On Thermoelastic Impact Modelling of Frozen Composite Target

During Pre – Heated Projectile Penetration Starts of Motion

JACOB NAGLER

NIRC,

Haifa, Givat Downes

ISRAEL

Abstract: - This study investigates a composite double-layer structure for improved thermal shock

resistance. A modified Hugoniot elastic limit model is presented for the composite, followed by a 2D

thermo-elastic impact simulation using commercial software. The simulation focuses on a composite

material under initial extreme low temperature conditions with alternating metallic (Steel, Aluminum)

and non-metallic layers (Kevlar 49, Graphite). The frozen target is subjected to pre- heated projectile.

The objective is to optimize the composite's durability by strategically placing reinforcement particles

within specific layers. The analysis explores the effect of different particle types (oil, water, Aluminum,

Steel) and sizes (0.3mm, 0.5mm, 1mm) on the composite's stress response. It was found that aluminum

and steel particles significantly reduce stress compared to fluid/gas particles, confirmed qualitatively by

literature. Kevlar particles within the SiCp layer enhance its resistance, while Aluminum particles within

the Kevlar layer offer weight reduction benefits. Moreover, for Kevlar, larger particles improve

resistance, and vice versa for the SiCp case. Considering weight, a particle size of 0.5mm is chosen for

both layers. Moreover, a finite element analysis of the optimized composite model subjected to thermo-

elastic impact loading demonstrates its superior performance compared to the non-reinforced composite.

Specific layer combinations (SiCp with Kevlar particles, Graphite or Kevlar with Aluminum particles)

show the most significant stress reduction. Finally, separate 3D ballistic analysis was performed for

Tungsten having 600m/sec projectile into 5 layered target with thickness of 2.8mm each layer and

appropriate interaction friction (SiCp - Steel 304 - Al 7075-T651 - Kevlar 49 - Graphite Crystalline)

during penetration time of 0.006sec at 300K. The dynamic explicit transient analysis was confirmed

with the predecessors' analytic calculations.

Key-Words: analytic model, FEM, thermal shock, thermo-mechanical loading, suspended particles,

thermoelastic response, composite material, initial frozen target, pre heated projectile, 3D dynamic

explicit ballistic model.

Received: April 14, 2024. Revised: September 3, 2024. Accepted: October 4, 2024. Published: November 4, 2024.

1 Introduction

Thermal shock happens when a material

undergoes a rapid temperature change, stressing

the material. A material's ability to handle this

stress is called thermal shock resistance.

Thermal shock can be affected by many factors

including the material's properties, how quickly

the temperature changes, and the shape of the

object. The entire process is temporary and

depends on how fast the temperature changes.

The importance of protective components or

elements (PCs, PEs) with variable material

properties to withstand high temperatures and

pressure, known as thermo-mechanical shock

created in short time duration, as consequently

thermo-mechanical stresses are being

developed, is meaningful for mechanical,

medical, environmental and civil engineering

industries [1] – [66].

Initially, PCs were designed for specific

limited range values of temperatures or heat

fluxes. In further development stages PCs were

designed to absorb high amount of energy

through smart decorative layers management.

The shield, actually become a protective system

to withstand variety high thermal stresses, and

to keep durability for reuse purposes. Those

protective systems were investigated over the

decades, for instance, light weight foam carbon-

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based materials combined with high thermal

conductivity Graphite foam creating phase

change through pores of foam has been

proposed by Klett and Conway [1]. Xie et al. [2]

have also investigated the micropores effect on

photothermal anti-icing and deicing process

through carbon-based photothermal

superhydrophobic thermal insulation. They [2]

showed that the microholes array structure can

increase light absorption and hydrophobicity,

including the inhibiting of the heat transfer from

the surface to the subcooled substrate, which

synergistically enhances significantly the

photothermal conversion.

In 2013, Hu et al. [3] have interlaced Hollow

glass microsphere (HGM) in silicon rubber

(SR) matrix due to their excellent heat isolation

property and light density features. Their study

involved with the percentage of broken HGM

effect on the overall composite shield properties

(increasing of mechanical, density and thermal

conductivity properties alongside of broken

HGM increase was found). The current study

examines pores filled with different gas or fluid

materials, simulated as shell particles

containing gas or fluid materials.

To understand, particularly, the effects of

nanofluids over thermo-physical properties, i.e.,

thermal conductivity and viscosity, that have

significant influence over heat transfer

coefficients in case of single- or two-phase

flow, one should read the study be Azmi et al.

[4]. Accordingly, here the nanofluids will be

integrated inside the pores, while their effect

will be examined. Yet, viscosity will not be

considered in the current essay since the fluid

will be assumed as a bulk.

Other studies concerning hollow

microspheres (HM) particles combination made

of different materials like ceramic, silica, and

glass-filled silicone rubber (SR) composites

performed by Zhao et al. [5]. The effect of

different hollow microspheres (HM) on the

mechanical and thermal properties of styrene-

butadiene rubber (SR) composites was

investigated [5]. They found [5] that hybrid HM

can effectively improve the thermal insulation

property of HM/SR composites because of

higher modulus of hybrid HM than the SR

matrix. The hardness of composites increases

with increasing single HM loading, but

decreases slightly at high filler loadings due to

the saturation of high modulus microspheres.

The tensile strength of composites is affected by

the strength of matrix, interfacial compatibility,

shape, and dispersion of particles. Also, HM,

HCM and HSM effect on interfacial

compatibility and optimal proportions was

investigated and well elaborated alongside

extensive comparisons, as well [5].

The case of 2D-asymmetric circular adjacent

particles, named pebble beds inside emulsion

has been investigated in the context of heat

conduction, by Liu et al. [6], using discrete –

element and finite-element method. Verified by

experiments, obtained results have accurately

predicted bed particle internal and external

distribution of temperature due to its

counterpart's particles.

Solid / Liquid phase change inside pores and

cavities, particular analytical examination has

been demonstrated by [7] – [8] in the context of

molding and thermal protection supersonic

cruise, respectively. Another example is based

on polymer layered silicate nanocomposites to

improve flammability resistance of heat shields

against ablation by improving the effective

thermal diffusivity property by Kokabi and

Bahramian [9]. In their studies the researchers

have not considered pores or material phase

change in their examination. Although the

current paper discussion is limited to pre-

ablation heat transfer that resulted by thermo-

mechanical impact process.

Cryogenic layered materials, consisting of

several functional layers including aerogel that

suitable for thermal insulation purposes under

extreme conditions and nonvacuum

applications was proposed by Fesmire [10]. The

protective system [10] is based on layer-pairs

working in combination, while each layer pair

is comprised of a primary insulation layer and a

compressible radiant barrier layer.

Wang et al. [11] reported on of carbonaceous

composite materials mixtures and matrices for

different heat protective applications (among

them heat exchangers and space radiators).

Other types of protective composite systems

against ultra-high temperatures include

Zirconium-doped hybrid composites as

reported by [12]. They also modified thermal

shock resistance coefficient to be dependent on

Young's modulus and fracture strength by

increasing the critical temperature difference of

rupture to some extent, while claiming that their

Zirconium-based ceramics coating could absorb

the heat shock (suitable for nose-tip and nozzle

as well as other exposed surfaces, like wings

leading edge).

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Multilayer protection systems with various

systematic layering methods have been

proposed by Xue et al. [13] (in the context of

Multi-laminar aligned silicone rubber (SR)

flexible hybrids (SABE) with highly oriented

and dispersed boron nitride (BN) and expanded

graphite (EG) filler network), Zhang et al. [14]

in the context of ramjet combustion chamber

design made of internal C/C-SiC layer / first

mid layer of carbon-phenolic / second mid layer

aerogels / outer metal layer, Renard and Puskarz

[15] in the context of firefighters protection

cloth examined (by FEM) configuration based

on various woven and non-woven textiles layers

assemblies, respectively. Guo et al. [16] has

recently extended the woven fabric composite

shield analysis by using inverse methods based

on particle swarm optimization algorithm.

Other types of protective shields based on

multiphase functional phases have been

suggested by Zang et al. [17]. He examined

empirically the synergistic effect between three

different functional phases of thermal

insulation, i.e., hollow ceramic microspheres

(HCMs), hollow silica microspheres (HSMs),

and hydroxyl silicone oil blowing agent, to

prepare a flexible and efficient thermal

insulation composite with low thermal

conductivity and high structural strength.

Metamaterials are also being modified and

examined to create thermal protection that is

robustly and can be fast printing production

[18]. Macak et al. [19] have predicted

analytically the thermal radiation heat fluxes

inside heterogeneous granular media over

protective graphite tube containing pebble bed

filled and nitrogen which is also can be

considered as phase transition for protective

shield future applications.

Impact generates stress and displacement

waves in both projectile and target [20].

Traditional modeling used equations and

material properties to predict stress and

displacement [21]-[23]. Finite element methods

(FEM) are used for advanced simulations. The

initial shock wave and its effect on the projectile

are of particular interest [24]-[26]. Different

materials and projectile shapes can influence

the non-linear process [27] - [31]. This study

proposes a thermo-mechanical analytic pulse

model to analyze the initial shock wave [32] –

[33]. The current model considers separation of

energy into thermal and mechanical

components with composite material

parameters to assess shield resistance and

improve armor design.

The discussion in the current work is limited

to shock-based thermoelastic analysis, which is

a pre-ablative analysis without chemical change

of the material itself during the passage of heat

and / or mechanical loads, yet, focused on

strength analysis without chemical ablation

phenomenon. Here, the projectile (i.e. bullet) is

pre- heated to over seven hundred Celsius

degrees while the target is in initial extremely

frozen conditions (-248.150C). The idea is to

observe clearly compression and tensile stress

wave during process and to examine the pre

heated projectile effect.

The discussion is an extension of the

previous study [34], while here we concentrate

on the resultant impact (principal) stress over a

composite target plate through thermoelastic

shock mechanism. The medium, which is the

thickness of the base plate, is significant for the

passage of shock waves, as we will argue later,

and certainly also for continuous material

change in a full ablative process. We would like

to keep away from the process a change /

plasticity of the ablative material as much as

possible, in such a way that the target plate will

damp the thermoplastic wave optimally before

the transition to plasticity (change of material,

thermoplastic waves). Two-dimensional (2D)

analysis includes the impact sensitivity of target

composite material (layered with and without

particles), strength, temperature and size

geometry. Usually, the projectile temperature is

maximum 900C and the penetration occur in

standard environmental conditions of 250C [35]

– [36] (e.g. the maximum temperature

difference will be 0C). Afterwards,

the optimized shield will be examined for full

elastic-plastic penetration of 600 m/sec bullet

under standard 250C temperature conditions.

The empirical existing literature mentioned

here focus mainly on double layered metal –

composite rigid plates. In 1969, Wilkins et al.

[37] have conducted study on multi-layer AD85

Alumina protective armor made of different

(mainly brittle) ceramics materials (e.g. TiC,

Al2O3, SiC, AD85, B4C, etc.) bonded to Al

6061T6 to investigate strength and durability

during impact and projectile penetration

moving at about 700 m/sec. According to the

researchers [37] ductility material property and

gradation should be considered for armor

design. New materials should be developed

focusing on ceramic-metal composites

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(cermets) containing less than 10% metal. Also,

more focus on understanding how the metal and

ceramic parts of cermets bond together.

Lightweight materials like boron and beryllium

compounds should be investigated. Optimizing

fiber strength and elasticity in fiberglass

composites is recommended. In 1997, Espinosa

et al. [38] have led numerical investigation of

ballistic penetration into multilayered structural

systems based on multiple plane micro -

cracking model. Two types of ceramics have

been considered for each shield test, i.e.,

Alumina (Al2O3) and SiC while the cover plate

was made from RHA steel. Another type of

target made of alternate layers of aluminum and

PMMA layered materials composition was

investigated. The projectile normal impact

velocity was 1500 m/sec. Their main

contribution was that they have found that the

design of the layers (material choice and

arrangement) is more important than the

specific type of ceramic used. Next, Kanel et al.

[39] focused on the complex response of brittle

materials (ceramics, glasses, rocks) under

dynamic compressive loads (explosions,

impacts). Unlike tensile loading, where these

materials shatter easily, compressive behavior

is less understood, especially at high strain rates

and hence, challenges in understanding and

predicting how brittle materials respond under

rapid compressive loads still exist. Their key

findings include:

 Interpreting failure is difficult:

Traditional methods (Hugoniot data,

shock wave profiles) are not sufficient

to distinguish between brittle

(cracking) and ductile (deformation)

failure.

 Spall strength can be misleading:

Material may still be ductile even with

reduced shear strength if spall strength

(resistance to tensile failure) is not zero.

 Failure mode depends on stress state:

Cracks may form under high

compressive stress even if unloading

shows some tensile stress. Observing a

failure wave is a clear sign of brittle

response.

 Cracking vs. plastic slip: Inelastic

deformation can occur through

cracking or slippage within the

material. Confining pressure can

suppress cracking and promote

ductility.

 Strain rate matters: High strain rates

can make material behavior more

sensitive to microscopic processes.

 Griffith's criterion for dynamic

failure: This approach seems to better

predict failure mode (brittle or ductile)

under dynamic compression compared

to yield criteria used for ductile metals.

