Behaviour of Steel Fibre Reinforced Concrete Beam under Cyclic Loading

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IOSR Journal of Mechanical and Civil Engineering (IOSR
-
JMCE)

e
-
ISSN: 2278
-
1684
,p
-
ISSN: 2320
-
334X,

Volume
6
, Issue
3

(Ma
y
.
-

Jun
. 2013), PP 01
-
0
4

www.iosrjournals.org

www.iosrjournals.org
1

| Page


Behaviour of Steel Fibre Reinforced Concrete Beam under Cyclic
Loading


Sreeja . M.D

Department o
f
Civil Engineering

SRM University
,

Kattankulathur
,

Chennai.


Abstract
:

This paper describes the influence of steel fibre distribution on the ultimate
strength of concrete
beams. An experimental & analytical investigation of the behaviour of concrete beams reinforced with
conventional steel bars and steel fibres under cyclic loading is presented. It is now well established that one of
the important prope
rties of steel fibre reinforced concrete (SFRC) is its superior resistance to cracking and
crack propagation. As a result of this ability to arrest cracks, fibre composites possess increased extensibility
and tensile strength, both at first crack and at ul
timate load and the fibres are able to hold the matrix together
even after extensive cracking. The net result of all these is to impart to the fibre composite pronounced post


cracking ductility which is unheard of in ordinary concrete. The transformation

from a brittle to a ductile type
of material would increase substantially the energy absorption characteristics of the fibre composite and its
ability to withstand repeatedly applied, shock or impact loading.

Tests on conventionally reinforced concrete
be
am specimens, containing steel fibres in different proportions, have been conducted to establish load
-
deflection curves.

It was observed that SFRC beams showed enhanced properties compared to that of RC beams
with steel fibres. The experimental
investigations are validated with the analytical studies carried out by finite
element models using ANSYS.

Keywords:
Steel fiber, concrete, properties, crack, ductility, technology.


I.

Intr
oduction

SFRC is a composite material made of cements, water, fine and

coarse aggregate, and a dispersion of
discontinuous, small fibres. These short discrete fibres are uniformly distributed and randomly oriented.

They
are mixed with concrete before pouring. The reinforced concrete structures are subjected to cyclic loads during
dynamic loads such as earthquake shocks, traffic loads on the bridges, etc. It is well known that plain concrete is
brittle and weak under

flexural loads. To eliminate the disadvantages of plain concrete is added fibers into
concrete mix
. All admixtures meeting ASTM specifications for use in concrete are suitable for use in SFRC.
Steel fiber
-
reinforced concrete (SFRC) has gained increased po
pularity in construction industries in recent
years.

Properties of Concrete Improved by Steel Fibres
:



Flexural Strength
:

Flexural bending strength can be increased of up to 3 times more compared to
conventional concrete.



Fatigue Resistance
:

Almost 1 1/2 ti
mes increase in fatigue strength.



Impact Resistance
:

Greater resistance to damage in case of a heavy impact.



Permeability
:

The material is less porous.



Abrasion Resistance
:

More effective composition against abrasion and spalling.



Shrinkage
:

Shrinkage cracks can be eliminated.



Corrosion
:

Corrosion may affect the material but it will be limited in certain areas.


The different types of steel fibres which are available is shown in Fig 1.2



Fig 1.2
Types

of steel fibres

Behavio
ur Of Steel Fibre Reinforced Concrete Beam Under Cyclic Loading

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1.1

Objectives


The
objective of this study is to:



Investigate the mechanical properties like flexural strength, modulus of elastic
ity flexure beams and
cylinders.



Investigate ductility requirement , moment rotation capacity, energy absorption capacity for SFRC beams
under cy
clic loading using hybrid steel fibers of different volume fractions



Improve the resistance of conventionally reinforced structural members to cracking, deflection and other
serviceability conditions, by utilizing the inherent material properties of fiber
concrete.


1.2

Need for the
R
esearch

To improve:



Ductility.



Energy absorption.



Moment rotation capacity.



Structural strength.



Confinement characteristics.


1.3 Scope


The scope of work is to study the behaviour of steel fibre reinforced beams under
cyclic loading and
comparing the results both analytically (using ANSYS
-

a general purpose finite element
-
modelling package)
and experimentally. The parameters investigated are:



Midspan Deflection



Strain measurement



Location & type of crack occurrence


1.
4 Research significance


It is clearly seen from the literature that the behaviour of beam is affected by the properties of core
concrete. Ductility is desirable in reinforced concrete frames under seismic loading. Ductility is generally
achieved by providing closely spaced horizo
ntal ties, but this causes difficulties in placing concrete in densely
reinforced portions resulting in bad concreting. To avoid such closely spaced stirrups, confinement
characteristics of core concrete has to be improved, which increases the ductility of

the core concrete. In this
respect, steel fibre reinforced concrete (SFRC) which posses ductility, toughness and tensile strength more than
the plain conventional concrete can be considered to replace the plain concrete .It is expected that use of SFRC
c
an eliminate partially or fully the ties ,thus avoiding the congestion of reinforcement.


