COMPUTATIONAL MODELING AND PROPERTIES OF METALLIC …

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COMPUTATIONAL MODELING AND PROPERTIES OF METALLIC FOAMS FOR

DEFENCE APPLICATIONS: REVIEW

PIYUSH AGRAWAL & DR. SHUSHANT SINGH

Mechanical Engineering Department, Uttaranchal University, Dehradun, 248007, India

ABSTRACT

Metallic foams locate more and more extra activity as structural materials, due to vast version in houses like excessive

stiffness in conjunction with very low particular weight, excessive energy-absorption capability, and blast mitigation

properties have an effect on resisting behavior, most fulfilling vibration and sound absorption capacity, and precise

thermal insulation. The light-weight constructions extensively used in automotive, aerospace, navy, wooden or bone

joints in scientific industry. Foams can be categorized as both open and closed porous. Open-celled foams are

characterized with the aid of interconnected voids and crash absorption functionality is of distinctive pastime for army

purposes associated to armored safety of motors or blast mitigation and therefore, it can play an essential position in this

context. Also, as metal foam is mild in weight, it leads to a giant financial savings of energy. As foams are commonly

vulnerable in tension, tensile power enhancement is one of the important challenges. Also, the current experimental and

computational simulation research on the crack propagation behavior of steel foams has primarily been confined and as

the application range is wide it is better to have constitutive model to predict the crack propagation behavior.

In this paper, the quite a number constitutive equations of different foams like aluminum, i.e Alpora,

polystyrene and PUR open celled foam, Titanium foams and alloys are discussed. The more than a few parameters like

yield function, yield stress von Mises fantastic stress equal plastic pressure price ε, plastic stress, plastic Poisson's ratio,

effect of porosity are and its steadiness whilst manufacturing is additionally mentioned .It is found that the density of all

types of foams has a very significant impact on its utility, thus its effects are discussed in detail. There hardening and

softening nature is investigated and the energy absorption capabilities are analyzed in the plastic region on number of

foam samples, ranging in density. There energy absorption capability is investigated by varying different parameters and

earlier performed tension, compression, uniaxial or biaxial and hydrostatic tension test and various other possible test to

understand the strength. Aluminum foams and its residences are mentioned whilst making ready by means of powder

metallurgy. The impact of inclination attitude on the temperature of a heated floor with and except steel foam in the case

of free convection warmness switch stipulations is analyzed. Micro-CT imaging is discussed on foam pattern with the aid

of preceding monotonic compression tests, alloys of binary, tertiary and Ti quaternary alloys, Ti-Nb-Ta-Zr, Ti-Nb-Ta-Mo

and Ti-Nb-Ta-Sn, with low elastic modulus of about 50 GPa primarily based on the molecular orbital calculation of

digital buildings foams and its houses and functions are referred to in the paper. The yielding conduct of 2D materials,

the impact of hydrostatic stress is discussed.

KEYWORDS: Powder Metallurgy, Metallic Foams, Yield Strength Stress, Von Mises Effective Stress, Equivalent Plastic

Strain Rate Ε, Plastic Strain Rate I, Plastic Poisson's Ratio 𝒗𝒑, Porosity Binary, Tertiary and Ti quaternary Alloys

Received: Oct 25, 2021; Accepted: Nov 15, 2021; Published: Nov 27, 2021; Paper Id.: IJPPTDEC20211

1. INTRODUCTION

Metallic foams have an large application area due to high stiffness in conjunction with very low specific weight,

high energy-absorption capability, their superior blast mitigation and impact resisting behavior, superior vibration

Orig

ina

l Article

International Journal of Plastic and Polymer

Technology (IJPPT)

ISSN (P): 2249–6904; ISSN (E): 2249–801X

Vol. 11, Issue 2, Dec 2021, 1–14

© TJPRC Pvt. Ltd.

2 Piyush Agrawal & Dr. Shushant Singh

Impact Factor (JCC): 2.5466 IBI Factor: 3.2

and sound absorption capacity, and good thermal insulation., thus residential application is also there currently folded

structures of metallic foams used mostly in automotive, aerospace, navy and other related industries due to high energy

absorption capacity and mechanical properties. Foams are generally interconnected voids having thermal and acoustic

absorbing capacity found in structural application areas especially closed cell foams as they have high strain energy

absorption capability, due to this in the modern era, high acceptable for the industrial. engineering applications also in

defense application crash absorption capability is of special interest and use for related to armored protection of vehicles or

blast mitigation. Also, as metallic foam is light in weight, it leads to a large savings of energy. As foams are generally

weak in tension, tensile strength improvement is one of the major challenges. Also increasing the impact toughness and

limit on failure under compressive stress are some of the most desirable properties for a better use of metallic foam in

military vehicle applications. As mostly the previous studies are on the compressive force, which limits its application

studies thus constitutive models are important to study the microstructure behavior.