Overall, the study highlights the challenges

in understanding and predicting how brittle

materials respond under rapid compressive

loads.

Alternatively, Candera and Chen [40] – [41]

investigated the complex impact response of

layered composite materials, like those used in

armor. Unlike metals and ceramics, the stress

waves in composites are irregular due to the

layered structure. They developed an analytical

solution to predict the stress response within a

layered composite under impact, considering

material properties and layer thickness factors.

Their study confirms that material

heterogeneity at the interfaces between layers is

the main reason for the observed complex stress

wave profiles for thin layered plates (most

effectively) and suggested it can be used for

designing optimal layered armor. The study

acknowledges limitations of the model for

thicker plates and complex 2D woven

composites, recommending further research in

these areas. In continually, Chen et al. [42]

investigated the wave structure in composite

materials under high velocity impact loading.

They claimed that homogenization methods,

effective for low velocity impacts, are not

suitable for this scenario. An analytical solution

was presented for layered composites under

high velocity impact, applicable in elastic cases

with extensions proposed for shock regimes.

The analysis assumes perfectly bonded

interfaces and damage-free constituents. Three

key heterogeneity factors influencing the

material response were identified:

 Impedance mismatch: Affects

reflection/transmission ratios, stress

wave structure, and wave arrival time.

 Interface density: Determines wave

train strength and oscillation frequency.

High density leads to shorter rise time

and higher frequency (shock regime:

overtaking effect).

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 Thickness ratio: Governs wave

propagation patterns, affecting rise

time, oscillation behavior, and mean

stress. Explains the anomaly of lower

measured wave speed compared to

constituents.

Overall, their study [42] provided valuable

insights into the wave behavior of composite

materials under high velocity impact loading.

Colombo et al. [43] explored a new lightweight

bulletproof, vehicle armor or any other blast

protection armor design. Their design combined

for the first-time ceramic tiles with a special

ceramic foam infiltrated with polymer to create

a lightweight ballistic protection system, which

also absorbs effectively and dissipate energy

from impacts. Due to their successful test

results, armor made with this design could stop

fragmentations (e.g. bullet calibers) using a

thinner ceramic tile (lighter weight) compared

to traditional methods. Rajendran et al. [44]

used a modified two-cap constitutive model to

simulate shock wave propagation in powdered

ceramics under impact loading. Their model

was validated with experimental data and

successfully captured the effects of factors like

shock intensity, material impedance, and

densification on the shock wave behavior, as

consequently, providing valuable insights into

the complex behavior of powdered ceramics

under shock loading, which is difficult to obtain

experimentally. The findings can be used to

improve constitutive models for predicting

damage in ceramic armor plates. The problem

of composite materials thickness effect when

struck by objects at high speeds (impact,

damage, and penetration) have been examined

by Gama and Gillespie Jr. [45]. They

accomplished it using a computer simulation

technique called explicit finite element analysis

(FEA). The model accurately predicts how the

material will break and how far the object will

penetrate at various speeds (validated with

experiments). Two main penetration phases are

identified: short-time shock compression and

long-time penetration. The model can be used

to design composite materials that absorb more

impact energy.

Specifically, Babei et al. [46] investigated

how the order and type of materials in a double-

layered target affect its resistance to being

penetrated by a projectile. They tested four

configurations: aluminum-aluminum,

aluminum-steel, steel-aluminum, and steel-

steel. Steel-steel offered the highest resistance,

followed by steel-aluminum, aluminum-steel,

and then aluminum-aluminum. The study also

successfully developed a computer model to

simulate these impacts, achieving good

accuracy. The model showed that the order of

materials matters, with steel absorbing more

energy when placed in the front layer compared

to aluminum. A previously existing analytical

model (Ipson and Recht) did not accurately

predict the impact resistance for aluminum-

steel and steel-aluminum targets. Another study

by Shanel and Spaniel [47] have explored using

computer modelling to design lighter,

composite armor for vehicles. They fired real

bullets at armor plates and compared the

damage to computer simulations. By adjusting

the model, they achieved good agreement with

reality. This validated model can now be used

to design composite armor without needing as

many real-world tests. This is important

because composite armor is lighter than

traditional metal armor, which can improve

vehicle performance. Islam et al. [48] study

addresses the challenge of simulating how

ceramic and ceramic-metal plates react to high-

speed impacts from metal rods. They developed

a computer model to analyze these impacts,

whilst testing different material models for the

ceramic and found that the JHB model produced

the most accurate results compared to real-

world experiments. Their model can predict

various damage forms in the plates, including

cracks, fragmentation, and bending. Peimaei

and Khademian [49] examined how adding

silicon carbide (SiCp) to aluminum plates

(Al7075) affects their ability to stop a projectile

(bullet) using FEA. They found that plates with

more SiCp (9%) absorbed more energy and

stopped the bullet completely, while those with

less SiCp (3% and 6%) absorbed less energy

and did not stop the projectile (bullet) entirely.

The study also explains the mechanics of how

the bullet interacts with the plate and how the

damage zone increases with more SiCp.

Fernando et al. [50] have proposed a new design

for armor using a layered metal system

(impedance-graded multi-metallic or IGMM) to

absorb the impact of high-speed projectiles. The

IGMM system uses metals arranged in a

specific order to weaken and reduce

shockwaves. The research showed that IGMM

targets were effective at reducing stress on

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impact and preventing metal spalling compared

to traditional monolithic targets. Ranaweera et

al. [51] addresses a gap in knowledge regarding

multi-metal layered armor (MMMLS). While

traditionally, heavy steel plates have been used,

they are impractical for lightweight

applications. MMMLS offers a solution but

research on it is scattered and lacks consensus

on the best design. Their study reviewed the

effects of various factors on MMMLS

performance, including metal types, thickness,

plate arrangement, and connection methods.

They found that steel-aluminum combinations

were most common, but the optimal plate order

is unclear. An interesting new concept,

impedance-graded systems, needs further

exploration. The study proposes several

avenues for future research:

 Including new metals like titanium and

exploring their alloys with steel.

 Investigating the impact of increasing

MMMLS layers beyond double- and

triple-layered systems.

 Validating the impedance mismatch

concept for optimal ballistic

performance.

 Exploring alternative connection

methods between metal layers.

 Researching continuous MMMLS

manufacturing techniques like

explosive welding and 3D printing.

 Comparing the ballistic performance of

continuous vs. discontinuous MMMLS

designs.

Overall, this study highlights the need for

further research to optimize MMMLS design

for superior ballistic protection while

maintaining a lightweight construction.

Goda and Girardot [52] investigated the

ballistic performance of ceramic/composite

armor using computer simulations. They

created impact simulation durability of a

ceramic plate backed by a composite layer

against moving projectile. The ceramic layer

stops the bullet initially, then shatters. The

composite layer catches the fragments and

absorbs energy. The study also showed the

ceramic and composite layers interaction

affects the armor functionality. Their model can

help design better armor by predicting how

different materials and designs will perform. In

similar way, Jasra and Saxena [53] examined

how the pre-stressed state of a material (tensile

or compressive stress) affects its fracture

behavior under high-speed impact. They

created a computer model to simulate a blunt

projectile hitting a flat steel plate under various

pre-stress conditions. The model showed that

pre-stress significantly affects how the plate

fractures. Tensile pre-stress improves the plate's

ballistic performance (resistance to penetration)

by reducing damage accumulation.

Compressive pre-stress weakens the plate and

makes it easier to penetrate. It might be

significant to real-world structures experience

residual stress from welding or other processes

(i.e. high-velocity impacts resistance), which

can act like pre-stress.

Current essay presents a modified

equation of the approximate Huogoniot elastic

limit [34], [54] – [59] which basically

corresponds through equation algebraic shape

for two kinds of developed stress type inside

rigid solid materials (i.e. especially, ceramics,

metals); spall strength () and elastic

strength (), respectively. The point on the

shock wave at which a material transitions from

a purely elastic state to an elastic-plastic state is

called the Hugoniot elastic limit (HEL) as

illustrated in Fig. 1. The Hugoniot elastic limit

is derived from the equation of state (EOS) [54]

– [55], a thermodynamic relationship between

pressure, density and temperature parameters

through mass, momentum and energy

conservation equations. The HEL

approximation stress is:

 

 (1)

where the free surface velocity (projectile

impact velocity), bulk longitudinal speed and

density represent by , respectively.

The spall strength represents the reflection of

the initial compression pulse from the free

surface that generates tensile stresses. Spalling

is initiated when stress reaches the fracture

threshold as illustrated in Fig. 1. Afterwards,

tensile stresses relax to zero as the fracture

develops. As a result, a compression 'spall

pulse' wave appears in the extended material

free surface velocity profile [56] and

accompanied with decaying velocity

oscillations due to subsequent wave reflections

between the sample surface and the fracture

surface. The spall strength [54] is characterized

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by shorter load duration while the drop in

surface velocity from the peak value () to the

onset of spallation-the so-called

“pullback’‘( ,  is the free

surface velocity just a head of the spall pulse) -

is proportional to the tensile stress in the spall

plane [57] – [58]:

 

 (2)

where the bulk sound speed and density

represent by , respectively. The

 󰇛󰇜󰇛󰇜󰇛󰇜 sound

speed [59] is dependent on the bulk modulus 

while the longitudinal sound speed 

󰇛󰇜󰇛󰇜󰇛󰇜 is dependent on

the Elastic Young's modulus (). Both

dependent on the bulk's Poisson's ratio and the

material density.

However, here we are interested in the

purely elastic state of material's limit, since the

idea is to delay the plastic transition as much as

possible, and to extend the elastic domain both

in terms of the amplitude of the maximum

allowable elastic yield stress and the elastic

flexibility behavior (i.e. high elastic straining).

As consequently, the discussion will focus on

the modified approximated Hugoniot elastic

limit (HEL) as brought by Nagler [34]:

 





 (3)

where  ,  and   are

the projectile's impact temperature difference at

the initial contact and material's heat capacity,

respectively. In the following sections 2 -3 we

will introduce algebraic procedure for the

composite (mainly, double) rigid layer case

accommodation alongside experimental

validation, respectively.

Remark that alternative analytic strength

equation is proposed by [12], [60] – [62]. The

mentioned method is based on the following

generalized double layer UHTC (Ultra-high

temperature ceramics) impact stress due to

surficial thermal shock:

  󰇟󰇠󰇟󰇠󰇛󰇜

󰇟󰇠󰇛󰇜󰇟󰇠󰇛󰇜 (4)

where 󰇟󰇠󰇟󰇠 are the base

material Young's modulus, ceramics material

Young's modulus dependent on temperature,

Poisson's ratio of base and ceramics materials

and the initial environment temperature,

respectively.

From here we will pass to discuss briefly on

the protective shield containing pores as appear

in [63] – [66] and their effect over the protective

shield, which will be also examined in the

current essay continually in Sec. 4 - 5. Wei et

al. [63] investigated how rapid temperature

changes (thermal shock) damage carbon

composite used in pantograph strips for electric

trains. They found that Thermal shock weakens

the material by increasing pore size and causing

cracks. This damage gets worse with repeated

heating and cooling cycles. The damage is

linked to the different expansion rates of

materials in the composite under temperature

changes. Water trapped in the pores worsens the

damage by rapidly turning to vapor during

heating. Overall, the study highlights the

importance of considering thermal shock

resistance when designing pantograph strips for

reliable performance. Ramírez-Gil et al. [64]

proposed a new design methodology for

lightweight ballistic resistant steel plates based

on holes. They achieved weight reduction by

creating holes in the steel plates using two

approaches: parametric design based on

biological structures and topology optimization.

Testing showed that the topology optimized

design achieved similar ballistic resistance to

solid plates while being lighter, which is a

significant improvement. Their study [64] is the

first to explore topology optimization for

designing ballistic resistant structures and paves

the way for new, lighter protective gear. The

study also identifies limitations, such as

potential crack formation in the perforated

plates and the need for more advanced

manufacturing processes for mass production.

Overall, this research offers a promising new

approach for the ballistic protection industry

using conventional materials and processes,

potentially making ballistic protection more

affordable and accessible. Moreover, Li et al.

[65] examined the hollow pores potential by

investigating how a metal plate that is already

deformed (due to an explosion for example) will

perform differently when hit by a projectile

compared to a static metal plate. They found

that the way the plate deformation manner

PROOF

DOI: 10.37394/232020.2024.4.4

Jacob Nagler

E-ISSN: 2732-9941

Volume 4, 2024

significantly affects its resistance against

projectile. Also, they used a combination of

experiments and simulations to explore this

effect in detail. In addition, they have found that

deformed plates can stop some projectiles better

than static plates, but it depends on the amount

of deformation and the shape of the projectile.

There are three main ways that deformation

affects how well a plate stops a projectile:

o The deformation can give the

plate some extra energy to

resist the projectile.

o The deformation can change

how much energy the plate

absorbs as it bends and

stretches.

o The deformation can change

the forces acting on the

projectile as it punches through

the plate.

Accordingly, one can design armor that takes

advantage of deformation to improve its

performance, but need to consider how much

deformation is helpful and how much is

harmful. Wen et al. [66] introduced a new type

of ceramic material, 9-cation porous high-

entropy diboride (9PHEB), with excellent

mechanical strength and thermal insulation

even at high temperatures. Traditional porous

ceramics struggle to be both strong and good

insulators. They created 9PHEB using a special

technique and it achieves both high strength and

good thermal insulation at up to 50% porosity.