1.5 Summary of review of literature



It is clearly seen from the literature that the

behaviour of RC beam is affected by the properties of Steel
fibre reinforced core concrete.



Many investigators have established that inclusion of high strength, high elastic modulus steel fibres of
short length and small diameter improves the tensile st
rength and ductility of concrete significantly.



The combination of steel fibres and stirrups demonstrates a positive composite effect on the ultimate load,
ductility and failure pattern of concrete beam.



II.

Materials and Methods

2.1 Materials:


The materials used in the experimental work are tested for their properties and the details are
furnished. Raw materials listed below were used for preparation of the specimens:



Ordinary Portland Cement (OPC)



Coarse aggregate with 10 mm
maximum size



Fine aggregate



Steel Reinforcement:


High Yield for main bar (
12

mm
,10 mm
) and;


Mild steel for shear reinforcement (
8

mm)



Crimped and Hooked end steel fibres



Plywood with thickness 12 mm to prepared formwork.




Behavio
ur Of Steel Fibre Reinforced Concrete Beam Under Cyclic Loading

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2
.
1
.
1

Details of Fibres


Fibre used


Hooked end, Crimped with following aspect ratios and
diameters. The

properties of fibres are
given in Table
2
.4



s.no

F
ibre

A
spect
ratio
(l/d)

Length

(mm)

D
iameter

(mm)

1

Hook
End
-
1

80

60

0.75

2

Hook
End
-
2

65

35

0.55

3

Hook
End
-
3

45

50

1.11

4

Crimped

50

50

1

Table
2
.4 Properties of Fibres


III.

Mix Design


Considering the capacity of beam testing machine, the grade of the concrete is
M3
0. The mix design of
the M20 grade concrete as per IS:
10262
-
1982.


W
ater

cement

Fine
aggregate

Coarse
aggregate

214.24

465.7

506.52

1123.6

0.4
6

1

1.08

2.4
1


3.1 Design Of RC Beam


The RC Beam is designed based on the load carrying capacity of the testing Equipment. The limiting
load applied on the beam
from the equipment is considered as 250kN.. The dimensions and reinforcement
details for the beam are given below.
The detailing of the beam is done as normal detailing and ductile detailing.


L
-

1800 mm B
-

150 mm D
-

225 mm


3.1.1
Fibre
proportions in

RC Beam

s.no

Proportions

1

Control beam without fiber & normal
detailing as per IS456

2

Control beam without fiber & ductile
detailing as per IS13920

3

Crimped fibre with AR
-
50+
Hook
ed

End
fibre with AR
-
80

4

Hooked end fibre with AR
-
80+
Hook
ed

End
fibre with AR
-
45


IV.

Experimental set up



All beams after casting are cured for 28 days
prior

to testing.
Cyclic Load
ing

is the application of
incremental Push and Pull Load. The analysis is also known as Push
-
Pull analysis. The
loads are applied
incrementally
as positive and negative loads
.
Hydraulic jack and load cell
s
(10tonn
e
s
or

25 tonnes)

are placed
above and below the beam in order to attain the effect of cyclic
loading. Each

beam is tested for corresponding
load increment and finally the4 behaviour of beam is studied.


4.1 Analytical investigation



The study on the structural frame is basically a deflection controlled analysis; hence the analysis is
carried out by the ap
plication of lateral force. The
3
D model is analysed and the displacement results are
observed from cyclic loading

by
applying

each load increment both in positive direction and in negative
direction. Figure showing the reinforcement details in ansys is
shown below.

Behavio
ur Of Steel Fibre Reinforced Concrete Beam Under Cyclic Loading

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| Page

.


Fig.4.1.1
Reinforcement

details

in ANSYS


V.

Schedule of w
o
rk



Cylinders

are casted by using the various fibre configurations in order t
o

g
et the corresponding
modul
u
s

of
elasticity
. The same results are compared

analytically using ANSYS software.


VI.

Conclusion



The experimental values of the
strain and deflection

of steel fiber reinforced

concrete beams are
compared with that of the corresponding

estimated values of the
strain and deflection

of reinforced c
oncrete

beams
without
fiber. The comparison reveals that the strength

depends on the
presence of fibre

and it increases
with decrease in the spacing of

stirrups (increase in the percentage of web reinforcement).

The ultimate strength
of SFRC beams is
analytically obtained. The analytical results were

compared with the experimental results
.


Acknowledgement


I would like to thank
Mrs

K.GOMATHI
, Assistant Professor, Civil Engineering Department
,
SRM
University

for guiding me in writing this paper
.