2. MATERIAL COMPUTATIONAL MODEL OF FOAMS:

Computational enhancement of foam- The yield attribute for a porous material ought to embody a hydrostatic stress time

duration due to the reality the cells of the foam fall down when compressed, and due to the voids that exist in the foam, the

extent changes (Gibson and Ashby, 1997). The continuum-based isotropic constitutive model for crushable foams,

proposed with the aid of Deshpande and Fleck (2000), which consists of this feature, was once as soon as carried out in the

cutting-edge project. . The yield characteristic Φ is described with the aid of the use of

Φ = 𝜎^

− 𝑌 ⩽ 0 (1)

and the yield stress Y can be expressed as

𝑌 = 𝜎p + 𝑅(휀^) (2)

Where R(ε)ˆ represents the strain hardening and εˆ is the equivalent strain. The equivalent stress, σ, is given by

Deshpande and Fleck (2000)

𝜎^ 2 =

1

[1+(𝛼/3)2][𝜎e

2 + 𝛼2𝜎m2 ] (3)

where σe is the von Mises effective stress and σm is the mean stress. The parameter α defines the shape of the

yield surface. The following definition of the parameter α is used (Deshpande and Fleck, 2000):

𝛼2 =9

2

(1−2𝑣𝑝)

(1+𝑣𝑃) (4)

The plastic rate-of-deformation and the equal pressure charge is described by means of the related go with the

flow rule (Lemaitre and Chaboche, 1990. Deshpande and Fleck (2000) confirmed that the equal plastic pressure charge ˙ εˆ

can be expressed explicitly as:

2

𝜀

2= [1 + (

𝛼

3)2](휀

˙

e2 +

1

𝛼2 휀˙

m2 ) (5)

where the volumetric and von Mises effective plastic strain rates are in turn defined as (Deshpande and Fleck,

2000):

Computational Modeling and Properties of Metallic Foams for Defence Applications: Review 3


휀˙

m =𝛼2𝜀

^

1+(𝛼/3)2

𝜎m

𝜎^ , 휀

˙

e =𝜀˙

1+(𝛼/3)2

𝜎e

𝜎^ (6)

The elongation in plastic region is assumed to be normal to the yield surface and is given by :

𝜖˙

𝑖𝑗p

=1

𝐻

∂Φ

∂𝜎𝑖𝑗

∂Φ

∂𝜎𝑘𝑙𝜎˘

𝑘𝑙 (7)

where, H is the hardening modulus and 𝜎˘

𝑖𝑗 is the Jaumann stress rate.

The Poisson's ratio 𝑣𝑝 in plastic region after earlier test in a uniaxial compression is given by the relation as:

𝑣p = −𝜖˙

11p

𝜖˙

33p

=(1/2)−(𝛼/3)2

1+(𝛼/3)2 (8)

The 𝑣𝑝and 𝛼 is found to be dependent on each other and tested independently also of (derived from the measured

ratio of hydrostatic to uni-axial strength) for the three different foams With the tangent modulus method, the hardening

modulus follows the relation:

𝐻 = [𝜎e

𝜎^ ℎ𝜎 + (1 −

𝜎e

𝜎^ )ℎ𝑝] (9)

There are different models used for foams by various researchers in the wide area of application, whether it is

used for helmets, seat cushions or various defense applications. The vibrational model used of PUR foam by W.n patten &

sha for seat cushions of cellular foams and pneumatic effects inside the foam cellular structure is considered and non linear

dynamic model is derived and stiffness is also considered as PUR is found to be mostly used in cushion industry. It is

found that this model is applicable to small strains only and for large deformations does not hold. Few researchers

considered the lumped models and degree of freedom, The elastic stress developed inside the cellular structure of foam and

the air or gas entrapped inside that and stress due to this is considered to develop constitutive equations for stress strain

relationship. It is given by the relation:

𝜎 = 𝜎e + 𝜎f (10)

This equation has assumptions like the cellular structure is not going outside boundary, the air inside foam is a

Newtonian fluid, the motion of cushion is in one direction that is vertical only, the flow of air is incompressible with low

Reynolds number.

For PUR open celled foam the stress strain is related as:

(𝜌∗

𝜌s)

2

휀, 휀 ⩽ 0.05 (11𝑎)

𝜎m = 0 ⋅ 05𝐸s (𝜌∗

𝜌s)

2

, 0 ⋅ 05 < 휀 ⩽ 휀D (1 −1

𝐷) (11b)

0⋅05

𝐷𝐸s (

𝜌∗

𝜌s)

2

(𝜀D

𝜀D−𝜀)

𝑚

, 휀 > 휀D (1 −1

𝐷)

There is also a equation derived considering shape function and the stress relation is found to be

𝜎m = 𝐸f휀𝐹(휀) (12)

Where 𝐸f is initial young’s modulus and 𝐹(휀) is given by :

𝐹(휀) = 𝑎(𝑐 + 𝑑1휀)−𝑝1 + 𝑏휀𝑞 (13)



Here a,b,c,d are positive constants

There are comparison done of quasi-static stress and stress of the developed shape functions with theoretical value

of foams used in different application like seats in sports car and luxury car. It is found that sports car seat can bear large

amount of stress in comparison to luxury car whereas the changing behavior is nearly same of hyperbolic form which is

given by the relation:

𝜎m = 𝐸f𝑎

(𝑐+𝑑1𝜀)𝑝1휀 (14)

The cushion of the foam is modeled to rectangular form and change in the matrix structure is noted with the

application of stress.

The parameters of the PUR foam is taken as: Foam cell length parameters, design parameters like Young’s

modulus of polymer and foam, Density and Viscosity of air and foam & Volume fraction of open cell matrix & Surface

factor Coefficients of shape function. The energy balance equation or Darcy equation is used to calculate the change in the

pressure of cellular matrix, kinetic energy loss due to friction and turbulence is considered and given as :

Now substituting the different variables in the equation we find that the total stress in PUR.

𝜎 = 𝐸f𝑎

(𝑐+𝑑1𝜀)𝑝1휀 +

𝜇𝐻2

3𝐾𝜁휀˙

+𝜌𝐻2

3𝐾b2𝜁2 휀

˙2 (15)

It is found after analyzing the equations that K and B are independent to each other for compressible as well as for

incompressible fluid.