This makes 9PHEB a promising material for

extreme environments requiring thermal

insulation.

Finally, examples of thermal shock space

applications including penetration variations

and double bumper shock shield in NASA

including different situational investigation of

penetrations can be found in [67] – [68],

respectively. The applications of Thermal

Protection System (TPS) materials, specifically

Polymeric Ablatives (PAs) in the aerospace

industry are numerous, based on Natali et al.

[68]. TPS materials protect vehicles and probes

during atmospheric re-entry and high-

temperature environments. PAs are the most

versatile type of TPS material due to their

tunable density, lower cost, and high heat shock

resistance compared to non-polymeric

materials. Nanostructured polymeric ablatives

(NPAs) show promise for improving heat

resistance and reducing weight, yet, further

understanding is required to optimize

processing techniques and cost. The future of

NPAs likely involves combining them with

heat-resistant fibers to improve performance.

2 Modified Hugoniot elastic limit

for composite double layer under

thermal shock analytic model

Suppose we have general material protective

shield specimen that is subjected to thermo-

elastic impact loading as appear in Fig. 2. The

exerted (input) acting force impact over the

material surface yields reaction (output) force.

The general kinematic and force equilibrium

over a plate with acting input (󰇛󰇜) / reaction

output (󰇛󰇜) forces in Cartesian coordinates

that is derived by Newton's 2nd law is:

󰇛󰇜󰇛󰇜󰇘󰇗 (5)

where  is the force vectors,  are the total

mass (specimen mass and projectile mass),

specimen dumping coefficient and stiffness

coefficient.  is the longitudinal dimension,

denoting the elastic impact wave propagation.

Now, the force difference also fulfills the

following stress equilibrium multiplied by the

projectile area section :

󰇛󰇜󰇛󰇜 (6)

Where the mechanical () and thermal

() stresses supply stresses supply the

uniaxial strain condition where are shear

stresses zero [34]:

  

;  

󰇛󰇜󰇛󰇜

(7)

Note that those relations are derived from the

generalized constitutive stress relation classical

thermo-elastic model equilibrium. In case of

rigid isotropic material with hollow pores:

 

󰇛󰇜󰇛󰇜





 

󰆄

󰆈

󰆅

󰆈

󰆆

 

󰇡 

󰇛󰇜󰇛󰇜

󰇢

󰆄

󰆈

󰆅

󰆈

󰆆

 

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DOI: 10.37394/232020.2024.4.4

Jacob Nagler

E-ISSN: 2732-9941

Volume 4, 2024





󰆄

󰆈

󰆅

󰆈

󰆆

 

󰇡 

󰇛󰇜󰇛󰇜

󰇢

󰆄

󰆈

󰆅

󰆈

󰆆



(8)

where  which is the volume fraction

of the active protective material that resists the

penetration of the projectile.  is the relative

free portion (fracture) of an inactive material

substance (voids, hollows, empty pores).

Observation in Eq. (8), might lead to the

comprehension, by substituting  into Eq.

(8), we return back to the impact peak stress in

the homogenous case [34].

In case we have particles or filled gas pores

mixed instead of hollow / empty pores, then by

superposition, Eq. (8) becomes:

 󰆓

󰆒󰆓 (9)

Where,



󰆒󰆓

󰇛󰆓󰇜󰇛󰆓󰇜󰆒󰆒󰆓󰆓

󰆓 (10)

while 󰆒󰆒󰆒󰆒 are the particles elastic

properties. In case of one-dimensional multi-

layer shield, then the conditions will be:

 

 

  (11)

There is a difference in terms of the

development of elastic impact stress for cases of

connecting particles/pores in a continuous row

or laterally, as well as the effects of spreading

the spacing in a row or column. The suggested

algorithm might be with the analytic / numerical

composite scheme, proved by [40] - [41], [43],

[69]. In similar way to (8), we can write the

classical equations for the thermo-elastic

micromechanical composite lamina stress as:

 





 (12)

where  and are the composite stress

and area of composite, fiber, and matrix,

respectively. Now,  and

 will supply Eq. (3), by:

󰇫







(13)

Next section, target layers component under

thermo-elastic loading shock will be examined

from mechanical impact loading prospective

instead of ballistic aspect in order to separate

between the mechanical and thermal

components that develops during the process at

the very initial motion start (few initial

microseconds). Finally, the protective shield

containing particles will be also examined

separately. The examination will be performed

using FEM (finite element method) procedure

by commercial software, focusing on internal

components material's layer, connectivity,

particularly, particles' material size. The

investigation will consider high pressure and

temperature loadings values, approximately

100atm and 726.85°C, respectively.

3 General approximate analytic

approach for energy absorption

evaluation and material selection

of composite shield

In order to examine the plastic aspect, we would

like to obtain a sufficient initial approximation

in order to estimate the deformations, strains

and displacements that develop against a

damage model. It should be understood that the

sensitivity to the materials properties is

ultimately derived from the behavior of the

deformation in the plastic state, i.e., the damage

criterion is combined with stress properties.

Hence, we need that averagely each layer

absorbs a certain percentage of the energy. In

each layer, we define in advance what

percentage of the total energy it will absorb,

then, we will get the stiffness of each layer

according to a certain percentage of the total

energy multiplied by the thickness of the layer

and divided by the cross-sectional area of the

sphere and the difference of the squared

displacement to failure.

The theory will be developed based on the

author previous papers [75] – [76]. Suppose we

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DOI: 10.37394/232020.2024.4.4

Jacob Nagler

E-ISSN: 2732-9941

Volume 4, 2024

have general composite shield specimen as

appear in Figs. 2 – 3. Now, we will consider the

specimen as spring with two states: linear -

elastic and non-linear plastic, such as each state

represents difference spring' stiffness constant.

The kinetic energy input 

 (,  are

the projectile mass and velocity, respectively)

will be transferred into spring potential energy

and heat losses as appear in the following

energy conservative equilibrium:







 

















 . (14)

Since



, where the stiffness

constants ( are the elastic and plastic

specimen material stiffnesses, respectively) are

dependent over the material states (plastic or

elastic) and displacements ( are the

elastic and plastic relative specimen

displacements, respectively). Now, using the

spring force – stress balance relations, we have

the Hooke's law,

  

󰆄

󰆅

󰆆

 , (15)

where and A are the Young' elastic

modulus, elastic strain and projectile are

section, respectively, whereas the power

Hooke's law fulfills the plastic state stress as

[77] – [78]:

  





 , (16)

where the maximum tensile stress 

 (or the true stress where the true strain

),  - hardening index (usually in rigid

metals ) maximum plastic strain value,

  such as   for hard

metals and rigid parts (even though graphite and

Kevlar materials stress-strain curves act

differently than in metals case due to their high

rigidly performance and their composition with

metals, it will be considered similarly [79] –

[80] as initial required Young's modulus

evaluation).  and  are defined as:

 , (17)

 , (18)

where  is the total layered target thickness.

Therefore, since   and  is few

millimeters size, then,  .

Accordingly, the elastic potential energy

expression becomes approximately zero.













  . (19)

By substituting back (16) and (18) – (19)

relation into (14), we obtain:



󰇻





 , (20)

where  ; Assuming the

projectile has cylinder geometry and since the

mass constitutes a multiplicative sum of volume

() and density as  while the

volume is  and the projectile length is

denoted by , we finally obtain an

approximation for the elasticity modulus as:

 



, (21)

where accepted literature typical values for the

maximum plastic displacement are about  

, since if the maximum strain is

  and the thickness width is about

few (2.5) millimeters, then by multiplying the

parameters, yields  mm. Remark that

for different velocities the ratio between

different materials is approximately equivalent

to the squared velocity to plastic displacement

ratio value as  . For 

,  8500 [kg/m3], , and the

total sum of layers are , then the

total elastic modulus equal to  

󰇟󰇠. In other words, the meaning is that in

case of 10 homogenously layers with single

layer thickness of 2mm, averagely, where each

layer absorbs the same proportional value of

kinetic energy, the required averagely elastic

modulus of each layer to withstand the plastic

stress and deformation will be 

 

󰇟󰇠.

In the case of impact slicing or cutting, one

may insert the Young's modulus of elasticity

expression (21) based on kinetic energy into the

stress relations derived by Mora et al. [105]-

[106] and Arnbjerg-Nielsen et al. [107] and

have closed analytical explicit solution for high

shear strain energy or buckling.

The transition from elastic to plastic energy

is the focus of the specimen mechanical energy

absorption, because in the elastic state the

deformation returns to its previous state while

in the plastic state it remains in its current state.

In reality, it is of course necessary to perform a

large number of firing tests experiments

because both the speed of the projectile changes

from experiment to experiment and the hitting

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DOI: 10.37394/232020.2024.4.4

Jacob Nagler

E-ISSN: 2732-9941

Volume 4, 2024

angle of impact. Remark, care must be taken to

have a middle layer that disperses the shocks so

that the wearer of the vest shield will not be

damaged by the concentrated shock. It is

customary to apply this layer of rubber, metallic

(e.g. aluminum compound) foam or Dyneema

materials. In many applications where thermal

energy is involved, the thermal strain fulfill a

linear relationship with temperature difference

  ( is the thermal expansion

coefficient) and therefore the total strain will be

composed from the mechanical and thermal

strain linear sum as  .

Moreover, it should be understood that

energy management of layers in layered

systems (Laminated system kinetic energy

management) is a complex thing. To illustrate,

we assumed that the energy is distributed in a

uniform / homogeneous way, and in any case,

the Young's modulus per layer is derived from

dividing by the number of layers (n). In more

thoroughly way of thinking, the energy terms or

terminology, when speaking in energy

language, it is necessary to decide how much

energy each layer absorbs and accordingly, the

Young's modulus / coefficient of elasticity is

determined. This process is carried out using

multi-level layer optimization. Example 1:

Absorption of kinetic energy:

 First layer: 40%.

 Second layer: 30%.

 Third layer: 20%.

 Fourth layer: 10%.

Example 2: Absorption of kinetic energy:

 First layer: 30%

 Second layer: 20%

 Third layer: 20%

 Fourth layer: 20%

 Fifth layer: 10%

The 'thumb rule' says that the first layers

sacrifice themselves for maximum energy

absorption in relative to the following layers. At

the same time, sometimes we would like to have

'strong' 'weak' layers materials in terms of

strength, arranged alternately, sometimes in a

direction perpendicular to the fibers (00, 900,

1800, 3600) and sometimes from other

considerations, such as heat transfer or shock

dissipation. In case of extremely high energies

(high kinetic energy, e.g. velocity > 600 m/sec)

the required Young's modulus of each layer is

high such as it is difficult to obtain materials in

reality with high Young's modulus values.

Therefore, we would like the energy

absorption to apply to as many layers as

possible with maximum Young's modulus

according to what currently exists in reality (i.e.

the stock market). On the other hand, there is

still room to consider as the number of existing

materials have a high energy absorption

capacity increasingly, to propose a different

multilayer arrangement than is customary

according to the discussed thumb rule.

Alternative way, is to vary the thickness or to

use larger strain materials with special

suspended particles.

Layers with high energy absorption

capacity with weak layers, alternately, for the

simple reasons of weight reduction, adaptation

to production capacity (like molding pressure),

heat transfer, shock dispersion or cost

reduction. The presented method will be used

continually when concerning the full plastic

projectile penetration.

The way in which the developed internal

stresses are distributed when hitting the target is

characterized by unique failure mode impacted

plate mechanism [98] – [99], either by a bullet

projectile or a hardened rigid part (metallic,

other), whether dependent on the angle of the

projectile impact in relation to the target [100]

or the projectile head shape and obliquity

incidence angle design [101] - [102], or even

impact with a projectile made of soft or fine

materials [103] – [107], each perpendicular

input force (component) or pressure might be

evaluated through the volumetric energy

expression according to the following

relationship (after making some algebraic

manipulation of Eq. (5) appearing in Ref. [34]):

 



󰇡

󰇢

(22)

where   (assisting the

impulse relation),  is the contact time

difference, usually 󰇟󰇠 [34]

and the extracted (or given by empirical

measurements) term of  from (22) represents

the perpendicular force component acting on

the target (whereas is given and

therefore  using Eq.

(3)), respectively. In case of distributed

pressure () input, the perpendicular force

term should only be divided by the effective

impact area () such as . The

internal stresses then can be readily

determined by substituting  or  loading

expressions into the developed stresses

PROOF

DOI: 10.37394/232020.2024.4.4

Jacob Nagler

E-ISSN: 2732-9941

Volume 4, 2024

relations in the appropriate literature [98] –

[99] which also suitable for high shear strain

energy which suitable also for slicing or

cutting applications [103] – [107]. Be

reminded that the input force can be also

found directly by 

 





 with the appropriate pressure

term



. Remark that

 is the resulting peak

stress while  is the input pressure.