References

[1].

S. Pant Avinash1, R. Suresh Parekar (2010) “Steel fiber reinforced concrete beams under combined torsion
-
bending
-
shear” Journal
of Civil Engineering (IEB) 38(1) 31
-
38

[2].

R.P. Dhakal and H.R. Song (2009) “Effect of bond on the behaviour of steel

fibre reinforced concrete beams” ICI Journal, Vol.
1,No.4

[3].

Mukesh Shukla

(2011)“
Behaviour of Reinforced Concrete Beams with Steel Fibres under Flexural Loading”

International Journal of
Earth Sciences and Engineering ISSN 0974
-
5904, Volume 04, No 06 SPL,
October, pp 843
-
846

[4].

Florian Finck(2010)

“Acoustic Emission analysis of SFRC Beams under cyclic bending loads”

Journal of Civil Engineering (IEB)
38(1) 21
-
28

[5].

Vengatachalapathy.V 1 , Ilangovan.R

(
2010

)“A Study on Steel Fibre Reinforced Concrete Deep Beams With and without Openings

International journal of civil and structural engineering, Volume 1, No. 3

[6].

Pant Avinash S, Parekar Suresh R(2009)

Steel Fiber Reinforced Concrete Beams Under Bending, Sh
ear And Torsion Without Web
Reinforcement” International Journal of Recent Trends in Engineering, Vol. 1, No. 6

[7].

I.J Sluys And R.De Borst (2010)“Computational modelling of impact test on steel fiber reinforced concrete beams” Journal of c
ivil
Engineering, V
ol. 2, No.4

[8].

Hai H. Dinh and James K. Wight(2009) “Shear behavior of steel fiber
-
reinforced concrete beams without stirrup reinforcement”
ISET Journal of Earthquake Technology, Technical Note, Vol. 44, No. 3
-
4

[9].

Hamid Pesaran Behbahani1, Behzad Nematollahi(20
11) “Flexural behaviour of steel
-
fibre
-
added
-
rc (sfrc) Beams with C30 and C50
classes of concrete” Engineering structures ,Science Direct 37

[10].

Gustavo J. Parra
-
Montesano’s(2010) “Shear
strength of beams with deformed s
teel fibres” International

journal

of

a
pplied

engineering

research,

Volume 1,

no1

IOSR Journal of Mechanical and Civil Engineering (IOSR
-
JMCE)

e
-
ISSN: 2278
-
1684
,p
-
ISSN: 2320
-
334X,

Volume
6
, Issue
3

(Ma
y
.
-

Jun
. 2013), PP
05
-
14

www.iosrjournals.org

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Influence

of the speed in advance and the laser’s power on the
zone affected thermically for steel C45



Sahbi Zantour
1
, Meher Gasbar
2
, Aleksandr Mikhaylov
3
, Hassen Kharroubi
2

1
(Department

electromechanical
,
Military Academy Fondek Jdid
/
Tunisia
)

2
(
A
gricultural Machinery
,
Superior School of Engineers of Rural Equipment Medjez El Bab
/ University
Jendouba
,
Tunisia
)

3
(
The Machine
-
Building Technology Department, Donetsk National Technical University
,
Ukraine)


Abstract
:

The

Laser cutting is a very importa
nt manufacturing technology. But this method has some
disadvantages, among which we find the emergence of a Thermically Affected Zone ZAT can dramatically alter
the characteristics of the processed material which affects its behaviour during its use. For t
his, we have tried in
this article to study the effect of the forward speed and the laser power in this area (thickness, hardening). In
this context, tests were made on steel C45 where we relied on the method of experiment plans to create a
mathematical mo
del Significant coefficients are obtained by carrying out a variance analysis ANOVA on the
level of 5% of significance. We find that the speed in advance and the power of the laser have a great effect on
the ZAT
.

Keywords:

Cutting, Laser CO2, Heat Affected

Zone.


I.

Introduction

The ZAT is obtained when the temperature of the sample of steel becomes higher or equal to the
specific temperature of the first structure of transformed metal. Steel is transformed into austenite.