And the equation of motion is:

𝑀𝑍¨

= −𝐸f𝑎𝐴

(𝑐𝐻+𝑑1|𝑍|)𝑝1 𝑍 −𝜇𝐴𝐻

3𝐾𝜁𝑍˙

−𝜌𝐴

3𝐾b𝜁2 |𝑍˙

|𝑍˙

− 𝑀𝑋¨

0 (16)

In the above model, the coefficients are independent to load.

Hydro and the yielding stress is related to density of air and foam as :

𝜎𝑝𝑙

ℎ

𝜎𝑦𝑏= 𝐶𝜙

3

2(

𝜌

𝜌𝑏) (17)

Plastic stretching collapsible strength given by:

𝜎𝑝𝑙

𝑤

𝜎𝑦𝑏= 𝐶 ∗ (1 − 𝜙)

𝜌∗

𝜌𝑏 (18)

The third is applied stress to the collapse strength, which is given by:

𝜎𝑝𝑙

𝑔

𝜎𝑦𝑏=

𝑃−𝑃0

𝜎𝑗𝑏 (19)

Thus the total,the collapse strength is expressed as :

𝜎𝑝𝑙∗

𝜎𝑦𝑏=

𝜎𝑝𝑙ℎ

𝜎𝑦𝑏+

𝜎𝑝𝑙𝑤

𝜎𝑦𝑏+

𝜎𝑝𝑙𝑔

𝜎𝑦𝑏= 0,3 ⋅ 𝜙

3

2 ⋅ (𝜌∗

𝜌𝑏)

3

2

+(1 − 𝜙)𝜌∗

𝜌𝑏+

𝑃−𝑃0

𝜎𝑦𝑏

(20)



For polystyrene foam at low stress strain the slope of the elongation curve is given as:

𝐸∗

𝐸𝑏=

𝐸𝑐∗

𝐸𝑏+

𝐸𝑔∗

𝐸𝑏+

𝐸𝑓∗

𝐸𝑏= 𝜙2 ⋅ (

𝜌∗

𝜌𝑏)

2

+𝑃0(1−2𝑣∗)

(1−𝜌∗

𝑝𝑏)⋅𝐸𝑏

+ (1 − 𝜙)𝜌∗

𝜌𝑏 (21)

Where 𝜌∗

𝜌𝑏= 1,2 ⋅ ((

𝑡𝑐

𝑙)

2

+ 0,7 ⋅ (𝑡𝑢

𝑙)

2

) (22)

And 𝜙 is the fraction of materials pertaining to the cell edges of thickness te; the remaining fraction is (1- 𝜙)

constitutes thickness of cell walls, the edge length tw and l is the edge length .The deformed cell structure after bending is

studied, the lateral to linear strain is analyzed by poisons ratio which approximately comes out to be 0.33. Compression of

gas entrapped in the cellular structure is analyzed by considering its volume change ratio which is given by:

𝑉

𝑉0= 1 − 휀 ⋅ (1 − 2𝑣 ∗) (23)

The ratio of the volume change when the gas fills inside the foam is given as volume decreases from Vog to Vg,

where:

𝑉𝑔

𝑉𝑔0 =

1−𝜀(1−2𝑣∗)−𝜌∗

𝜌𝑏

1−𝜌𝑏 (24)

Application of boyle law is used to find the young’s and shear modulus G*:

𝐺∗

𝐸𝑏≈

3

8[𝜙2 ⋅ (

𝜌∗

𝜌𝑏)

2

+ (1 − 𝜙)𝜌∗

𝜌𝑏] (25)

For Alpora foams, constitutive relation found to be:

𝐸𝑑(휀𝑎) =∫

∫ 𝑎0

𝜎(𝜀)𝑑𝜀

𝜎𝑎, 0 ⩽ 휀𝑎 ⩽ 1 (26)

i.e. Energy dissipation of Alpora foam at a particular strain and an integration can found the total energy at

different strain rates and the maximum stress that can be found by differentiating the equation, which gives:

𝜎𝑝𝑙 =∫

𝑐40 𝜎(𝜀)𝑑𝜀

𝜀𝑑 (27)

It is found that the strain rate obeys an power law, thus designing of the product with polystyrene foam can be

done with respect to yield stress or to be precisely lower yield stress, considering the density, which is given by the

equation:

𝜎𝑝𝑙

𝜎𝑦𝑠= 𝐴 (

𝜌0

𝜌𝑠)

𝐵

(28)

Where 𝜌𝑠 is the density of the base material. It is been observed that as per the asby Gibson and Ashby’s, the

exponent by which the stress strain graphs of this manufacturer foam is 1.5 and the actual behavior is found to be 1.7 thus

the stress and strain are normalized and static and dynamic stress-strain curves are plotted, assuming the quasi static and

plateau stress to be plotted as:



𝜎𝑝𝑙

𝜎𝑦𝑠= 0.59 (1 + 𝐶휀

˙𝑝) (

𝜌0

𝜌𝑠)

1.7

(29)

Where C is the sensitivity of the strain rates and the value of C is found to be 1.4 of the Alpora foam. In

densification of foam analysis, the densification strain is linearly related to the density of foam:

휀𝑑 = 1 − 𝐷 (𝜌0

𝜌𝑠) (30)

Whereas Energy dissipation is found be be after experiment is

𝑤 = 0.59𝜎𝑦𝑠 (1 + 0.14휀˙

0.17) ((𝜌0

𝜌𝑠)

1.7

− 5.0 (𝜌0

𝜌𝑠)

2.7

) (31)

and directly proportional to the strain rates. At the value of D=5, the energy absorption capacity of Alpora foam is

safe. It is found that at relatively low densities, the energy absorption capacities increases, but as the density increases,

there is less space and movement of the cell structure, known as less densification strain.