4 General approximate analytic

approach for energy absorption

evaluation and material selection

of protective ablative insulation

In the same manner as in Sec. 3, an approach to

evaluate erosion (ablation) rate in protective

energy applications (e.g. external or internal

(liquid, solid or hybrid) rocket motor (SRM) or

spaceship insulations, internal protection in

nuclear core, etc.) will be introduced [82] –

[85]. Indeed, the case of ablation concerns

material removal or thermochemical phase

change (virgin >> gas / pyrolysis >> char) while

the previous section was concerning material

deformation. However, since the char state

occur when threshold temperature is achieved

() and hence minimum energy balance

between the external thermal gas energy and the

material minimum thermal capacity energy

until prescribed threshold char temperature is

obtained could be used as follows. In other

words, the problem we are trying to solve is

what is the maximum distance () and the

minimum time () for char state formation for

a given threshold temperature to rise in order to

estimate the optimal erosion rate. It is assumed

in the process that the calculation is strict and

maintains a linear relationship between the total

relative distance of the erosion (material

removal) and the speed of the erosion rate

through time difference (). In addition, the

calculation assumes overloading region of

erosion rate. Accordingly, the classical

unsteady transient state energy equilibrium is:

󰇛 󰇜󰇛󰇜 ,

(23)

where the left-hand side term (󰇛 

󰇜) represents the resulting thermal energy

developed inside the ablative material caused

the equilibrium right-hand side term, such as the

flowing gas thermal convective energy

󰇛󰇛󰇜󰇜. The parameters

represent the

shield apparent area for the heat entrance,

ablative heat capacity, charred temperature of

the protective ablative material, gas surface

temperature, the environment initial

temperature, the thermal convective coefficient,

the ablative protective shield mass and time

difference, respectively. Now, by simple

algebraic manipulation, Eq. (23) becomes in the

following relationship form:





 . (24)

By substituting  and using

the erosion rate term  with some

algebraic manipulation, yields the expression

for the erosion rate speed:





 , (25)

where   and are the

protective shield ablative material specimen

density and volume, respectively. In this stage,

we will write the convective coefficient

parameter as the ratio between the heat flux ()

and the temperature difference () created

over the ablative material external / outer

surface, by: 

 . (26)

Substituting relation (26) back into (25)

gives:



󰇛󰇜 , (27)

and the appropriate total charred erosion

distance is:



󰇛󰇜 , (28)

where  is the total heating (e.g. burning) time.

Moreover, the more generalized energy case

that considers also the heat radiation, turns (23)

into: 󰇛 󰇜󰇛󰇜

 (29)

where  is the total manipulation between the

view factor () and the Stefan-Boltzmann

constant (). After similar algebraic

manipulation, the radiative and convective

erosion rate will have the following shape:

 









 . (30)

Illustratively, empirical evidence shows

through distinguisher references [82] – [85] that

in many burning cases in SRM the heating flux

PROOF

DOI: 10.37394/232020.2024.4.4

Jacob Nagler

E-ISSN: 2732-9941

Volume 4, 2024

rate fulfills 󰇣

󰇤, using (26), the

convective thermal coefficient is equal to 

󰇣

󰇤, where 

, respectively. Assuming [82] – [85] that

in Carbon – Carbon heat protective insulation

shield parameters are  , 

󰇣

󰇤󰇣

󰇤 , based on (27) –

(28) the obtained values for the erosion rate and

distance are 󰇟󰇠 and 

󰇟󰇠 for total burning time of 5.7sec, which

are confirmed by the literature references [84] –

[85] in the overloading erosion region. Suppose

we have also radiation involved (from one

surface to another only,  , 

󰇟󰇛󰇜󰇠), the contribution term to

the erosion rate will be 0.14󰇟󰇠 (see

[86]) and the total theoretical value is about

 󰇟󰇠.

5 2D thermo-elastic impact FEM

simulation of elastic wave

propagation inside protective

composite made of homogenous

isotropic material layers

As part of the examination of the shock

wave's propagation along the composite

material layers axial axis, a 2D finite elements

simulation framework will be developed for

four isotropic homogenous material's layers as

follows: Steel - Al - Kevlar - Graphite.

The whole Abaqus FEM explicit transient

temperature-displacement coupled equations

are reported by Koric et al. [70], full procedure

is brought there by Eqs. 1-24, while extensive

numerical elasto-plastic method is brought by

[71] - [72]. Based on Badurowicz and Pacekv

[73], suppose we have both thermal energies

accompanied with mechanical pressure,

representing kinetic energy of a piercing bullet

projectile into a given armor. While here, pre-

heated projectile accompanied with mechanical

pressure hitting frozen target is concerned. The

Armor's axi-symmetrical geometry including

the analysis properties, boundary and initial

conditions (B. C., I. C.) appear in Table 1. Also,

the armor materials properties layers are

exhibited in Table 2. FEM axi-symmetrical

analysis and modelling will be performed by

Abaqus commercial software. For current

instance, the land diameter of the contact area

will be considered as the 5.56×45 [mm] NATO

bullet [74]. The points of measurement for the

principal stress were taken at the bottom base of

each layer located in the axial axisymmetric

axis, as shown in Fig. 1.

As expected, described in Fig. 5, SiCp

material first layer absorbs high kinetic energy

which yields meaningful thermal energy values

that are conveyed / transformed to the next

metallic steel layer, and so on, such as the

mechanics loadings are absorbed by the

metallic layers plates and the thermal loadings

are absorbed by both metallic and non-metallic

layers which increase the shield survivability

and durability. Since the initial conditions occur

under an extremely low temperature (-

248.150C), compressive stresses are developed,

alternately, when the material experiences high

temperature values, tensile stresses are

developed. Since the heat is generated in short

time through thermal shock, the compressive

stresses are accompanied with tensile stresses

and later through shock vibrations behavior, the

compressive state is dominated over the tensile

state.

The materials data is based on MATWEB

database. One can infer from Fig. 5 that most

metals (with the exception of the non - metallic

Kevlar 49 and Crystalline Graphite) are able to

experience high temperatures and high

mechanical stresses, yet, as the metal is tending

to be brittle together with mechanical strength

increase, and hence its resistance to mechanical

loads may increase, although simultaneously,

its resistance to thermal loads may decrease.

6 FEM examination of particles

effect on a 2D homogenous

isotropic material layer subjected

to thermo-elastic impact loading

Next step, a variety of insulation materials

types, based on different shapes of pores filled

with gas, fluid or solid (simulated as particles)

states matter, will be tested separately for their

resistance ability to withstand thermal shock

using finite element commercial software 2D

model. The FE model is based on heat transfer

conduction mechanism for the following cases;

(i) Different types of cavity filling (air, water,

oil, Aluminum or metal); (ii) Different sizes of

circular cross section filled cavities / particles;

The current discussion is limited to orderly

uniform particles partition and distribution

along the material specimen as possible.

PROOF

DOI: 10.37394/232020.2024.4.4

Jacob Nagler

E-ISSN: 2732-9941

Volume 4, 2024

The areas of interest that will be examined

for adding particles and having the main

absorption potential in the composite armor are

the upper layer (1st) and the two lower layers (4th

and 5th), so that most of the mechanical elastic

wave part is absorbed by the upper layer, and

from this, we would like to increase its

properties for resistance to high thermal stresses

while preserving its mechanical resistance

against high mechanical impact elastic stresses,

considering the weight of a minimal protective

layer, optimally.

Moreover, we would like to improve the

resistance of the ended two insulation layers of

the shield to the development of elastic stresses

during the optimization process of adding the

particles, while subjected only to high

temperature effect. It is important to define that

these particles are part of the two-dimensional

model and therefore the direction of length

dimension into the page is infinite. Therefore, in

reality, these particles will be considered as

long cylindrical rods or as an array (row) of

spherical / cylindrical particles, separated at a

distance of up to about 5 millimeters from each

other in such a manner that their continuity and

mutual functioning and in relation to the

protective layer will not be damaged.

The 2D thermal shock impact FEM

simulation of elastic wave propagation

(compression and tension are represented in the

perpendicular principal stress plots by positive

and negative signs, respectively) inside single

protective homogenous isotropic material layer

to be used as reference is depicted in Figs.6a –

c. The numerical data values of elements type

and number, boundary and initial conditions,

geometry are elaborated in Table 3. We will

mention that isotopic material has the same

properties in every direction while homogenous

material has the same properties at every

location (point in the material). In our case, the

particles are made of different materials and due

to their size affects the non-homogeneity and

non-isentropic nature of the whole layer that

they reside in it. Figs. 7a-c illustrate the

modelling and meshing of generalized layer

with particles when configuration is altered

according to the given data and configuration of

material in Table 3. The point of measurements

in all cases are in the bottom of the layer at the

axi-symmetric axis as appear in Fig. 6c and Fig.

7c, respectively. Analyzing Fig. 8 might lead to

the expectation / comprehension that

Aluminum or Steel particles reduces

significantly the developed elastic wavy

principal stresses over the different types of

layers due to their thermo-mechanical ant

thermal loadings, respectively. Specifically, for

instance, Graphite layer without Al particles

peak stress versus same single layer containing

Al particles yields 50% decrease in peak stress;

in the case of Steel particles it becomes 67%

decrease difference. In the case of Kevlar 49, it

is less significant than Graphite, Yet,

comparison between Kevlar layers with Al or

Steel particles relative to homogenous isotropic

layers gives reduction percentage difference of

87.5% and 73.3%, respectively. In conclusion,

Steel particles are most efficient to use as

strengthen additive (positive material

contamination) for the described homogenous

layers. However, since the gain difference is not

meaningful and since the ratio between the

densities fulfills, we would

select the Aluminum particles to reduce the

weight of the protective shield per layer.

Observing Fig. 9 for the various

configurations of SiCp with and without various

types of particles teaches that the existence of

particles in the SiCp material increases

significantly the chance to resist and withstand

high thermo-mechanical loadings, particularly,

Kevlar particles.

The Kevlar particles are not only support or

provides elastic protection, which is already

present in the ceramic material, but mainly

provides thermal protection at a low weight

compared to the metals, steel and aluminum and

even the non-metallic Graphite. Particularly, for

example, Graphite particles make the material

less resistance against thermo-elastic shock

even in relative to SiCp material with no

particles at all (72% increase in impact peak

stresses); The Kevlar 49 particles improves the

resistance against impact peak stress by 22%

(reduction) compared to Steel (35%) and Al

(25%) which cause to peak stress increase,

respectively.

Figs. 10a-b illustrations demonstrates that

oil and water particles with coated elastic shell

made of closed foam cells affects similarly

(quantitatively and qualitatively) over the

Graphite principal stress behavior thermal

shock resistance performance. All kinds of fluid

/ gas shell particles making the Graphite layer

less resistant against the thermal shock, while

air particles have the highest weakening

material potential. On the other hand, in the

Kevlar 49 case, the air and oil particles behaves

PROOF

DOI: 10.37394/232020.2024.4.4

Jacob Nagler

E-ISSN: 2732-9941

Volume 4, 2024

/ affects similarly while this time, the water

particles make it less resistant. In conclusion for

both cases the gas and liquid particles makes

both Kevlar 49 and Graphite materials less

durable against the thermal shock (tens of

percent decrease in resistance) which is

confirmed qualitatively by the literature [63].

Alternatively, visco-elastic modelling should be

considered in future instead of enclosed elastic

foam.

7 FEM investigation of rigid

particles effect on a 2D

homogenous isotropic material

layer subjected to thermo-elastic

impact loading

Now, after selecting the most efficient and

optimal weight layer – particles mixture, we

will turn into particles size effect over the whole

layer contained the suspended particles

examination. Two kinds of layer examinations

were performed:

 SiCp with immersed Kevlar 49

particles versus reference homogenous

SiCp layer.

 Kevlar 49 layer containing Al particles

versus reference homogenous Kevlar

49 layer.

The particles size diameters typical values of

each examination were 0.3, 0.5 and 1mm. The

mesh and modelling appear in Fig. 11 and Table

4, respectively.

It is derived from Fig. 12a that in the case of

Kevlar 49 lamina, the layer's resistance to

thermal shock increases with increasing Al

particle size. Although the quantitative

difference between a particle of size 0.3mm and

0.5mm in the magnitude peak stress aspect is not

significant (1% maximum and 0.5% maximum

difference, respectively), yet, compared to

200% maximum difference in the case of 1mm

diameter size. Accordingly, together with the

consideration of the insulator weight 

 , the particle diameter size of 0.5mm

will be selected.

On the contrary, one can also infer from Fig.

12b that in the case of SiCp lamina, the layer's

resistance to thermal shock decreases with

increasing Kevlar 49 particle size. Although as

similar to the previous case, the quantitative

difference between a particle of size 0.3 and

0.5mm in the magnitude obtained peak stress

aspect is not significant as in the case of 1mm

diameter size (1% maximum compared to 176%

maximum difference). Accordingly, together

with the consideration of the insulator weight

 , the particle diameter size

of 0.5 mm will be selected.

8 FE final optimal axi-symmetrical

composite layered model

configuration results subjected to

thermo-elastic impact loading

Finally, the selected layers mixed with the

suspended selected particles material and size

will be introduced compared with their

counterparts without the internal particles

through axi-symmetrical FE model. The mesh

and modelling appear in Fig. 12 and Table 3,

respectively.

Observing at Figs. 14a-b might lead to

understanding that indeed the SiCp first layer

with the Kevlar 49 particles experiences lower

thermo-mechanical impact stress than the

homogenous layer case without particles (25%).