During the
cooling, austenite undergo
es a phase shift of the solid state and is transformed into martensite. The sample
preserves the same chemical composition that austenite, but it changes of crystalline structure quadratic.
Martensite has a great tenacity for simple steels. The part of the

steel which undergoes this austenitic
transformation is called the ZAT (Thermically Affected Zone). The ZAT can be characterized by mechanical
micro hardness testing and optically by an optical microscope. These measurements are used to estimate the
width

of the ZAT in the morphology of the optimal cut. Neila
Jebbari al
. [1] have studied the ZAT metal C45
with the assistance of CO2 gas. Fig. 1 shows some examples of grooves with different machining conditions.
ZAT, characterized by whitish areas surroundin
g the grooves are clearly observable in the photos. The
morphology of the ZAT is quite repetitive in general. It is possible to note a reduction in width when going
towards the bottom of the groove. In Fig. 1 (a), irregularities on the edges of the groove
can be observed. This
can be attributed to the effect of feedback, which is created when the beam diameter is small impact. The effect
of the laser power can be observed in Fig. 1 (c) (P = 2500 W), wherein the depth of the groove is twice as large
as those

of FIG. 1 (a) and (b) (P = 1500 W). When the cutting speed is high, the groove depth and width of the
ZAT become weak due to the short time of laser
-
matter interaction (Fig. 1 (d)). Fig. 1 (b) is obtained in optimal
machining parameters, where a great reg
ularity in the form of the groove and of the TAZ can be noticed. ZZAT
widths of ZAT were measured at the top of the groove and the average values are displayed on the experimental
curves.



Fig.2 shows the evolution of the experimental value of the width o
f the
ZAT (Z
ZAT
)
depending on the
diameter D of laser impact.
(Z
ZAT
)

increases to a maximum at D = 0.17 mm, and thereafter, it decreases to a
limit value. This result confirms the possibility of using the interaction time (increasing with D) and the lase
r
power density (decreasing with D) to optimize machining.



Fig.1 Morphology of the ZAT


Influence of the speed in advance and the laser’s power on the zone affected thermical
ly for steel C45

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| Page

Fig. 3
(Z
ZAT
)
shows

that changes linearly with


and at the same time, it is

linear with
V
-
1

(Fig. 4). In general,
the width of the
ZAT

as a linear function of
x
V
-
1
, i
t can be written as follows:


Fig. 5 shows that


and


depends

on
the

diameter D and
the impact of the beam
. At the optimum value of the
diameter D of the laser impact (D = 0.17 mm) and from the fitted curves

of
Z
ZAT

(
Fig. 5),

it

can be deduced that

=
0.0012mm
0.75
(kg s)
-
0,25

and

= 0,027 mm.













Fig.2

Influence of the diameter of the

laser beam at the impact on
the width of the ZAT


Fig.4 Influence

of cutting speed on the width of the ZAT

Fig.3 Influence

of the power of the laser across the width of the ZAT

Influence of the speed in advance and the laser’s power on the zone affected thermical
ly for steel C45

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| Page



In the same context, there is more research on the HAZ made
by IA Choudhury and S. Shirley [2], these
experimental trials have st
udied three different types of thermoplastics polypropylene (PP), polycarbonate (PC)
and polymathy methacrylate (PMMA).

Davim et al. [3] reported in their research that the HAZ PC was between 0.1 and 0.3mm and that of PMMA was
between 0.05 and 0.25mm. Thus

the results of this research [2] is reasonably agree with those of Davim et al.
[3]

The size of the
ZAT

reflects the quality of laser cutting of polymeric materials.
The ZAT

data were used to
develop the model equations for the input parameters (cutting s
peed, laser power and air pressure).
These
equations are as follows:




These equations represent an overview of the extent of the HAZ and its dependence on the parameters of laser
treatment. The analysis of variance for all these
equations

has proved s
ufficient, at intervals of 95%. Ratios
lack
of adjustment to the pure error in all cases was

less than the F
-
statistic of 9.01.

From these equations, it is clear
that the ZAT is extended with the laser power and decreases with the cutting speed and air pre
ssure. The laser
power is the most important variable affecting the ZAT. More cutting speed, the lower the duration of
combustion and therefore smaller ZAT. Other tests that highlight the influence of the feed rate made
by J. Wang
and WCK. Wong [4] concl
uded that if the feed rate and low ZAT will be of considerable thickness, so to get a
good surface quality with minimal ZAT, it was necessary to increase the feed rate. This study is in agreement
with the total research done with L. Shanjin and W. Yang [5]
, which has the same tests but changing the type of
gas assistant using argon and compressed air.
(Fig.
11).

After
CO
2

laser cutting, a thermally affected zone ZAT
occurred is covered by a thin white layer [6], this area is under the influence directly by t
he laser power and Pu
feed speed Vf.


Experience:

The experiments were made
in the company LASER Industires in
Tunis;

the machine used is
TRUMATIC L3030 that has a capacity of 5000W maximum switching.

Was us
ed as the material of steel C45

The chemical co
mposition and mechanical properties are given in the tables (Tab 1 and Tab 2). The reason for
choosing this type of material is its frequent use in general industry which gives great importance to the
possibility of improving its cutting qualities. The cho
ice of cutting conditions was based on experience and
some preliminary tests.