Constitutive Model of Aluminum for the Extrusion Material in Strain-Hardening

For the uniaxial tensile test:

𝜎 = 𝜎𝑒 = 𝑌 = 𝑌0 + 𝑄1 (1 − exp (−𝑐1휀𝑝𝑙)) + 𝑄2 (1 − exp (−𝑐2휀𝑝𝑙)) + 𝜎𝑣 (32)

Where 𝜎 is the uniaxial stress, 𝜎𝑒 = √3

2𝜎𝑖𝑗

𝐷𝜎𝑖𝑗𝐷 and 휀

˙

𝑝𝑙 = √2

3휀˙

𝑖𝑗𝑝

휀˙

𝑖𝑗𝑝

is plastic strain and evaluated plastic strain rate

sensitivity. Langseth and Lademo found negligible strain rate sensitivity. It is also found that in extrusion and axial

crushing, ductile or rupture is there. In the damage theory, the Defective stress˜ is

𝜎~

=𝜎

1−𝐷 (33)

Where D is the isotropic damage variable 1. 0 ⩽ 𝐷 < 1

Central constitutive equation in all types to calculate effective stress is:

𝜎~

=𝜎

1−𝐷= 𝑌0 + 𝑄1(1 − exp (−𝑐1𝑟)) + 𝑄2(1 − exp (−𝑐2𝑟)) (34)

Where r is the damage-accumulated plastic strain .Finally for the uniaxial and hydrostatic loading following

model is suggested:

𝜎 = 𝜎𝑝 + 𝛾𝑒

𝑒𝐷+ 𝛼 ln [

1

1−(𝑒

𝑒𝐷)

𝛽] , 𝑒𝐷 = 1 − [𝜌𝑓

𝜌𝑓0] ( 35)

Where r is t. There are different models used for foams by various researchers in the wide area of application,

whether it is used for helmets, seat cushions or various defense applications are as follows:

Researcher Constitutive Model

LS Dyna 26 𝑓𝑖𝑗 = |𝜎𝑖𝑗| − 𝑌𝑖𝑗 = 0

Ls dyna 126 𝑓𝑖𝑗 = |𝜎𝑖𝑗| − 𝑌𝑖𝑗 = 0



Abaquas 𝑓 = √(𝑝 −1

2(𝑝𝑐 − 𝑝𝑡))

2

+ (𝜎𝑒

𝑀0

)2

− 𝑎 = 0, 𝑀0 =𝑏

𝑎

Deshpande and Fleck 𝑓 = √

1

1 + (𝛼/3)2(𝜎𝑒

2 + 𝛼2𝑝2) − 𝑌 = 0, 𝛼 = 𝛼(𝑣𝑝)

Miller 𝑓 = 𝜎𝑒 − 𝛾𝑝 +

𝛼

𝑑𝑝2 − 𝑑 = 0, 𝑑 = 𝑑0𝑌

Miller 𝛾 = 𝛾(𝛽, 𝑣𝑝), 𝛼 = 𝛼(𝛾, 𝑣𝑝), 𝑑0 = 𝑑0(𝛼, 𝛾), 𝛽 = 𝑌0/𝑌𝑡0

Schreyer

𝑓 = √(𝜎 − 𝑏): (𝜎 − 𝑏) − 𝑌 = 0

= √3Γ𝜎𝑒2 +

9

2𝛼𝑝2 + 81𝛿2𝑝4 − 3𝛽𝑝 + 9휁𝑝2 − 𝜅 = 0

DISCUSSIONS

The PUR model used to be proven successful in design and vibrational evaluation of in many applications like chassis,

suspension and automobile seats for better standards. There polystyrene foams used in a different application area of

automobile helmets and packaging industry, there energy absorption capability is studied by FEM coding. Expanded

polystyrene is of various densities under static and dynamic loading is testing by falling different weights and strain rates

are measured. The parameters that are taken, load magnitude, impact energy and the acceleration the helmet has got after

striking, keeping the European standard of 5 kg mass of the helmet and transferred acceleration to the head after striking

should be less than 7.5 m/s^2.The energy absorption capability is refined or changed by varying the density of the material

and thickness of the material by reducing the size of the helmet.

The important conclusions of polystyrene foams (EPS) and polycarbonate (PC) shells are that there is no

considerable difference in the mechanical properties under compression test and free volume, under static or dynamical

loading the small increase in the strain rate, there is a increase in the elastic modulus, thus all the characteristics taken in

the static test will not lead in to the design error. The dynamic test on PC and EPS, the thickness of the foam does not play

a significant role in the design criteria whereas the density plays an important role in designing and observed that high

density PC and EPS shows the brittle behavior at high loads thus high density foams can be used for different application

areas. It is also evident from the test that cell crushing is not uniform at the cell structure, but at the borders it is significant

which leads to good energy absorption strength. It is seen that there is pre extended beads in the foam and increase in the

stress leads to higher energy absorption, due to the assimilation of the beads. Thus it can be concluded that if the internal

structure of the foam can be managed, the strength can be used to best.