The Aluminum and Steel homogenous layers in

both cases behave qualitatively and

quantitatively the same. The Graphite 5th layer

with the Al particles also exhibits lower peak

principal stresses development than

homogenous layer case in the initial composite

configuration (400%). Nevertheless, the Kevlar

49 4th layer with particles presents less better

performance (500%) due to the overall stress

wave propagation through the materials layers,

especially the 4th (Graphite) that transfers

higher mechanical impact. Accordingly, we

might re-select / alternate homogenous Kevlar

49 layer without particles instead the current

Kevlar 49 layer with the Al particles. On the

other hand, since the maximum principal stress

value on the Kevlar 49 layer is about ~ 0.5GPa

and the ultimate strength is about ~3GPa, and

therefore the existing layer could be utilized

unchanged because the mechanical energy

transferred to the 5th last protective layer is

small enough.

PROOF

DOI: 10.37394/232020.2024.4.4

Jacob Nagler

E-ISSN: 2732-9941

Volume 4, 2024

9 3D full ballistic impact FEM

simulation of projectile

propagation inside protective

composite made of homogenous

isotropic material layers and

analysis

Suppose a projectile made of Tungsten [87,

88] gain velocity of 600m/sec hitting a

composite homogenous layered target initially

pinned () at 300K

temperature based on the mechanical and

damage properties given data in Table 2 and

Table 5 during time of 0.006sec as appear in

Fig. 15a. The obtained contact stress

() in Eq. (3) will

be 󰇟󰇠. The

approximate elastic modulus (21) required from

the whole protective shield is equal to 







󰇛󰇜

󰇟󰇠. The dynamic friction between all

shield plates was   and combined

tangential and normal behavior (Fig. 15b). The

general dynamic friction value between the

projectile body and shield plates was 

and also assumed tangential and normal

behavior (Fig. 15b). Each plate geometry was

100mmx100mmx2.8mm. The layers total

thickness sum was 14mm. The projectile and

each separate (individually) single protective

layer nominal element size was 2mm and

2.5mm, respectively. Elements type in the

whole analysis was C3D8R while projectile

(partially) wedge elements type was C3D6 as

appear in Fig. 16. The projectile finite elements

model includes 1189 elements (1102 linear

hexahedral elements of C3D8R type + 87 linear

wedge elements of type C3D6) appropriate to

1500 nodes. Each finite element layer 1600

linear hexahedral elements of C3D8R type

appropriate to 3362 nodes. The total assembly

elements are summed to 9189 elements with

18310 nodes. The shield plates material order

alongside the references, from up to bottom is:

SiCp [87], Steel 304 [89], Al 7075-T651 [90],

Kevlar 49 [91-93], Graphite Crystalline [94],

respectively. Type of analysis performed using

Abaqus commercial software was 3D stress

dynamic linear explicit transient.

The selection of each material damage

model was laid on their empirical behavior

under axial impact as reported by [87] – [94] as

appear in Table 5:

 The mechanism of tensile,

compression and shear have been

accounted for each material

behavior.

 The Kevlar fiber plate was assumed

to be isotropic and its properties

were taken in the longitudinal

projectile entrance direction only.

Analyzing the results appear in Figs. 17a-e

show that the projectile stops by decreasing

velocity and the shield configuration holding

him and resist its full perforation (during the

fourth Kevlar 49 layer penetration). It is also

demonstrated by Von-Mises, Principal stress

and displacement after 0.0006sec duration of

time. Also, both analytically above calculations

were confirmed by the results

(be 󰇟󰇠 versus

󰇟󰇠 and the young's modulus calculation

has proved to be effective prediction to the

protective shield strength withstanding against

the kinetic energy).

Note that the Graphite layer might be

alternative replaced by the more lightweight

material of aluminum foam, the results will be

improved in the context of strength ballistic

withstanding. The aluminum foam crushable

model data can be found in [95] whereas the

empirical material's nature appear in [96] – [97].

For each protective application it is always

recommended to use the NATO standard

STANAG (e.g. NATO STANAG 4569 for

logistic and light armored vehicles, NATO

STANAG 2920 for personal protective vest

guard, etc.). In future, personal light weight

protective configuration should be examined

for seven layers (each single layer geometry is

100mmx100mmx3mm) against impact velocity

higher than 600m/sec in the following order (1st

configuration: AL/4BC – Boron Carbide -

AL/4BC – Rubber - Boron Carbide – AL/4BC -

Boron Carbide, 2nd configuration: SiCp - Boron

Carbide – SiCp – Rubber – Dyneema - Boron

Carbide - Dyneema, 3rd configuration: AL/4BC

- Boron Carbide - AL/4BC – Rubber - AL/4BC

- Boron Carbide - AL/4BC).

PROOF

DOI: 10.37394/232020.2024.4.4

Jacob Nagler

E-ISSN: 2732-9941

Volume 4, 2024

10 Conclusion

Current study presented analytic

development of modified Hugoniot elastic

limit for composite double layer under

thermal shock analytic model. Also, two-

dimensional (2D) thermo-elastic impact FEM

simulation response of elastic wave's

propagation along the composite material

layers axial axis made of homogenous

isotropic material layers (Steel - Aluminum –

Kevlar 49 - Graphite) was developed using

commercial software (Abaqus) with explicit

transient temperature-displacement coupled

equations. The idea behind the mechanism

was that SiCp material first layer absorbs high

kinetic energy which yields meaningful

thermal energy values that are conveyed /

transformed to the next metallic steel layer,

etc., such as the mechanics loadings are

absorbed by the metallic layers plates and the

thermal loadings are absorbed by both

metallic and non-metallic layers which

increase the shield survivability and

durability. Accordingly, the layers

improvement was focused on the upper layer

(1st) and the two lower layers (4th and 5th),

respectively, whilst most of mechanical

elastic wave part is absorbed by the upper

layer, and the thermal energy created could be

absorbed by the two ended insulation layers.

The idea is to improve the thermal energy

resistance of the first insulation layer, and

simultaneously, to increase the strength of the

two ended insulation layers, while preserving

the existing advantages qualities (properties)

of each layer, without weakening them by the

suspended particles.

Moreover, FEM examination of particles

(oil, water, Aluminum or Steel) effect on a 2D

homogenous isotropic material insulation

layers subjected to thermo-elastic impact

loading was performed in order to optimize

the composite layered protective durability.

Moreover, different sizes of selected

materials' particles diameter were

investigated in the context of developed

principal peak stress during the thermo-elastic

response. In all cases the principal stress was

measured in the layer bottom at the axi-

symmetrical axis. Also, in all cases a

parentage difference comparison was made

with the homogenous case. It was found that

that Aluminum or Steel particles reduces

significantly the developed elastic wavy

principal stresses over the different types of

layers (i.e. Graphite or Kevlar layer

containing Al or Steel particles) due to their

thermo-mechanical ant thermal loadings,

respectively. Although Steel particles are

most efficient to use as strengthen additive for

the described homogenous layers, yet,

Aluminum particles were selected due to

weight reduction per layer considerations.

Additionally, the existence of particles in the

SiCp material were found to increase

significantly the chance to resist and

withstand high thermo-mechanical loadings,

particularly, Kevlar 49 particles compared to

Steel and Al. All kinds of fluid / gas (water,

oil and air) shell particles making the

Graphite or Kevlar layers less resistant

against the thermal shock, while air particles

have the highest weakening material potential

against thermal shock resistance performance

as supported by literature [61].

Now, selecting the most efficient and

optimal weight layer – particles mixture, we

have investigated particles size effect over the

whole layer contained the suspended particles

examination; SiCp with immersed Kevlar 49

particles versus reference homogenous SiCp

layer and Kevlar 49 layer containing Al

particles versus reference homogenous

Kevlar 49 layer. The particles size diameters

typical values of each examination were 0.3,

0.5 and 1mm. It was derived that in Kevlar

49 lamina case, the layer's resistance to

thermal shock increases with increasing

particle size, in contrast, a vice versa behavior

was found in the case of SiCp lamina.

Although in both cases the quantitative

difference between a particle of size 0.3mm

and 0.5mm in the magnitude peak stress

aspect was not found to be numerically

significant, compared to 1mm diameter size.

Accordingly, together with the consideration

of the insulator weight the particle diameter

size of 0.5mm was selected for both cases.

Finally, FE final optimal axi-symmetrical

composite layered model subjected to

thermo-elastic impact loading was analyzed.

An overall good qualitative and quantitative

resistant against thermo-mechanical impact

was obtained by the composite armor with

immersed particles compared to the

composite layers without the particles. It was

found that, indeed the SiCp first layer with the

PROOF

DOI: 10.37394/232020.2024.4.4

Jacob Nagler

E-ISSN: 2732-9941

Volume 4, 2024

Kevlar 49 particles, Graphite 5th layer with

the Al particles experiences lower thermo-

mechanical impact stress than the

homogenous layer case without particles. The

Aluminum and Steel homogenous layers in

both cases behave qualitatively and

quantitatively the same. The Graphite 5th

layer with the Al particles also exhibits lower

peak principal stresses development than

homogenous layer case in the initial

composite configuration. Although the

Kevlar 49 4th layer with particles presents

less better performance due to the overall

stress wave propagation through the materials

layers, especially the 4th (Graphite) that

transfers higher mechanical impact.

Accordingly, we might re-select / alternate

homogenous Kevlar 49 layer without

particles or alternatively, due to relatively

small maximum principal stress value, the

mechanical energy transferred to the 5th last

protective layer is small enough, and hence to

rely on the 4th layer as it is.

A dynamic Tungsten projectile full 3D case

was examined over 5 layers target. The

projectile was moving by velocity of

600m/sec hitting a composite homogenous

layered target initially pinned

(u_1=u_2=u_3=0) at 300K temperature

during penetration time of 0.006sec. The

dynamic friction value between all shield

plates was μ_(plates,d)=0.5 and combined

tangential and normal behavior. Each plate

geometry was 100mmx100mmx2.8mm. The

layers total thickness sum was 14mm. The

projectile and each separate (individually)

single protective layer nominal element size

was 2mm and 2.5mm, respectively. Type of

analysis performed using Abaqus commercial

software was 3D stress dynamic linear

explicit transient analysis. The contact stress

and the total elastic modulus were pre-

calculated analytically and confirmed later

through the analysis results. The shield plate's

material order based on literature data from

up to bottom was: SiCp - Steel 304 - Al 7075-

T651 - Kevlar 49 - Graphite Crystalline,

respectively.

The selection of each material damage model

was laid on their empirical behavior under

axial impact as reported by classical

literature, considering the mechanism of

tensile, compression and shear. The Kevlar

fiber plate was assumed to be isotropic and its

properties were taken in the longitudinal

projectile entrance direction only. It was

found that the projectile stopped by

decreasing velocity and the shield

configuration resistance from completing full

perforation supported by projectile velocity

alongside layers' stress and displacement

results. In case the Graphite layer is

alternatively replaced by the more lightweight

material of aluminum foam, the results will be

improved in the context of strength ballistic

withstanding.

In future, further research should be made in

the context of anisotropic and non-

homogenous layers, especially on polymeric

mixtures with and without particles,

integrated or independent with metallic

layers, subjected to thermo-mechanical

impact loading during the short contact

period. Also, visco-elastic modelling should

be considered to model pores or particles

filled with gas or fluid with instead of

enclosed elastic foam.

Also, personal light weight protective

configuration should be examined for seven

layers (each single layer geometry is

100mmx100mmx3mm) against impact

velocity higher than 600m/sec in the

following order (1st configuration: AL/4BC –

Boron Carbide - AL/4BC – Rubber - Boron

Carbide – AL/4BC - Boron Carbide, 2nd

configuration: SiCp - Boron Carbide – SiCp –

Rubber – Dyneema - Boron Carbide -

Dyneema, 3rd configuration: AL/4BC -

Boron Carbide - AL/4BC – Rubber - AL/4BC

- Boron Carbide - AL/4BC).

References

[1] Klett, J., Conway, B., 2000. Thermal

management solutions utilizing high thermal

conductivity graphite foams. In: Proceedings of

the 45th International SAMPE Symposium and

Exhibition, pp. 1933-

1943.https://www.osti.gov/servlets/purl/77096

[2] Xie, Z., Wang, H., Deng, Q., Tian, Y., Shao,

Y., Chen, R., Zhu, X., and Liao, Q., (2022) Heat

transfer characteristics of Carbon-Based

Photothermal Superhydrophobic materials with

thermal insulation micropores during Anti-

icing/Deicing, J. Phys. Chem. Lett. 13 (43),

10237–10244. DOI:

10.1021/acs.jpclett.2c02655

[3] Hu, Y., Mei, R., An, Z., Zhang, J., (2013)

Silicon Rubber/ Hollow Glass Microsphere

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Jacob Nagler

E-ISSN: 2732-9941

Volume 4, 2024

composites: Influence of Broken Hollow Glass

Microsphere on Mechanical and Thermal

Insulation Property, Composites Science and

Technology 79 64-69. DOI:

10.1016/j.compscitech.2013.02.015

[4] Azmi, W. H., Sharma, K. V., Mamat, R.,

Najafi, G., Mohamad, M.S. (2016) The

enhancement of effective thermal conductivity

and effective dynamic viscosity of nanofluids –

A review, RSER 53 1046-1058. DOI:

10.1016/j.rser.2015.09.081

[5] Zhao, X. W., Zang, C. G., Sun, Y. L., Zhang,

Y. L., Wen, Y. Q., Jiao, Q. J., (2018) Effect of

hybrid hollow microspheres on thermal

insulation performance and mechanical

properties of silicone rubber composites, J.