Assistant gas pressure is 16 bar, the laser frequency is 20 000 Hz with a distance de1.2
mm from the nozzle. We chose three different speeds (560 mm / min, 1400 mm / min and 2240

mm / min) with
4 different power levels (3 kW, 3.5 kW, 4 kW and 5 kW), where 12 samples.




Fe %

S %

Mn %

C %

Si %

P %

Mo %

C 45

98

0.045

0.5

〮8

〮㐵


〮5

〮4

〮〴0

〮1




R ⡍灡)

Re ⡍灡)



䌠㐵

㜳7

㐱4



Each sample was 灡sse搠t桲o畧h a serie
s of 灲e灡ration be景re starting the analysis. Firstly, they were coate搬
an搠then

di搠the 灯lishi湧n then ma摥
chemical
attack;

it was 畳e搠for the ㌥ Nital which consists of ㌥3Nit物c
Aci搠an搠㤷┠Et桡nol.

Each sample was vis畡lize搠批 o灴ical microsco灥 to o灥rate the mo摩fication of the
Fi朮5 Infl略nce




and



over the wi摴栠of the
Z


Tab


Physical pro灥rties of
the 䌴5

Tab ㄺ Chemical 䍯m灯sition of the 䌴C

Influence of the speed in advance and the laser’s power on the zone affected thermical
ly for steel C45

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8

| Page

ZAT metal and to measure it. They were then passed through the SEM (scanni
ng electron microscope) in order
to visualize the white layer. Then, it was microhardness tests to know the evolution of the hardness in the ZAT.
After that, we measured the surface roughness with two different devices (3S Surface Scan for 2D profiles and
MICROMESURE 2 for 3D profiles).


II.

R
esult

and

discussion

:

2
-
1 Width of ZAT

The principle of laser cutting is greatly heated surface of the material to be cut until it melts and the
molten part will be removed with the assist gas. But on the other hand, it i
s absolutely necessary to find a game
that is warm to a temperature that could change its metallurgical and mechanical
characteristics;

this part is
called the heat affected zone (
ZAT
).

Found below (Table 3) the results obtained under extreme conditions wh
en measuring the width of the
ZAT

after an observation wi
th an optical microscope (Fig. 6
).



Num

Vf (mm/min)

Pu (W)

ZAT (µm)

1

560

3000

164,526

2

2240

3000

126,062

3

560

5000

231,638

4

2240

5000

143,017






III.

Modeling and Discussion

Pour cela on a
utilisé la
méthode statistique ANOVA avec niveau de confiance de 95%
et ont a trouvé
les résultats suivants (tab.
4
).

For better appreciate the effect of the feed rate Vf and the laser power Pu on the
thickness of the ZAT, and Vf, Pu and the distance from
the plane 0 (surface of the part) of the hardness of the
HAZ, modeling was done using the method of experimental design [7]. For this we used the statistical method
ANOVA with a confidence level of 95% and found the following results (Table 4).




Source
of variance

df

SS

MS

F
test


F
theoric

Vf

1

8075,340995

8075,341

372,7911

>

7,71

Pu

1

3533,602208

3533,60221

163,12568

>

7,71

Vf,Pu

1

1257,879052

1257,87905

58,068894

>

7,71

Err
or

4

86,6474

21,6618394





TOTAL

7

12953,4696






According to the ANOVA
table (Table 5) we can see that the calculated
F
test

feed speed Vf, the laser beam
power Pu and their interaction are higher
F
theoric
, where these three parameters affect the thickness of the HAZ
and we can not ignore any parameters.

The model calculation
gives the following result:


Tab.3:

Width of the ZAT as a function of cutting parameters

Fig. 6

M
icroscopique

picture of the
ZAT for

a cuts out
with surface

Vf = 560 mm/min
and

Pu = 5000 W

Tab.4:

Table ANOVA for the measurement thickness of the ZAT of C45

Influence of the speed in advance and the laser’s power on the zone affected thermical
ly for steel C45

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| Page

120
150
4800
3600
3000
2000
4800
4200
180
210
240
800
1200
1600
400
ZAT
Pu
Vf
Diagramme de surface de ZAT et Vf ; Pu
Tab.5:

Comparaison
between the exprimental resukt and the theorical resultsof the ZAT

N
u
m of test

Vf (mm/min)

Pu (W)

ZAT theorical
(µm)

ZAT exprimental
(µm)

Err
or

1

560

3000

164,526

164,526

0,00%

2

560

3500

182,41
9

185,85
5

1,88%

3

560

4000

199,48
4

201,738

1,13%

4

560

5000

231,638

231,638

0,00%

5

1400

3000

137,97
3

139,245

0,92%

6

1400

3500

146,5
30

141,039

3,75%

7

1400

4000

154,3
70

150,91
7

2,24%

8

1400

5000

168,41
8

168,655

0,14%

9

2240

3000

126,062

126,062

0,00%

10

224
0

3500

130,95
5

135,46
7

3,45%

11

2240

4000

135,34
7

141,751

4,73%

12

2240

5000

143,01
7

143,017

0,00%


According to the model found above, it can be concluded that the
ZAT

and proportional to
the laser beam power
(Pu) (fig.7
) and inversely proportional to
t
he feed rate (Vf) (fig.8
).