The Aluminum foam are also tested by the previous researchers like Alporas, used in aerospace and automobile

industry, found to have a high sensitivity to strain rates, they show different deformation and low and high strains due to

the inertia effects, which is called as micro inertia, as this is at the cell structure level. Empirical relations of the past results

are taken and change in the density with change in the strain rates effects on the energy absorption is analyzed in the range

of 1x103 to 2.2x 10 2 /sec. It is homogenous in composition and found to be high energy absorbing material.



CONCLUSIONS AND OUTLOOK

For PUR foam, of car seat application the non-linear characteristics and fluid damping effects are studied and found that

non linear characteristics indicates mechanical properties of open celled foams, damping is related as friction loss,bending

and buckling. This model evaluates the different weights on foams seats as well as for the chassis and suspension. The

important conclusions of polystyrene foams (EPS) and polycarbonate (PC) shells are that there is no considerable

difference in the mechanical properties under compression test and free volume, under static or dynamical loading the

small increase in the strain rate, there is a increase in the elastic modulus, thus all the characteristics taken in the static test

will not lead in to the design error. The dynamic test on PC and EPS, the thickness of the foam does not play a significant

role in the design criteria whereas the density plays an important role in designing and observed that high density PC and

EPS shows the brittle behavior at high loads thus high density foams can be used for different application areas. It is also

evident from the test that cell crushing is not uniform at the cell structure, but at the borders it is significant which leads to

good energy absorption strength. It is seen that there is pre extended beads in the foam and increase in the stress leads to

higher energy absorption, due to the assimilation of the beads. Thus it can be concluded that if the internal structure of the

foam can be managed, the strength can be used to best.

The Aluminum foam are also tested by the previous researchers like Alporas, used in aerospace and automobile

industry, found to have a high sensitivity to strain rates,they show different deformation and low and high strains due to the

inertia effects, which is called as micro inertia,as this is at the cell structure level. Empirical relations of the past results are

taken and change in the density with change in the strain rates effects on the energy absorption is analyzed in the range of

1x103 to 2.2x 10 2 /sec. It is homogenous in composition and found to be high energy absorbing material..

The extensive variation in like low particular weight, excessive electricity absorption functionality excessive

stiffness offers a utility vicinity like timber or bones .The Characterization of the foams is additionally executed via

interconnected voids advert spatially separated bubbles, in the electrical utility it saves energy, Crash absorption

functionality or have an impact on durability is additionally studied .Different sorts of foams are analyzed,like steel foams

there porosity influence and geometry increase there mechanical properties, The microstructure of aluminum foams are

studied and impact of inclination attitude on the temperature of a heated floor is mentioned formerly to there mechanical

voids which advocate that with the variant in temperature has a linear relation with the sine of inclination. Aluminum foam

temperature effectivity is mentioned and micro-CT imaging is studied and alloying factors are delivered to shape

ZA22/SiCp foam and ZA22 and there strength absorption ability is analyzed.

The hydrostatic strength of an isotropic foam with various alloying are taken in to account, the cell wall

stretching, bending and geometrical imperfections, cell wall waviness of 2D cellular materials is studied, the hydrostatic

strength of the regular honeycomb structure predict nearly circular yield surfaces and reduce the hydrostatic strength to the

same level as the uniaxial strength. Cell wall misalignments, Biaxial, shear and ax-symmetric loadings are also studied..

The plastic Poisson's ratio'' where the radial to axial strains yield criterion is analyzed .it is found that polymer foams

adopts a non-associated flow rule where plastic normality is satisfied. X-ray diffraction studies is done on Ti –foams there

energy absorption capacities, peak bearing stresses, compressive strength, porosity effects and relation with relative density

is discussed, Brittle compressive behavior, Ti binary, tertiary and quaternary composites are analyzed and the results

comparison is done to find the best industrial application.



There is research on the constitutive models on the aluminum foams for quasi static or low velocity loading in the

order of 10 m/s. The coding in the LS Dyna is done for the axial loading and in elastic bending test of different densities is

taken, hydrostatic pressure and volumetric strains are plotted. Models obtained from the LS Dyna are compared with the

other models. Hydro Al foam is manufactures with the rolled casting process with the chemical formula as ALSi8Mg and

the material property shows anisotropy. The casted foam is cut by spark cutting and the distribution of cell size with foam

density, with direction is represented. Different densities of foam are taken (𝜌1 = 0.17, 𝜌2 = 0.34 and 𝜌3= 0.51 gm/cm3)

are taken and the relation between the geometric cell size and anisotropy is investigated and the cell size of perfect sphere

is given the shape factor 1 and shape ratios R ZX, RZY, and RXZ is taken where RZX is the ratio between the longest cell in z

direction and x direction and the cell shape factor is calculated by comparing the area and circumference. It is found that

the cell size is inversely related to foam density and the shape factor reaches to 1, as the foam density increases. In the

plane yz and zx the there is a non uniformity or variation in the shape factor of 1 whereas in the xy plane the cell are

having shape factor 1 with uniformity. Approximately 600 low density foams and 1600 high density foams are investigated

and the effects of various types of loading like tension, compression, hydrostatic compression, dynamic compression,

extrusion, indentation, diagonal loading, perpendicular loading and axial crushing is done in x,y and z direction.

Another batch of (𝜌1 = 0.17, 𝜌2 = 0.34 and 𝜌3= 0.51 gm/cm3) was also tested on the same lines.Young’s

modulus with the effect of strain and hardening and loading rate sensitivity is analyzed. Earlier researchers have used the

pneumatic accelerators but this the Instron 250 KN with loading rate 20mm/min was used. Impact force is calculated with

impact load (54kg) of projectile motion.