APPL. POLYM. SCI. 46025. DOI:

10.1002/app.46025

[6] Liu, X., Gui, N., Yang, X., Tu, J., and Jiang,

S., (2021) A DEM-embedded finite element

method for simulation of the transient heat

conduction process in the pebble bed, Powder

Technology. 377 607-620. DOI:

10.1016/j.powtec.2020.09.021

[7] Tomita, S., Celik, H., Mobedi, M. (2021)

Thermal analysis of solid/liquid phase change

in a cavity with one wall at periodic

temperature. Energies 14, 5957. DOI:

10.3390/en14185957

[8] Zhang, C., Wang, Y., Jin, Z. G., Ke, H. B.,

and Wang, H., (2022) Experimental study of the

thermal storage and mechanical properties of

microencapsulated phase change composites

during a supersonic cruise RSC Adv. 12, 6114-

6121. DOI: 10.1039/D1RA08434H

[9] Kokabi, M., Bahramian, A. R., (2009)

Ablation mechanism of polymer layered silicate

nanocomposite heat shield, Journal of

Hazardous Materials 166 445–454. DOI:

10.1016/j.jhazmat.2008.11.061

[10] Fesmire, J.E. (2016) Layered composite

thermal insulation system for nonvacuum

cryogenic applications, Cryogenics 74 154-165.

DOI: 10.1016/j.cryogenics.2015.10.008

[11] Wang, Q., Han, X. H., Sommers, A., Park,

Y., Joen, C.T., and Jacobi, A. (2012). A review

on application of carbonaceous materials and

carbon matrix composites for heat exchangers

and heat sinks, IJR 35 7-26. DOI:

10.1016/j.ijrefrig.2011.09.001

[12] Gudivada, G., Kandasubramanian, B.,

(2019) Zirconium-Doped Hybrid Composite

Systems for Ultrahigh Temperature Oxidation

Applications: A Review, Ind. Eng. Chem. Res.

58, 4711−4731. DOI:

10.1021/acs.iecr.8b05586

[13] Xue, Y., Wang, H., Li, X., and Chen, Y.,

(2021) Exceptionally thermally conductive and

electrical insulating multilaminar aligned

silicone rubber flexible composites with highly

oriented and dispersed filler network by

mechanical shearing, Composites: Part A 144

106336. DOI:

10.1016/j.compositesa.2021.106336

[14] Zhang, X., Wang, Y., Wang, Y., Liu, B.,

and Bai, X., (2022) Preliminary study on the

thermal insulation of a multilayer passive

thermal protection system with carbon-phenolic

composites in a combustion chamber, Case

Studies in Thermal Engineering 35 102120.

DOI: 10.1016/j.csite.2022.102120

[15] Renard, M., and Puszkarz, A.K., Modeling

of Heat Transfer through Firefighters

Multilayer Protective Clothing Using the

Computational Fluid Dynamics Assisted by X-

ray Microtomography and Thermography,

Materials 15(15):5417. DOI:

10.3390/ma15155417

[16] Guo F, Zhao X, Tu W, Liu C, Li B, Ye J.

Inverse Identification and Design of Thermal

Parameters of Woven Composites through a

Particle Swarm Optimization Method,

Materials. 2023; 16(5):1953. DOI:

10.3390/ma16051953

[17] Zang, C., Pan, H., and Chen, Y. J., (2023)

Synergistic Effects between Multiphase

Thermal Insulation Functional Phases on the

Mechanical and Heat Insulation Properties of

Silicone Rubber Composites, ACS Omega 8

(31), 28026–28035. DOI:

10.1021/acsomega.2c03572

[18] Sha, W., Xiao, M., Zhang, J. et al. (2021)

Robustly printable freeform thermal

metamaterials, Nature Comm. 12 7228. DOI:

10.1038/s41467-021-27543-7

[19] Macak, J., Goniva, C., and Radl, S., (2023)

Predictions of the P1 approximation for

radiative heat transfer in heterogeneous

granular media, Particuology 82 25-47. DOI:

10.1016/j.partic.2023.01.003

[20] Kılıç, N., Ekici, B., (2018) Ballistic

resistance of high hardness armor steels against

7.62 mm armor piercing ammunition, Materials

and Design, 44, 35–48. DOI:

10.1016/j.matdes.2012.07.045

[21] Hunter, S. C., (1957) Energy absorbed by

elastic waves during impact, JMPS, 5, 162-171.

DOI: 10.1016/0022-5096(57)90002-9

PROOF

DOI: 10.37394/232020.2024.4.4

Jacob Nagler

E-ISSN: 2732-9941

Volume 4, 2024

[22] Corcoran, J. C., and Kelly J. M., (1961)

Phenomena of penetration in light weight rigid

personnel armor materials, Beckman &

Whitley, Dept. of Army Quartermasters

Research and Engineering Command,

AD273060.

https://apps.dtic.mil/sti/pdfs/AD0273060.pdf

[23] Hutchings, I. M., (1979) Energy absorbed

by elastic waves during plastic impact, J. Phys.

D: Appl. Phys. 12 1819. DOI: 10.1088/0022-

3727/12/11/010

[24] ARPA, (1964) Theoretical and

experimental study of low-velocity penetration

phenomena, Report, U. S. Army Natick

Laboratories, Contract No. DA 19-129-AKC-

150(X) (OI 9114).

https://apps.dtic.mil/sti/pdfs/AD0467443.pdf

[25] Florence A. L., Ahrens, T. J., (1967)

Interaction of projectiles and composite armor,

Report, Stanford Research Institute Menlo

Park, California 94025.

https://apps.dtic.mil/sti/pdfs/AD0652726.pdf

[26] Asada, M. K., (1984) An analytical

evaluation of spall suppression of impulsively

loaded aluminum panels based on a one-

dimensional stress wave propagation model,

Thesis, Naval Postgraduate School, California.

https://core.ac.uk/download/pdf/36712387.pdf

[27] Anderson, C. E. Jr., and Bodner, S. R.,

(1988) Ballistic impact: the status of analytical

and numerical modeling, Int. J. Impact Eng. 7

(1), 9-35. DOI: 10.1016/0734-743X(88)90010-

[28] Espinosa, H. D., Dwivedi, S., Zavattieri, P.

D., and Yuan, G., (1998) A numerical

investigation of penetration in multilayered

material/structure systems, Int. J. Solid Struc.

35 (22), 2975-3001. DOI: 10.1016/S0020-

7683(97)60353-4

[29] Herrmann, W., Bertholf, L.D., Thompson,

S.L., (1975) Computational methods for stress

wave propagation in nonlinear solid mechanics,

In: Oden, J.T. (eds) Computational Mechanics.

Lecture Notes in Mathematics, 461 Springer,

Berlin, Heidelberg. DOI: 10.1007/BFb0074151

[30] Merzhievsky, L. A., Resnyansky, A. D.

(1995) The role of numerical simulation in the

study of high-velocity impact, International

Journal of Impact Engineering, 17 4–6. DOI:

10.1016/0734-743X(95)99880-Z

[31] Corbett, G. G., Reid, S. R., and Johnson,

W., (1996) Impact loading of plates and shells

by free – flying projectiles: A review,

International Journal of Impact Engineering, 18

141-230. DOI: 10.1016/0734-743X(95)00023-

[32] Goldsmith, W., (1999) Review: Non-ideal

projectile impact on targets, International

Journal of Impact Engineering, 22 95—395.

DOI: 10.1016/S0734-743X(98)00031-1

[33] Yarin, A. L., Roisman, I. V., Weber, K.,

Hohler, V., (2000) Model for ballistic

fragmentation and behind-armor debris,

International Journal of Impact Engineering, 24

171-201. DOI: 10.1016/S0734-

743X(99)00048-2

[34] Nagler J. (2023) Thermoelastic impact

modeling for projectile–target–muzzle

components during penetration start of motion,

The Journal of Defense Modeling and

Simulation 0 1-23. DOI:

10.1177/15485129231210300

[35] Colen, A. J., Hanson, L. F., Frits G. R., and

Hanson C. G. (2017) Thermal Energy Produced

by Medium Velocity Pistol Projectiles and the

Effects on Peripheral Nerve Tissue, SMRJ. 2

DOI:10.51894/001c.6345

[36] Kerampran, C., Tomasz, G., and Sielicki,

P. W. (2020) Temperature Measurement of a

Bullet in Flight, Sensors 20 7016. DOI:

10.3390/s20247016

[37] Wilkins, M. L., Cline, C. F., and Honodel

C. A. (1969) Fourth Progress Report of Light

Armor Program, Lawrence Radiation

Laboratory, University of California,

Livermore, UCRL - 50694. DOI:

10.2172/4173151

[38] Espinosa, H. D., Dwivedi, S., Zavattieri, P.

D., and Yuan, G., (1998) A numerical

investigation of penetration in multilayered

material/structure systems, Int. J. Solid Struc.

35 (22), 2975-3001. DOI: 10.1016/S0020-

7683(97)60353-4

[39] Kanel, G. I., Bless, S. J., and Rajendran, A.

M. (2000) Behavior of brittle materials under

dynamic loading, IAT. The University of Texas

at Austin, IAT.R 0219.

https://apps.dtic.mil/sti/pdfs/ADA386439.pdf

[40] Chandra, N., and Chen, X., (2003)

Experimental characterization and modeling of

damage in composites under ballistic impact,

U.S. Army research office, ADA413347.

https://apps.dtic.mil/sti/citations/tr/ADA41334

[41] Chen, X., Chandra, N., and Rajendran, A.

M. (2004) Analytical solution to the plate

impact problem of layered heterogeneous

material systems, IJSS 41 4635 - 4659.

https://doi.org/10.1016/j.ijsolstr.2004.02.064

PROOF

DOI: 10.37394/232020.2024.4.4

Jacob Nagler

E-ISSN: 2732-9941

Volume 4, 2024

[42] Chen, X., Candara, N., and Rajendran, A.

M. (2004) The effect of heterogeneity on plane

wave propagation through layered composites,

CST 64 1477 - 1493. DOI:

10.1016/j.compscitech.2003.10.024

[43] Colombo, P., Zordan, F., & Medvedovski,

E. (2006). Ceramic–polymer composites for

ballistic protection, Advances in Applied

Ceramics 105 78–83. DOI:

10.1179/174367606X84440

[44] Rajendran, A.M., Ashmawi, W.M. and

Zikry, M.A. (2006) The modeling of the shock

response of powdered ceramic materials,

Comput Mech 38 1–13. DOI: 10.1007/s00466-

005-0712-3

[45] Gama, B. A., and Gillespie, J. W. Jr. (2011)

Finite element modeling of impact, damage

evolution and penetration of thick-section

composites, IJIE 38 181-197. DOI:

10.1016/j.ijimpeng.2010.11.001

[46] Babaei, B., Shokrieh, M. M., and

Daneshjou, K. (2011) The ballistic resistance of

multi-layered targets impacted by rigid

projectiles, 530 208-217. DOI:

10.1016/j.msea.2011.09.076

[47] Shanel, V., and Spaniel, M. (2014)

Ballistic impact experiments and modelling of

sandwich armor for numerical simulations,

Procedia Engineering 79 230-237. DOI:

10.1016/j.proeng.2014.06.336

[48] Islam, R. I. Md. Zheng, J.Q., Batra, R. C.

(2019) Ballistic performance of ceramic and

ceramic-metal composite plates with JH1, JH2

and JHB Material Models, International Journal

of Impact Engineering 137 103469. DOI:

10.1016/j.ijimpeng.2019.103469

[49] Peimaei, Y., and Khademian, N. (2020)

Elasto-plastic simulation of bullet penetration

into Al7075-SiCp composites armor, The 7th

International Conference on Composites:

Characterization, Fabrication and Application

(CCFA-7), Tabriz, Iran.

https://civilica.com/doc/1226067

[50] Fernando, P.L.N., Mohotti, D.,

Remennikov, A., Hazell, P. J., Wang, H., and

Amin, A., (2020) Experimental, numerical and

analytical study on the shock wave propagation

through impedance-graded multi-metallic

systems, IJMS 178 105621. DOI:

10.1016/j.ijmecsci.2020.105621

[51] Ranaweera, P., Weerasinghe, D.,

Fernando, P., Raman, S.N., and Mohotti, D.

(2020) Ballistic performance of multi-metal

systems, International Journal of Protective

Structures 11 379-410. DOI:

10.1177/2041419619898693

[52] Goda, I., and Girardot, J. (2021) Numerical

modeling and analysis of the ballistic impact

response of ceramic/composite targets and the

influence of cohesive material parameters,

International Journal of Damage Mechanics 30

1079-1122. DOI:10.1177/1056789521992107

[53] Jasra, Y., and Saxena, R. K. (2022)

Fracture behavior of prestressed ductile target

subjected to high velocity impact – Numerical

study, ACM 16 101-118.

https://acm.kme.zcu.cz/acm/article/view/779

[54] Gautam, P. C., Gupta, R. Sharma, A. C.,

and Singh, M. (2017) Determination of

Hugoniot Elastic Limit (HEL) and Equation of

State (EOS) of Ceramic Materials in the

Pressure Region 20 GPa to 100 GPa, Procedia

Engineering 173 198 – 205. DOI:

10.1016/j.proeng.2016.12.058

[55] Sauer, C., Bagusat, F., Ruiz-Ripoll, M. L.,

Roller, C., Sauer, M., Heine, A., and Riedel, W.