This conclusion can also be seen from the curve effects (Fig. 9), which we can conclude the iso curve response of the
thickness of the ZAT (Fig. 10).











Fig.7
:

Effetc of the power of the laser beam Pu on the thickness of the ZAT

Fig .
8
:

Effect of the speed in advance Vf on the thickness of the ZAT

Fig.9
:

Curve of the effect
s of the speed in advance and the power of the laser Pu
on the thickness of the ZAT

(mm/min)

(W)

(µm)

Influence of the speed in advance and the laser’s power on the zone affected thermical
ly for steel C45

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| Page

Pu (W)
V
f

(
m
m
/
m
i
n
)
5000
4500
4000
3500
3000
2200
2000
1800
1600
1400
1200
1000
800
600
>




<
140
140
160
160
180
180
200
200
220
220
ZAT (µm)
Contour Plot of ZAT (µm) vs Vf (mm/min); Pu (W)



I
-
2 Hard facing

The
Hardness is usually defin
ed as resistance of the material resiliently stressed. It is considered one of
the most important properties of metals, mainly because the hardness test is a very simple test to drive though
included some complicated phenomena such as plastic multiaxial be
havior.

In this study we focused only on the
hardness in the HAZ only. The microhardness measurements were performed with the measuring device:
Testwell.

Measurement type: Vickers hardness at a load of 50g.

Hold time (Duel time) = 10.





The penetration

is a straight pyramid with a square base and with an apex angle of 136 ° under a load F = 0.5 N.
Measuring the diagonal
"
d
"
of the footprint.

The test is performed at room
temperature;

the load is applied gradually and steadily until the selected force is

reached. The holding time of the load is 10 seconds.

The impression obtained has a shape of a p
yramid with a square base (Fig.11
).

A light spot appears on an observation screen of square shape (base of the pyramid).

It takes the average of the two diagona
ls of the impression: d, and calculates the Vickers hardness (HV50) in the
form:


Found below (Table 6) the results obtained under extreme conditions during the hardness measurement made
with the device of micro hardness.



Num

Vf (mm/min)

Pu (W)

D (µm
)

Hardness (VH)

1

560

3000

10

204

2

2240

3000

10

197

3

560

5000

10

231

4

2240

5000

10

218

5

560

3000

510

187

6

2240

3000

510

175

7

560

5000

510

203

8

2240

5000

510

189

Fig.10
:

C
urve

iso
answer thickness of the
ZAT


Fig.11

:
Hardness

Test
.


Tab.6:

Measurements of hardness according to the parameters of cut and surface’s depth

Influence of the speed in advance and the laser’s power on the zone affected thermical
ly for steel C45

www.iosrjournals.org
11

| Page





Modeling
and discussion:

For

better appreciate the effect of the feed rat
e Vf and the laser power Pu on the thickness of the
ZAT
,
and Vf, Pu and the distance from the plane 0 (surface part) of the hardness of the
ZAT
, modeling was done
using the method of experimental design [7].

For this we used the statistical method ANOVA wi
th a confidence
level of 95% and found the following results (Table 4).


Tab.7:

ANOVA

Table

(
Hardness

of

C45

steel
)

Source of
variance

df

SS

MS

F
test

F
th
eorical

Vf

1

1088,297858

1088,29786

2,0749306

5,32

Pu

1

3092,596658

3092,59666

5,8962934

5,32

D

1

45
50,58

4550,58

8,6760602

5,32

Vf, Pu

1

24,808968

24,808968

0,0473004

5,32

Vf, D

1

10,829858

10,829858

0,020648

5,32

Pu, D

1

150,580658

150,580658

0,2870946

5,32

Vf, Pu, D

1

12,280968

12,280968

0,0234147

5,32

Erro
r

8

4195,9875

524,498436





TOTAL

7

13
125,96245







The ANOVA table and the Fisher test shows that a significant level of 5%.