Aluminum foam which is largely appreciated due to its vital mechanical and natural properties., recyclability and

non-toxicity which are added benefits, Low Density due to its light-weight metal structure is also there. The studies on

inclination microstructure with the aluminium alloy and without aluminium alloy on thermal stresses comparison is also

done by Laughlin et al. (2013). Salimon et al. (2005). M. Paknezhada, et,al. (2017), investigated experimentally the affect

of inclination mind-set on the temperature or thermal effectivity of aluminum foam, which is in the vertical function and is

about 17%. Due to aluminum foam reduces the floor temperature reduces up to sixteen °C which is in the vertical

characteristic.

Resuls of Alpora states that at the value of D=5, the energy absorption capacity of Alpora foam is safe. It is found

that at relatively low densities, the energy absorption capacities increases, but as the density increases, there is less space

and movement of the cell structure, known as less densification strain.In the Alporas foam it is found that the yield surfaces

are of quadratic shape in the stress space of mean stress versus effective stress, with the hydrostatic yield strength

comparable to the uniaxial yield strength comparison between measured and predicted shear response of the high density.

The final effective stress has been normalized by the uniaxial yield strength = 2.0 MPa. Despande and fleck suggested that

the misalignments, in the cell structure or cell wall waviness or any cell misalignments induced the bending stress

especially in 2D honeycombs They also studied the variation of hydrostatic stress percentage and observed the change in

mean and effective stress for various materials and strain hardening response is also measured and found that as the yield

surfaces evolve with plastic strain they remain quadratic in shape, with no evidence of corner development. It is observed

that under uniaxial compression they evolve in approximately a geometrically self-similar manner while under hydrostatic

compression they elongate along the hydrostatic axis. The three foams tested consistently show greater hardening under

hydrostatic compression than under uniaxial compression and for better yielding behavior the isotropic material is



suggested.

S. F. Aida et,al (2016) studied micro structural evaluation, porosity and density were also investigated and found

that volume of sodium chloride (nacl) in the debris sample affects porosity. M. J. Mirzaalia, et,al. (2016), also studied

porosity and found that porosity gradient have a negligible effect on the mechanical properties for a closed cell aluminum

foams. Ashby et al (2000) altered the grain structure and found different useful application properties like mechanical,

thermal, acoustic, electrical and chemical.. Zhao et al (2004) concentrates on structural applications such as energy

absorption, the most important considerations are porosity, specific strength, ductility, compression and cost.

The findings of Tizian Bucher, et. al (2016) compared the performances of the geometrical accuracy or

complexity in microstructure geometry with porosity is analyzed, which is required to get a excellent settlement with

experimental facts have developed on the thermal elements of laser forming of closed phone aluminum foam.

It has been experimentally found that by using combining perfect alloying elements, electricity absorption can be

multiplied significantly. For, example, Yu et al. (2009) suggested that strength absorption ability of ZA22/SiCp foam used

to be extensively greater than the ZA22 foam due to the dispersion of SiC particle on the mobile phone wall which makes

the wall difficult to withstand buckling and collapse. J. Liu et al. (2010) located that ZA22/Al2O3 foams exhibit greater

electricity absorption ability than ZA22 foam due to presence of Al2O3 fibre having extra dissipating strength mechanism

and debonding between fiber- matrix interface. Mondal et al. (2009) said that ZA27/SiCp foam indicates greater electricity

absorption fee amongst all ZA alloys foam due to the excessive yielding strength.

Dependence on yielding properties done by Gibson et. al., 1989; Zhang et. al., 1997; Miller, 2000. Recently

primarily based on certain multi-axial checking out data, Deshpande and Fleck (2000) worked on open and closed phone

metal foams (of relative density much less than 0.3) underneath proportional to loading.

Miller (2000) proposed a continuum plasticity framework for steel foams. Drucker-Prager found three adjustable

parameters to suit the yield floor, uniaxial tensile compressive yield strengths, and the ratio of radial to axial plastic

pressure in an uneven test, they observed the changes in density of foam, elastic and inelastic behavior, thermal stresses

behaviour i.e. the “plastic Poisson's ratio''. (Hill, 1967; Gurson, 1977) and found that they follow the power law relation,

even in the composites studied by Mondal et al. (2009, 2014) developed ZA27/SiCp composites where count plastic

normality is also satisfied.

Shah Ansari (2015) studied manufacturing processes and compressive strength of Zinc and aluminium composite

foam by adding SiC particles or short fibers of Al2O3 The compressive strengths of ZA22 is about 2.6 MPa and that of

ZA22/SiCp and ZA22/Al2O3 is about 3.5 MPa and 2.6 MPa, respectively. The elastic modulus, defined as the slope of the

stress-strain in the linear region, of ZA22 is about 290 MPa and that of ZA22/SiCp and ZA22/Al2O3 is about 290 MPa and

130 MPa, respectively. The peak stress indicate the ductile-brittle behavior of the composite foams which shows different

values due to cell wall material composition, surface morphology, cell size and the uneven mixture content of blowing

agent during casting method. The plateau stress values for ZA22, ZA22/SiCp and ZA22/Al2O3 foams are about 2.5 MPa,

2.8 MPa and 3.2 MPa, respectively indicate the ductile-brittle behavior of the composite foams which is important to for

ductile-brittle transformation. In general, composite foams show more brittle compressive behavior than plain ZA22 foam.

