1 5

7 Pressure results 2 5

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INTRODUCTION

Goals, Scope, Status, and Prior Work

The goal of this effort is to support the development of novel transparent armor systems
based on functionally graded materials (FGM) through modeling and simulation. One requirement of
transparent armor is that it must maintain its transparency after multiple projectile hits. For this to be
successful, the base material must be resistant to crazing or cracking. Crazing and cracking are
partially the products of the buildup of hydrostatic tensile stresses within the material (ref. 1). On
impact, the material must disperse tensile stress waves created during projectile impact.

In the models developed, the FGMs are tested based on alumina and glass [calcium oxide
(CaO)- zirconium dioxide (Zr02)-silicon dioxide (Si02)]. The FGM was developed using varying
concentrations of each material from 100 to 0% end to end. The hypothesis adopted for this analysis
is that varying the concentration will affect the microstructure of the FGM, such that tensile shock
waves created during projectile impact will dissipate and decrease as they travel through the
thickness of the FGM.

A related piece of work prior to this report is the glass ceramic FGM report. This report
showed a one-dimensional model where particle distribution was introduced instead of layers. An
impactor was used instead of displacing surface nodes.

BRIEF CONCLUSIONS

The FGM breaks up the reflecting pressure wave as shown in figure 1, but the highest tensile
wave that was found on the impact surface was not attenuated compared to the control model. A
possible solution would be to modify the impact surface zone by changing from a 100% pure material
at the surface to a composite material in order to disperse the surface tensile wave.

Figure 1
Pressure plot

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METHOD

Model Information, Procedures, and Possible Errors

General purpose finite element software ABAQUS Explicit 6.12 (ref. 2) was used to simulate
projectile impact into the FGM. The FGMs with varying distributions of alumina and Ca0-Zr02-Si02
were developed using the Digimat composite modeling software. In Digimat, several three-
dimensional (3D) FGMs were created with varying particle density to create the gradient.

The ABAQUS analyses were dynamic with nonlinear materials and nonlinear geometry. All
the parts were modeled as deformable elements using S4R and S3R [quadrilateral 4-node and 3-
node stress/displacement (S) plane strain shell elements with reduced (R) integration and hourglass
control] plane strain elements with reduced integration and hourglass control. Friction is assumed
negligible and set to 0.0. All contact surfaces as well as the particles and matrix shared nodes
forming a perfect bond. Damping was set to 2% alpha, and the initial conditions consisted of giving
the impactor a velocity of 24,000 in./sec.

Assumptions

A two-dimensional (2D) plane strain assumption was used in the ABAQUS analyses to
reduce computational cost. The 3D unit cell with varying particle concentrations through the
thickness of the part were imported from Digimat and converted to 2D. The sides of the unit cell were
used to create the 2D model. These sides were repeated to widen the amount of glass simulated.
This distance was increased to reduce the effect of shock waves reflected from the sides, such that
they would not interfere in the results. Figure 2 depicts the 3D and 2D unit cells.

Figure 2

3D Digimat unit cell and 2D plane strain model for ABAQUS

The material properties for alumina and CaQ-ZrQ2-SiQ2 were taken from reference 3. The
particles created with Digimat are assumed to be ellipsoids with aspect ratios of 1, they were
randomly oriented in the matrix, and they can interpenetrate each other. The graded material is as
follows: 100%/0% glass/alumina, 80%/20% glass/alumina, 50%/50% glass/alumina, 20%/8%
glass/alumina, and 0%/100% glass/alumina. There are no voids in the model and there is perfect
bonding between the matrix and the particles. Material alpha damping was assumed to be 2%.

A rigid impactor was used to create the stress waves. The impactor shape, size, and velocity
were selected to create clear stress waves, which are also shown in figure 2.

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Parts and Instances

The impactor in figure 2 shown in green was modeled as a hemisphere with a radius of 0.5
in. The FGM target was 5 in. thick and 16 in. tall. A control system consisting of 50%/50%
glass/alumina was also modeled with the same dimensions to show impact of varying the internal
microstructure with the FGM. Both the control and functionally graded assemblies are one part with
two materials assigned [(fig. 3) CaO- Zr02-Si02 shown in red, alumina shown in tan].