F
calculated

for Pu and D are higher
F
theorical

so they are meaningful answer. But
F
calculated

of Vf is less than
F
theorical

but it is not negligible, so Vf is
quite
significant influence on the response. On all interactions,
F
calculated

shows that they can be ignored and do
not affect the response. The model calculation gives the following result:




Tab.8: Comparaison between exprimental results and theor
ical results of hardness


Num of test

Vf (mm/min)

Pu (W)

D (µm)

Theorical
hardness
(
VH
)

Exprimental
hardness (VH)

Erro
r

1

560

3000

10

209,888

204

3%

2

560

3500

10

215,4493

214,5

0%

3

560

4000

10

220,3856

223,5

1%

4

560

5000

10

228,8884

231

1%

5

1400

30
00

10

200,6489

205,2

2%

6

1400

3500

10

205,9653

210

2%

7

1400

4000

10

210,6843

220,65

5%

8

1400

5000

10

218,8128

225,45

3%

9

2240

3000

10

196,0687

196,5

0%

10

2240

3500

10

201,2638

204

1%

11

2240

4000

10

205,8751

211,11

3%

12

2240

5000

10

213,818

21
7,5

2%

Fig.12
:

P
rint of the Micro hardness of the various zone Constituting the
termically affected zone.

Influence of the speed in advance and the laser’s power on the zone affected thermical
ly for steel C45

www.iosrjournals.org
12

| Page

1

560

3000

210

191,8503

197,25

3%

2

560

3500

210

196,9336

202,5

3%

3

560

4000

210

201,4457

207

3%

4

560

5000

210

209,2178

207,45

1%

5

1400

3000

210

183,4052

191,05

4%

6

1400

3500

210

188,2647

196,5

4%

7

1400

4000

210

192,5782

202,5

5%

8

1400

5000

210

200,0081

209,7

5%

9

2240

3000

210

179,2186

178,95

0%

10

2240

3500

210

183,9672

187,5

2%

11

2240

4000

210

188,1822

191,22

2%

12

2240

5000

210

195,4426

192

2%

1

560

3000

110

195,547

200,7

3%

2

560

3500

110

200,7282

211,5

5%

3

560

4000

110

20
5,3273

217,5

6%

4

560

5000

110

213,2491

226,5

6%

5

1400

3000

110

186,9391

192,22

2%

6

1400

3500

110

191,8923

202,5

6%

7

1400

4000

110

196,2889

208,95

6%

8

1400

5000

110

203,862

207,95

2%

9

2240

3000

110

182,6718

187,5

3%

10

2240

3500

110

187,512

195

4%

11

2240

4000

110

191,8082

191,65

0%

12

2240

5000

110

199,2084

202,95

2%


According to the model found above, it can be concluded that the HAZ and proportional to the laser beam
power (Pu) and inversely proportional to the feed rate (Vf) and the dept
h from the surface (D)

(Fig.13
).

This
conclusion can be

seen from curve effects (Fig. 14
), where one can conclude Iso curve responses har
dness
(fig.15, fig.16, fig.17
).




MB

Fig.13
:

Evolution
of the hardness of the
steel C45

according to the
depth D


Influence of the speed in advance and the laser’s power on the zone affected thermical
ly for steel C45

www.iosrjournals.org
13

| Page

2240
560
210
205
200
195
190
5000
3000
510
10
210
205
200
195
190
Vf
M
e
a
n
Pu
P
Main Effects Plot for Dureté
Data Means




Pu (W)
V
f

(
m
m
/
m
i
n
)
5000
4500
4000
3500
3000
2200
2000
1800
1600
1400
1200
1000
800
600
>






<
200
200
205
205
210
210
215
215
220
220
225
225
230
230
(VH)
Dureté
Contour Plot of Dureté (VH) vs Vf (mm/min); Pu (W)




D (µm)
V
f

(
m
m
/
m
i
n
)
500
400
300
200
100
2200
2000
1800
1600
1400
1200
1000
800
600
>





<
175
175
180
180
185
185
190
190
195
195
200
200
(VH)
Dureté
Contour Plot of Dureté (VH) vs Vf (mm/min); D (µm)




D (µm)
P
u

(
W
)
500
400
300
200
100
5000
4500
4000
3500
3000
>




<
190
190
200
200
210
210
220
220
230
230
(VH)
Dureté
Contour Plot of Dureté (VH) vs Pu (W); D (µm)





Fig.14
:

Effects of the speed in advance Vf and the power of the laser Pu and the
de
pth D on hardness of C45

Fig.15
:

Iso response curve
hardness according

to the speed in
advance Vf

and the
power of the laser
beam Pu

(D = 10µm)


Fig.17
:

Iso response curve as a function of the hardness feedrate Vf and the depth
from the surface D (Pu = 3000 W)

Fig.16
:

Iso response curve hardness versus the depth from the surface D and the laser
beam power Pu (Vf = 560

mm / min)

Influence of the speed in advance and the laser’s power on the zone affected thermical
ly for steel C45

www.iosrjournals.org
14

| Page

IV.

Conclusion:

After CO2 laser cutting of steel C45, there

is a
ZAT

heat that appears undergoing metallurgical and
physical changes important this area is under the influence directly:




The

speed in advance
:

-

Is proportional to the thickness of the
ZAT
.