Amit Chege et al. (2017) examined the energy absorption capacity of car bumper by using different materials such

as foam, honeycomb, double cylinder model, double cylinder model filled with foam and double half cylinder model. The



results show that the two double half cylinder has the better energy absorption than others. Arun Basil Jecob et al. (2016)

performed individual crash test analysis of car bumper made up of steel honeycomb structure and aluminum foam using

Ls-Dyna. Both the materials show the better impact absorption capacity than current steel bumper of the car. C Ramesh

Kannan et al. (2014) studied different shapes for the crush can and cuboids seems to be suitable and suggested that the

aluminum is the best material for crush can.

Titanium (Ti) metal and its composites have been essentially utilized as mix with the living tissues of human

subsequently ther are popularly utilized in the clinical business, additive assembling techniques, for example, specific laser

liquefying (SLM) and particular electron pillar softening have been created, Ti froths for spinal interbody The porosity of

the acquired Ti froth was controlled by the size and weight of the sintered body. The normal macrospore size controlled by

CT imaging of the Ti froth sintered at 1400○C for 2 h was 268 mm when 69% of the space holder granules were 250-500

mm in size, while it was 333 mm on normal when 70% of the space holder granules were 500 -1400 mm in size. The pore

size expanded with the expanding size of the space holder granules yet just marginally. The porosity and the pore size of

the Ti froth diminished with expanding temperature and the time took into account the warmth treatment. Fig. 4.5 shows a

few instances of Ti froth containing pores of various volumes and sizes arranged by the powder sintering strategy.

The compressive strength is additionally in the prior writing for tube shaped examples 6 mm in width and 6 mm

long at a crosshead speed of 1 mm/min, as indicated by ISO 13314. The 0.2% yield strength was taken as the compressive

strength. It is clear that the compressive strength of the Ti froth increments with expansions in the sintering temperature,

while the porosity diminishes. The versatile modulus of thick Ti metal is around 100 GPa, which is a lot higher than that of

human cortical bone at 15e20 GPa.

Commercial foams like þ and Ti alloys (having low young’s modulus) which exhibits large variation in strength,

ductility and toughness by controlling alloy composition in terms of volume and thus controlling phases and

microstructure. Ti quaternary alloys, Ti-Nb-Ta-Zr, Ti-Nb-Ta-Mo and Ti-Nb-Ta-Sn, with low elastic modulus of about 50

GPa based on the molecular orbital calculation of electronic structures (called discrete variation X cluster method, DV-X

cluster method) proposed by Morinaga et al.2) Ti alloys possess almost similar values from 80 to 110 GPa which are

approximately one half that of steels which can be changed with the alloy composition with the addition of carbide or

boride, their industrial applications is expanded to a large extent. This result suggests that the theoretical method is

applicable to the development of Ti alloys with low elastic modulus. This paper discuss the measure of the composition

dependence of Young’s modulus in relation to phase stability and to discuss the applicability of the theory described above

to the development of low Young’s modulus Ti alloys, using simple Ti-V and Ti-Nb binary alloys and Sn-added ternary

alloys.

There are two models that are taken and both the experimental observations support the assumption of associated

law. In the first model the yield surface is constrained which evolve in a geometrically self-similar manner, and the

hardening law is calibrated against hydrostatic and uniaxial compression data. The other model predicts the stress versus

strain response of the foams under proportional loading conditions to reasonable accuracy and for the second model, the

magnitude of stresses is different in all directions which gives rise to anisotropy and the hardening behavior gives rise to

the yield surface. The hardening behavior gives rise to yield surface and the different hardening behavior of foams can be

used for the prediction of stress strain relationship. Although it is complex in nature, thus different isotropic materials are

tested for non proportional stress strain behavior and alternative hardening models are needed for further study. It is



additionally found, that metal foams advance anisotropy underneath massive plastic strains. For example, when a pattern of

the excessive density Alporas is compressed uniaxially to a logarithmic axial stress of 0.70, the subsequent transverse

power is observed to be about twice the modern axial energy.

REFERENCES

1. Aida, S. F., M. N. Hijrah, A. H. Amirah, H. Zuhailawati, and A. S. Anasyida. "Effect of NaCl as a space holder in producing

open cell A356 aluminium foam by gravity die casting process." Procedia Chemistry 19 (2016): 234-240.

2. Amit Chege, Kshitij, Abhishek Kale, Mohammad Rafiq B Agrewale, Dr. K.C.Vora, 2017: Design and development of impact

energy absorbing bumper, international journal of scientific and engineering research, Issn: 2229-5518, Volume 8, Issue 3,

March 2017.

3. Arun Basil Jecob, Arunkumar O. N, 2016: Improving the crashworthiness of an automobile bumper, iosr journal of

mechanical and civil engineering, E-Issn: 278-1684 (2016) Pp 67-79.

4. Ashby, M., Evans, A., Fleck, N., Gibson, L., Hutchinson J., Wadley H., 2000. Metal Foams: A Design Guide. Butterworth-

Heinemann, USA.

5. Bucher, Tizian, Christopher Bolger, Min Zhang, Chang Jun Chen, and Y. Lawrence Yao. "Effect of Geometrical Modeling on

the Prediction of Laser-Induced Heat Transfer in

6. Metal Foam." Journal of Manufacturing Science and Engineering 138, no. 12 (2016): 121008.

7. C. Ramesh Kannan, P. Padmanabhan, G. Rajkumar, 2014: Optimization of bumper design by using crash test, international

journal of engineering research & technology (Ijert), Issn: 2278-0181, Vol. 3, Issue 11, November-2014.