(2022) Hugoniot data and equation of state

parameters for an ultra-high-performance

concrete, J. dynamic behavior mater. 8, 2–19.

DOI: 10.1007/s40870-021-00315-6

[56] Kanel, G. I., Razorenov, S. V., Utkin, A.

V., Fortov, V. E., Baumung, K., Karow, H. U.,

Rusch, D., and Licht, V. (1993) Spall strength

of molybdenum single crystals, J. Appl. Phys.

74 7162–7165. DOI: 10.1063/1.355032

[57] Joshi, K. D., Rav, A. S., Gupta, S. C., and

Banerjee, S., (2010) Measurement of spall

strength of A12024-T4 and SS304 in plate

impact experiments, J. Phys.: Conf. Ser. 215

012149. DOI: 10.1088/1742-596/215/1/012149

[58] Mukherjee, D., Rav, A., Sur, A., Joshi, K.

D., and Gupta, S. C. (2014) Shock induced spall

fracture in polycrystalline copper, AIP Conf.

Proc. 24 1591 608–610. DOI:

10.1063/1.4872691

[59] Shawoon K. R., Trabia, M., O’Toole, B.,

Hixson, R., Becker, S., Pena, M., Jennings, R.,

Somasoundaram, D., Matthes, M., Daykin, E.,

Machorro, E. (2016) Study of Hypervelocity

Projectile Impact on Thick Metal Plates, Shock

and Vibration 2016, Article ID 4313480, 1-11.

DOI: 10.1155/2016/4313480

[60] Li, D., Li, W., Li, D., Shi, Y., and Fang, D.

(2013) Theoretical research on thermal shock

resistance of ultra-high temperature ceramics

focusing on the adjustment of stress reduction

factor, Materials 6 551-564. DOI:

10.3390/ma6020551

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Jacob Nagler

E-ISSN: 2732-9941

Volume 4, 2024

[61] Wang, R. and Li, W. (2017)

Characterization models for thermal shock

resistance and fracture strength of ultra-high

temperature ceramics at high temperatures,

Theoretical and Applied Fracture Mechanics 90

1-13. DOI: 10.1016/j.tafmec.2017.02.005

[62] Kou, W., Li, W., Cheng, T., Li, D., and

Wang, R. (2017) Thermal shock resistance of

ultra-high temperature ceramics under active

cooling condition including the effects of

external constraints, ATE 110 1247-1254. DOI:

10.1016/j.applthermaleng.2016.09.004

[63] Wei, W., Song, Y., Yang, Z., Gao, G., Xu,

P., Lu, M., Tu, C., Chen, M., and Wu, G. (2019)

Investigation of the impacts of thermal shock on

carbon composite materials, Materials 12, 435.

DOI: 10.3390/ma12030435

[64] Ramírez-Gil, F. J., Silva, E. C. S.,

Montealegre-Rubio, W. (2021) Through-

thickness perforated steel plates optimized for

ballistic impact applications, Materials &

Design 212 110257. DOI:

10.1021/acs.iecr.8b05586

[65] Li, L., Zhang, Q. C., and Lu, T. J. (2022)

Ballistic penetration of deforming metallic

plates: Experimental and numerical

investigation, IJIE 170 104359. DOI:

10.1016/j.ijimpeng.2022.104359

[66] Wen, Z., Tang, Z., Liu, Y., Zhuang, L., Yu,

H., and Chu, Y. (2024) Ultrastrong and High

Thermal Insulating Porous High-Entropy

Ceramics up to 2000 °C. Adv. Mater, 36,

2311870. DOI: 10.1002/adma.202311870

[67] Christiansen, E. L. (1991) Shield Sizing

and Response Equations, NASA, Lyndon B.

Johnson Space Center Houston, Texas 77058.

https://ntrs.nasa.gov/citations/19920010785

[68] Natali, M., Kenny, J. M., and Torre, L.

(2016) Science and technology of polymeric

ablative materials for thermal protection

systems and propulsion devices: A review,

PMS 84 192-275. DOI:

10.1016/j.pmatsci.2016.08.003

[69] Oved, Y., Luttwak, G. E., and Rosenberg,

Z., (1978) Shock wave propagation in layered

composites, JCM 12 84-96.

DOI:10.1177/002199837801200107

[70] Koric, S., Hibbeler, L.C., and Thomas B.G.

(2009) Explicit coupled thermo-mechanical

finite element model of steel solidification, Int.

J. Numer. Meth. Engng. 78 1-9. DOI:

10.1002/nme.2476

[71] Ming, L. and Pantalé, O. (2018) An

efficient and robust VUMAT implementation

of elastoplastic constitutive laws in

Abaqus/Explicit finite element code,

Mechanics & Industry 2018; 19: 308. DOI:

10.1051/meca/2018021

[72] Abaqus Software Manual, (2022):

https://docs.software.vt.edu/abaqusv2022/Engl

ish/SIMACAEANLRefMap/simaanl-c-

couptempdisp.htm

[73] Badurowicz P and Pacek D. (2022)

Determining ricocheting projectiles'

temperature using numerical and experimental

approaches, Materials 2022 15 928. DOI:

10.3390/ma15030928

[74] Kolmakov, A.G., Bannykh, I.O., Antipov,

V.I., Vinogradov, L.V., and Sevost'yanov, M.A.

(2021) Materials for bullet cores, Russ. Metall

2021: 351–362.

DOI:10.1134/S0036029521040133

[75] Nagler, J. (2021) On analytical ballistic

penetration fundamental model and design,

WSEAS TRANSACTIONS on HEAT and

MASS TRANSFER, 16 177-191. DOI:

10.37394/232012.2021.16.21

[76] Nagler, J. (2022) Simple approximate

solutions for dynamic response of suspension

system, WSEAS TRANSACTIONS on

SYSTEMS, 21 20-31. DOI:

10.37394/23202.2022.21.2

[77] Dieter G. E. (1986) Mechanical behavior

under tensile and compressive loads, ASM

Handbook 8 99–10. DOI:

10.31399/asm.hb.v08.a0003261

[78] Liu, B., Villavicencio, R., and Soares, C.

G. (2013) Failure characteristics of strength-

equivalent aluminium and steel plates in impact

conditions in: Analysis and Design of Marine

Structures – Guedes Soares & Romanoff (eds),

Taylor & Francis Group, London, ISBN 978-1-

138-00045-2, 167-174. DOI: 10.1201/b15120-

[79] Seisson, G., Hebert, D., Bertron, I.,

Chevalier, J. M., Hallo, L., Lescoute, E.,

Videau, L., Combis, P., Guillet, F., Boustie, M.,

and Berthe, L. (2013) Dynamic cratering of

graphite: experimental results and simulations,

International Journal of Impact Engineering 63

18- 28. DOI: 10.1016/j.ijimpeng.2013.08.001

[80] Manigandan, S. (2015) Computational

investigation of high velocity ballistic impact

test on Kevlar 149, AMM 766-767 1133-1138.

DOI: 10.4028/www.scientific.net/AMM.766-

767.1133

[81] Li, G. (2017) Impact modelling of Kevlar

fabric composite panels, Conference: 63rd

CASI Aeronautics Conference and 24th CASI

Aerospace Structures & Materials Symposium

PROOF

DOI: 10.37394/232020.2024.4.4

Jacob Nagler

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At: Toronto.

https://www.researchgate.net/publication/3207

36489_Impact_Modelling_of_Kevlar_Fabric_

Composite_Panels

[82] Sun, L., Bao, F., Zhang, N., Hui, W.,

Wang, S., Zhang, N., and Deng, H. (2016)

Thermo-structural response caused by structure

gap and gap design for solid rocket motor

nozzles, Energies 9 430. DOI:

10.3390/en9060430

[83] Concio, P., Migliorino, M.T. and Nasuti, F.

(2021) Numerical approach for the estimation

of throat heat hlux in liquid rocket engines.

Aerotec. Missili Spaz. 100 33–38. DOI:

10.1007/s42496-020-00060-4

[84] Wang, L., Tian, W., Chen, L. et al. (2021)

Investigation of Carbon–Carbon nozzle throat

erosion in a solid rocket motor under

acceleration conditions. Int. J. Aeronaut. Space

Sci. 22 42–51. DOI: 10.1007/s42405-020-

00277-4

[85] Tian, H., He, L., Yu, R., Zhao, S., et al.

(2021) Transient investigation of nozzle erosion

in a long-time working hybrid rocket motor,

AST 118 106978. DOI:

10.1016/j.ast.2021.106978

[86] Turchi, A., Bianchi, D., Thakre, P., Nasuti,

F., and Yang, V. (2014) Radiation and

roughness effects on nozzle thermochemical

erosion in solid rocket motors, Journal of

Propulsion and Power 30, 314-324. DOI:

10.2514/1.B34997

[87] Sun, M., Cao, W., Hu, D., Zhang, N., and

Chi, R. (2021) Effect of Cover Plate on the

Ballistic Performance of Ceramic Armor.

Materials 14 1. DOI: 10.3390/ma14010001

[88] Holmquist, T. J., Johnson, G. R., and

Gooch, W. A. (2005) Modeling the 14.5 mm

BS41 projectile for ballistic impact

computations (originally from the book:

Computational Ballistics II), WIT Transactions

on Modelling and Simulation 40 61-

75.https://www.witpress.com/Secure/elibrary/p

apers/CBAL05/CBAL05007FU.pdf

[89] Dean, J., Fallah, A. S., Brown, P. M.,

Louca, L. A. and Clyne, T. W. (2011) Energy

absorption during projectile perforation of

lightweight sandwich panels with metallic fibre

cores, Composite Structures 93 1089-1095.

DOI:10.1016/j.compstruct.2010.09.019

[90] Aslam, M. A., Ke, Z., Rayhan, S. B.,

Faizan, M., and Bello, I. M. (2020) An

investigation of soft impacts on selected

aerospace grade alloys based on Johnson-Cook

material model, J. Phys.: Conf. Ser. 1707

012008.DOI: 10.1088/1742-

6596/1707/1/012008

[91] Zhu, D., Mobasher, B., Rajan, S.D. (2011)

Dynamic tensile testing of Kevlar 49 fabrics, J

Materials in Civil Eng, 23 1-

10.DOI:10.1061/(ASCE)MT.1943-

5533.0000156

[92] Zhu, D., Vaidya, A., Mobasher, B., and

Rajan, S. D. (2014) Finite element modeling of

ballistic impact on multi-layer Kevlar 49

fabrics, Composites: Part B 56 254–262. DOI:

10.1016/j.compositesb.2013.08.051

[93] Xuan, H., Hu, Y., Wu, Y. and He, Z. (2018)

Containment ability of Kevlar 49 composite

case under spinning impact, J. Aerosp. Eng., 31

04017096.DOI: 10.1061/(ASCE)AS.1943-

5525.0000806

[94] Seisson, G., Hebert, D., Bertron, I.,

Chevalier, J. M., Hallo, L., et al. (2013)

Dynamic cratering of graphite: experimental

results and simulations, International Journal of

Impact Engineering, 63, 18-28.DOI:

10.1016/j.ijimpeng.2013.08.001

[95] Novak, N., Vesenjak, M., Duarte, I.,

Tanaka, S., Hokamoto, K., Krstulović-Opara,

L., Guo, B., Chen, P., and Ren, Z. (2019)

Compressive Behaviour of Closed-Cell

Aluminium Foam at Different Strain Rates.