Figure 3

Control and FGM models

Material Properties

In order to capture acoustic wave movement correctly, linear elastic constants were used
(table 1). A damping of 2% was applied in order to capture the natural damping of the material. The
properties were recorded (ref. 2).

Table 1

Material properties

Density

Modulus

{ps\)

Poisson's

Ratio

Alpha Damping
(%J

AluminaA

3.7e^4

5.197

0.2

2.0

Ca0-Zr02-Si02

2.7e-4

1.395

0.27

2.0

Interactions and Constraints

Contact friction between the impactor and FGM target was assumed to be 0.0. Initial velocity
of the impactor was 24,000 in./sec; this value was chosen to create strong acoustic waves.
Symmetry boundary conditions (fig. 4) were applied to the top and bottom of the FGM target to
capture a fixed boundary.

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Figure 4

Boundary conditions

RESULTS

Tensile Pressure (psi)

The field output that most readily shows the difference between the control and FGM target is
tensile pressure. Both materials in the target being ceramic based, the micro-cracking and spall of
the target will be very sensitive to the material as it undergoes tension loading. The highest tensile
region observed appears to be the same in both the FGM and the control targets as shown in figure
5. Light gray represents pressures from internal compressive waves generated. Figures 6 and 7
show the progression of the stress wave through the target. The wave reflected from the back
surface is dispersed in the FGM material, but the surface tensile wave is not attenuated.

S, Pressure
(Avg: 75%)

I +1.145e+05

+o.oooe+oo

-1.667e+04

-3.333e+04

-5.0006+04

-6.667e+04

-0.333e+O4

-l.OOOe+05

-1.167e+05

-1.333e+05

-1.5006+05

-1.6€7e+05

-1.8336+05

-2.0006+05

-2.5046+05

Figure 5

Pressure results (time = 23.47 ps)

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(a) (b)

3.21 MS 12.27 ms

Figure 6

Pressure results 1

Control

I 4 1.136€;+0S

+o.-aooe+oo
'i.6&?e+o*a
-3.333e+tn
-5.0004+04
-*.&&74+04
-S.333e+04
-1.0004+05
-1.1*74+05
-1.5334+05
-1.5004+05
-1.5674+05
-1.8334+05

(a)

23.47 MS

(b)

31.47 ms

Figure 7

Pressure results 2

CONCLUSIONS AND PATH FORWARD

The overall goal of this particular study was to provide proof of concept through modeling and
simulation to predict the impact of a functionally graded material (FGM)-based target on the
shockwaves generated from an impactor. Most armor systems are comprised of a single material or
a composite layup of several materials. The intent of this study was to provide insight into the
effectiveness of morphed microstructure.

Qualitatively, results suggest that a target with varying microstructure and particle density
breaks up a shockwave more effectively than a homogenous target. The particles appear to
effectively break up and minimize pressure build up from reflecting waves created in the structure as
well. However, there appears to be little or no effect on the surface tensile wave. This is likely
because at the surface both targets are identical. The potential impact of high tensile stresses on the
surface is crazing. One potential solution would be to vary the composition at the impact surface as
well rather than start off with 100% of a single material. The particles and microstructure may help
disperse the surface wave and reduce the tensile stresses at the impact surface.

Future work proposed includes modifying the surface layers to have some particles at the
impact surface and varying the particle distributions, shapes, and sizes. Other potential studies will
include adding voids, validating models against actual penetration tests, and defining failure criteria
for the FGM matrix.

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REFERENCES

1. Young, R. and Lovell, P.A., Introduction to Polymers, 3rd Edition, CRC Press- Taylor & Francis
Group LLC, Florida, 2011.

2. ABAQUS, ABAQUS 6.11-1, Dassault Systemes Simulia Corporation, Providence, Rl, latest
edition, 2011. See also URL http://www.simulia.com.

3. Cannillo, V., Lusvarghi, L., Manfred ini, T., Montorsi, M., Siligardi, C., and Sola, A., Functionally
Graded Materials: prevision of properties and performances, OOF Workshop, 24-25 August
2006.

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U.S. Army ARDEC
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RDAR-MEE-M, M. Miller (3)

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RDAR-MEF-E, L. Reinhardt
A. Haynes
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