8. Chen, J.Y., Huang, Y., Oritz, M., 1998. Fracture analysis of cellular materials: a strain gradient model. J. Mech. Phy. Solids

46, 789–828.

9. Deshpande, V. S. and Fleck, N. A. 2000: Isotropic Constitutive Models for Metallic Foams, Journal of the Mechanics and

Physics of Solids, 48, 1253 – 1283.

10. D. P. Mondal, M. D. Goel, and S. Das, 2009, Compressive deformation and energy absorption characteristics of closed cell

aluminum-fly ash particle composite foam, Mater. Sci. Eng. A, 507 (1–2) 102–109

11. D. P. Mondal, M. D. Goel, N. Bagde, N. Jha, S. Sahu, and a. K. Barnwal, 2014, Closed cell ZA27-SiC foam made through stir-

casting technique, Mater. Des., 57, 315–324.

12. Gibson, L.J., Ashby, M.F., Zhang, J., Triantafillou, T.C., 1989. Failure surfaces for cellular materials under multi-axial loads

— I Modelling. Int. J. Mech. Sci. 31, 635–663.

13. Gibson, L.J., Ashby, M.F., 1997. Cellular Solids: Structure and Properties, 2nd ed. Cambridge University Press, Cambridge.

14. Gioux, G., McCormack, T.M., Gibson, L.J., 2000. Failure of aluminium foams under multiaxial loads. International Journal of

Mechanical Sciences, in press.

15. Gurson, A.L., 1977. Continuum theory of ductile rupture by void nucleation and growth: Part I Ð

16. Yield criteria and ¯ow rules for ductile porous media. Journal of Engineering Materials and Technology, 2.

17. Hill, R., 1967. The essential structure of constitutive laws for metal composites and polycrystals.,Journal of Mechanics and

Physics of Solids 15, 79.



18. J. A. Liu, S. R. Yu, Z. Q. Hu, Y. H. Liu, and X. Y. Zhu, 2010, Deformation and energy absorption characteristic of Al2O 3f/Zn-

Al composite foams during compression, J. Alloys Compd., 506 (2) 620–625.

19. J. Banhart, J. Baumeister, “Production Methods for Metallic Foams”, Materials Research Symposium Proceedings, Vol. 521,

pp. 121-132, 1998.

20. Jha N, Mondal DP, Majumdar JD, Badkul A, Jha AK, Khare AK (2013) Highly porous open cell Ti-foam using NaCl as

temporary space holder through powder metallurgy route. Mater Des 47: 810–819.

https://doi.org/10.1016/j.matdes.2013.01.005

21. Kitazono, K., Sato, E., Kuribayashi, K., 2003. Novel manufacturing process of closed-cell aluminum foam by accumulative

roll-bonding. Scripta Materialia 50, 495-498.

22. Laughlin, D., Hono, K., 2013. Porous Metals. Physical Metallurgy, 5th ed., Elsevier, Amsterdam.

23. Mahadev, Sreenivasa C. and Shivakumar K M, 2018: A Review on Production of Aluminium Metal Foams, IOP Conf. Series:

Materials Science and Engineering 376 (2018) 012081 doi:10.1088/1757-899X/376/1/012081

24. Michael F. Ashby & LU Tianjian, 2003: Metal foams: A survey; Vol. 46 No. 6 SCIENCE IN CHINA (Series B)

25. Miller, R.E., 2000. A continuum plasticity model of the constitutive and indentation behaviour of foamed metals. International

Journal of Mechanical Sciences, in press.

26. Mirzaali, M. J., F. Libonati, P. Vena, V. Mussi, L. Vergani, and M. Strano. "Investigation of the Effect of Internal Pores

Distribution on the Elastic Properties of Closed-Cell Aluminum Foam: A Comparison with Cancellous Bone." Procedia

Structural Integrity 2 (2016): 1285-1294.

27. Paknezhad, M., A. M. Rashidi, T. Yousefi, and Z. Saghir. "Effect of aluminum-foam heat sink on inclined hot surface

temperature in the case of free convection heat transfer." Case Studies in Thermal Engineering 10 (2017): 199-206.

28. Papantoniou, I., Kyriakopoulou, E., Pantelis, D., Athanasiou-Ioannou, A., Manolakos, D., 2018. Manufacturing process of

AA5083/nano-γAl2O3 localized composite metal foam fabricated by friction stir processing route (FSP) and microstructural

characterization. Journal of Materials Science 53, 3817-3835.

29. Subairu, Sikiru Olanrewaju. "A Critical Analysis of Component-Based Software Engineering." (2016). IASET: Journal of

Computer Science and Engineering (IASET: JCSE) ISSN(P): Applied; ISSN(E): Applied Vol. 1, Issue 2, Jul - Dec 2016; 19-24

30. .Dayanand, Lal N., Behnam Ghorbani, and Solmaz Vaghri. "A survey on the use of GNS3 for virtualizing computer networks."

(2016). International Journal of Computer Science and Engineering (IJCSE) ISSN(P): 2278-9960; ISSN(E): 2278-9979 Vol. 5,

Issue 1, Dec – Jan 2016, 49-58

31. Deepa, S., and R. Umarani. "Steganalysis on images based on the classification of image feature sets using SVM

classifier." International Journal of Computer Science and Engineering (IJCSE) 5.5 (2016): 15-24.

https://doi.org/10.1016/j.matdes.2013.01.005

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