Materials 12, 4108. DOI: 10.3390/ma12244108

[96] Vengatachalama, B., Poh, L. H., Liu, Z. S.,

Qinc, Q. H., Swaddiwudhipong, S. (2019)

Three-dimensional modelling of closed-cell

aluminium foams with predictive macroscopic

behavior, Mechanics of Materials, 136

103067.DOI: 10.1016/j.mechmat.2019.103067

[97] Chi, R., Serjouei, A., Sridhar, I., and Tan,

G.E.B. (2013) Ballistic impact on bi-layer

alumina/aluminium armor: A semi-analytical

approach, IJIE 52 37-46. DOI:

10.1016/j.ijimpeng.2012.10.001

[98] Moslemi Petrudi, A., Vahedi, K., Rahmani,

M., and Moslemi Petrudi, M. (2020) Numerical

and analytical simulation of ballistic projectile

penetration due to high velocity impact on

ceramic target. Frattura Ed Integrità Strutturale

14 226–248.DOI: 10.3221/IGF-ESIS.54.17

[99] Sundaram, S. K., Bharath A. G., and

Aravind B. (2020) Influence of target dynamics

and number of impacts on ballistic performance

of 6061-T6 and 7075-T6 Aluminum alloy

targets, Mechanics Based Design of Structures

and Machines 50 993–

1011.DOI:10.1080/15397734.2020.1738245

[100] Pacek, D. and Badurowicz, P. (2024)

Numerical and experimental analysis of the

PROOF

DOI: 10.37394/232020.2024.4.4

Jacob Nagler

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influence of projectile impact angle on armour

plate protection capability, Defence Science

Journal, 74 439-446. DOI:

10.14429/dsj.74.19308

[101] Goda, I. (2023) Ballistic resistance and

energy dissipation of woven-fabric composite

targets: insights on the effects of projectile

shape and obliquity angle, Defence

Technology, 14-32.DOI:

10.1016/j.dt.2022.06.008

[102] Rodríguez-Millán, M., Díaz-Álvarez, A.,

Bernier, R., Miguélez, M. H., Loya, J. A. (2019)

Experimental and numerical analysis of conical

projectile impact on Inconel 718 Plates, Metals

9, 638. DOI: 10.3390/met9060638

[103] Reyssat, E., Tallinen, T., Le Merrer, M.,

Mahadevan, L. (2012) Slicing softly with shear,

Phys. Rev. Lett. 109, 244301. DOI:

10.1103/PhysRevLett.109.244301

[104] Deibel K.R., Lammlein, S., and Wegener,

K. (2014) Model of slice-push cutting forces of

stacked thin material, JMPT 214 667-672. DOI:

10.1016/j.jmatprotec.2013.10.009

[105] Mora, S., Tallinen, and Pomeau, Y.

(2020) Cutting and slicing weak solids, Phys.

Rev. Lett. 125, 038002.

DOI:10.1103/PhysRevLett.125.038002

[106] Mora, S. (2021) Effects of the blade shape

on the slicing of soft gels. Eur. Phys. J. E 44,

151. DOI: 10.1140/epje/s10189-021-00158-y

[107] Arnbjerg-Nielsen, S. F., Biviano, M. D.

and Jensen, K. H. (2024) Competition between

slicing and buckling underlies the erratic nature

of paper cuts, Phys. Rev. E 110 025003. DOI:

10.1103/PhysRevE.110.025003

Contribution of Individual Authors to the

Creation of a Scientific Article (Ghostwriting

Policy)

The author contributed in the present research, at all

stages from the formulation of the problem to the

final findings and solution.

Sources of Funding for Research Presented in a

Scientific Article or Scientific Article Itself

No funding was received for conducting this study.

Conflict of Interest

The author has no conflict of interest to declare that

is relevant to the content of this article.

Creative Commons Attribution License 4.0

(Attribution 4.0 International, CC BY 4.0)

This article is published under the terms of the

Creative Commons Attribution License 4.0

https://creativecommons.org/licenses/by/4.0/deed.en

_US

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APPENDIX

Fig. 1 Ideal free surface velocity profile versus time to exemplify the Hugoniot elastic limit and the

spall strength

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Fig. 2 (a) material specimen subjected to general thermo-elastic impact loading

Fig. 3 Two-dimensional generalized double layer protection shield material schematic description: (a)

Two adjacent different materials protective shield (b) Two adjacent different materials protective shield

with one side pores or particles (c) Homogenous protective shield material with pores or particles (d)

Two adjacent different materials protective shield consisting different pores or particles

󰇛󰇜

󰇛󰇜

















(a)

(b)

(c)

(d)

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Fig. 4 Circular plate axi-symmetrical FE model: (a) Boundary conditions (b) FEM meshing model. (c)

Points of measurements (Marked by Red points)

(a)

(b)

(c)

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Fig. 5 Composite metallic circular plate axi-symmetrical FE 2D model results

-4

-3

-2

-1

0,0E+00 5,0E-07 1,0E-06 1,5E-06 2,0E-06 2,5E-06

Principal Stress (Out of plane) Syy [GPa]

Time [sec]

SiCp 1st Layer

Steel 2nd Layer

Al7075-T651 3rd Layer

Kevlar 49 4th Layer

Graphite (C) 5th Layer

(a)

(b)

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Fig. 6 Circular homogenous isotropic plate axi-symmetrical FE model: (a) Boundary conditions (b)

FEM meshing model. (c) Points of measurements (Marked by Red points)

Fig. 7 Circular plate axi-symmetrical FE model with particles: (a) Boundary conditions (b) FEM

meshing model. (c) Points of measurements (Marked by Red points)

(c)

(a)

(b)

(c)

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Fig. 8 Graphite versus Kevlar materials single layer under thermal shock 2D FEM model results

Fig. 9 SiCp versus Steel materials single layer (Al, steel. SiCp) under thermo-elastic shock 2D FEM

model results

(a)

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Fig. 10 (a) Graphite versus (b) Kevlar materials (air, oil, water) single layer under thermal shock 2D

FEM heat - transfer model results

Fig. 11 Circular plate axi-symmetrical FE meshing model with different particles sizes: (a) 0.3mm (b)

0.5mm (c) 1mm

(b)

(a)

(b)

(c)

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Fig. 12 plots of selected configuration under the influence of various particles size effects

(a)

(b)

(a)

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Fig. 13 Circular plate axi-symmetrical FE optimized composite model configuration: (a) Boundary

conditions (b) FEM meshing model. (c) Points of measurements (Marked by Red points)

(a)

(b)

(c)

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Fig. 14 Upgraded composite metallic circular plate axi-symmetrical FE 2D model results with particles

versus the initial composite configuration made of homogenous layers.

Fig. 15 3D FE model of projectile and composite shield configuration made of homogenous layers: (a)

boundary conditions (b) dynamic friction interaction boundary.

(b)

(a)

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Fig. 16 3D FE model of projectile and composite shield configuration made of homogenous layers: (a)

projectile geometry (b) projectile FE meshing (c) single plate meshing (d) side view of assembly

meshing (e) isometry view of assembly meshing.

(a)

(b)

(c)

(d)

(e)

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Fig. 17 3D FE model of projectile and composite shield configuration made of homogenous layers: (a)

projectile velocity point of measurement (b) projectile FEM velocity behavior (c) Maximum principal

stress results of 3D FE assembly model (d) Von-Mises stress results of 3D FE assembly model (e)

displacement magnitude results of 3D FE assembly model (f) displacement in the z axial direction of 3D

FE assembly model

(a)

(b)

(c)

(d)

(e)

(f)

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Table 1 Armor geometrical properties per B.C., I.C. as input data for the FEM

Table 2 Protective shield components materials properties

Physical Property

Value [M.K.S.]

Target geometrical features

Five straight disk plates (layers) with diameter of 72

[mm] and 2.8 [mm] width, respectively. Total width =

14 [mm].

Mechanical loading simulating bullet

projectile ballistic penetration

󰇛󰇜󰇛󰇜󰇟󰇠

󰇟󰇠󰇟󰇠

characterized by land diameter

of 5.56 [mm] (impact dynamic pressure suits to

velocity impact of 1000 m/sec).  – the total shield

length. The contact acting area circular diameter equal

to 5.56 [mm] and the equivalent total pressure by the

projectile is 

󰇟󰇠.

Mechanical boundary conditions

 

 

Thermal boundary and initial conditions

simulating bullet projectile ballistic

penetration

󰇛󰇜󰇛󰇜󰇟 

󰇠

 󰇟 

󰇠

Analysis and element mesh rules details

(No., size, type)

Abaqus:

Type: Axi-symmetric, CAX4RT, Quad.

Number of elements: 5400. Element Size: 0.3 [mm]

Analysis type: plain – strain. total time = 5 󰇟󰇠

Materials

Densit

Young's

Modulus

[GPa]

Poisson's

ratio

Longitudinal

Sound of

velocity

Expansion

coefficient

Thermal

cond.

Specific

heat

capacity

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Table 3 Armor geometrical properties per B.C., I.C. as input data for the FEM of single

isotropic and homogenous versus non-homogenous and non-isotropic layers

[kg/m3]

[m/sec]

[ 

]

[

 

]

[ 

]

SiCP

3215

410

0.14

11772



120

750

304 Steel

7850

210

0.33

6160



44.5

440

Al7075-

T651

2700

0.31

6037



167

910

Kevlar 49

1440

112

0.36

10450



0.04

1420

Graphite

(Crystallin

2250

0.3

2335

1.4e-6

2.2

707

Tungsten

15000

255 (shear

modulus)

0.28

5200



250

Physical Property

Value of single homogenous

layer

[M.K.S.]

Value of single

Non-homogenous

layer

[M.K.S.]

Target geometrical features

Single straight disk plate

(layers) with diameter of 72

Single straight disk

plate (layers),

containing two rows of

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[mm] and 2.8 [mm] width,

respectively.

12 particles each

(particle diameter = 0.5

mm), divided

uniformly, with

diameter of 72 [mm]

and 2.8 [mm] width,

respectively.

The material configurations

SiCp, Kevlar 49 and Graphite

single layers

1. SiCp with

Al/Steel/Kevla

r 49 particles

2. Kevlar 49 with

Al/Steel/Air/O

il/Water

particles.

3. Graphite with

Al/Steel/Air/O

il/Water

particles.

All particles have

elastic properties

due to their

enclosed – cell

foam shell.

Mechanical boundary conditions

for single SiCp layer only

 

 

󰇛󰇜󰇛󰇜

󰇟󰇠

󰇟󰇠󰇟󰇠

Same

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Table 4 Armor geometrical properties per B.C., I.C. as input data for the FEM selected single

non-homogenous and non-isotropic layer under the influence of particle size effects

Thermal boundary and

initial conditions for all SiCp,

Kevlar and Graphite types of

single layers

󰇛󰇜󰇛󰇜

󰇟 

󰇠

 󰇟 

󰇠

Same

Analysis and element mesh

rules details (No., size, type)

Abaqus:

Type: Axi-symmetric,

CAX4RT, Quad.

Number of elements: 1080.

Element Size: 0.3 [mm]

Analysis type: plain – strain.

total time = 5 󰇟󰇠

Same

Number of elements:

9028. Element Size:

0.1 [mm]

Same

Physical Property

Value of single

Non-homogenous and non-isotropic layer

[M.K.S.]

Target geometrical features

Single straight disk plate (layers), containing two rows of 12

particles each, divided uniformly, with diameter of 72 [mm] and

2.8 [mm] width, respectively.

The material configurations

1. SiCp with Kevlar 49 particles.

2. Kevlar 49 with Al particles.

The two cases were examined for particle diameter nominal

sizes of 0.3, 0.5 and 1mm.

PROOF

DOI: 10.37394/232020.2024.4.4

Jacob Nagler

E-ISSN: 2732-9941

Volume 4, 2024

Table 5 Protective shield components materials plastic properties (Table 2 continuation)

Mechanical boundary conditions

for single SiCp layer only

 

 

󰇛󰇜󰇛󰇜󰇟󰇠

󰇟󰇠󰇟󰇠

Thermal boundary and

initial conditions for all SiCp and

Kevlar types of single layers

󰇛󰇜󰇛󰇜󰇟 

󰇠

 󰇟 

󰇠

Analysis and element mesh

rules details (No., size, type)

Type: Axi-symmetric, CAX4RT, Quad.

Number of elements (range): 10207-11535, Element Size: 0.1

[mm]. time = 2.5 󰇟󰇠

Materials

Densit

[kg/m3]

Young's

Modulus

[GPa]

Poisson's

ratio

Longitudinal

Sound of

velocity

[m/sec]

Expansion

coefficient

[ 

]

Thermal

cond.

[

 

]

Specific

heat

capacity

[

 

]

SiCP

Material parameters of Abaqus JH2 model:

PROOF

DOI: 10.37394/232020.2024.4.4

Jacob Nagler

E-ISSN: 2732-9941

Volume 4, 2024

304 Steel

Johnson – Cook Plastic Parameters:

A = 310[MPa], B = 1 [GPa], n = 0.65, m = 1,  󰇟󰇠,  󰇟󰇠,

C=0.07, 󰇗󰇟󰇠

Ductile damage parameters:  , Stress triaxiality = 1/3, 󰇗 

[1/sec],  

Al7075-

T651

Johnson – Cook Plastic Parameters:

A = 520[MPa], B = 477 [MPa], n = 0.52, m = 1,  󰇟󰇠,  

󰇟󰇠, C=0.001, 󰇗󰇟󰇠

Johnson – Cook Damage Parameters:

 

Kevlar 49

Plastic Parameters: 󰇟󰇠,  󰇟󰇠,  

Hardening Parameters – Power law Model: , Multiplier = 0.9

Ductile damage parameters:  , Stress triaxiality = 0.3, 󰇗 

󰇟󰇠,  

PROOF

DOI: 10.37394/232020.2024.4.4

Jacob Nagler

E-ISSN: 2732-9941

Volume 4, 2024

Graphite

(Crystallin

Plastic Parameters: 󰇟󰇠,  󰇟󰇠,  

Ductile damage parameters:  , Stress triaxiality = -1/3, 󰇗 

[1/sec],  

Tungsten

Johnson – Cook Plastic Parameters:

A = 3 [GPa], B = 89 [GPa], n = 0.65, m = 1,  󰇟󰇠,  󰇟󰇠,

C=0.016, 󰇗󰇟󰇠

Johnson – Cook Damage Parameters:

 

PROOF

DOI: 10.37394/232020.2024.4.4

Jacob Nagler

E-ISSN: 2732-9941

Volume 4, 2024