-

Is inversely proportional to the hardness of the
ZAT
.




The
Laser
’s power

-

-

It is proportional to the thickness of the
ZAT
.

-

-

It is proportional to the hardness of the
ZAT
.


Bibliographic reference:

[1]

Neila Jebbari, Mohamed Mondher Jebari, Faycal Saadallah, Annie Tarrats
-
Saugnac, Raouf Bennaceur, Jean Paul L
onguemard
(2007).
"Thermal affected zone obtained in machining steel XC42 by high
-
power continuous CO
2

laser".
Optics and Laser
Technology 40 (2008) 864
-
873.

[2]

I.A. Choudhury, S. Shirley (2009). "Laser cutting of polymeric materials: An experimental in
vestigation".
Optics and Laser
Technology 42 (2010) 503
-
508.

[3]

Davim JP, Barricas N, Conceição M, Oliveira C. "Some experimental studies on CO
2

laser cutting quality of polymeric materials".
Journal of Materials Processing Technology 2008; 198 (1
-
3):99
-
104.

[4]


J. Wang, W.C.K. Wong. “CO
2

laser cutting of metallic coated sheet steels”.
Journal of Materials Processing Technology 95 (1999)
164
-
168.

[5]


Lv. Shanjin, Wang Yang. “An investigation of pulsed laser cutting of titanium alloy sheet”.
Optics and L
aser in Engineering 44
(2006) 1067
-
1077.

[6]

B. Tirumala Rao, Rakesh Kaul, Pragya Tiwari, A.K. Nath. “Inert gas cutting of titanium sheet with pilsed mode CO
2

laser”.
Optics
and Laser in Engineering 43 (2005) 1330
-
1348.

[7]


Sivarao, T.J.S. Anand, Ammar,
Shukor. “RSM Based Modeling for Surface Roughness Prediction in Laser Machining”.
Inetrnational Journal of Engineering & Technology IJET
-
IJENS Vol: 10 No 04.

IOSR Journal of Mechanical and Civil Engineering (IOSR
-
JMCE)

e
-
ISSN: 2278
-
1684
,p
-
ISSN: 2320
-
334X,

Volume
6
, Issue
3

(Ma
y
.
-

Jun
. 2013), PP
1
5
-
2
4

www.iosrjournals.org

www.iosrjournals.org


15

| Page


Review on Design Optimization of Liquid Carrier Tanker for
Reduction of Sloshing Effects



1
Sunil M Mahajan
,

2
Ashwin D Patil,

3
V. N. Bartaria

(Asst.Professor, SITRC Sandip Foundation

)

(PG

Student of

SRES
-
COE, Kopergaon
)

(
Professor &

HOD, Mechanical Eng
ineering, LNCT, Bhopal)




Abstract
:
This Paper Reviews Briefly The Current Research On Sloshing And Its Effect In Liquid Carrier
Tanker. The Aim Of This Paper To Study The Basics Of Sloshing And Its Prevention (Mainly In Liquid Carrier
Tanker)

The Liquid

Sloshing Is Free Surface Fluctuation Of Liquid When Its Container Is Excited By External
Vibrations Such As Earthquakes. The Liquid Sloshing May Cause Various Engineering Problem, For Example
Instability Of Ships In Aero Engineering And Ocean Engineering,

Failures On Structural Systems Of The
Liquid Container. The Tanker Used For The Transportation Of Liquid Over The Road
-
Ways Is An Integral
Part Of The Carrier/Vehicle. The Tanker Is Expected To Withstand The Unbalanced Forces On Account Of
Transit Over Un
even And Irregular Surfaces/Contours Of The Road As Also Due To Sudden Acceleration Or
Deceleration (Due To Application Of Brakes).

Keywords
-
Sloshing, Impact, Baffle, Simulation



I.

I
NTRODUCTION

Sloshing can be defined as dynamic load acting over a tank stru
cture as a result of the motion of a
fluid with free surface confined inside the tank. Liquid sloshing is a kind of wave motion inside a partially
filled tank. The sloshing phenomenon is of great practical importance to the safety of the liquid transport.
Under external excitations, with large amplitude or near the natural frequency of sloshing, the liquid inside a
partially filled tank is in violent oscillations. In this

paper

we will see the background behind the sloshing
phenomena to define the problem i
n proper manner. Also we will see the research work carried related to this
problem, proposed methodology to go for solution and scope of work.

The tanker used for the transportation of liquid over the road
-
ways is an integral part of the Carrier/
Vehicle.

The tanker is expected to withstand the unbalanced forces on account of the transit over uneven and
irregular surfaces/ contours of the road as also due to sudden acceleration or deceleration (due to application of
brakes). As a result, `sloshing’ of the
liquid is experienced within the tanker. Different aspects of analyses are
necessary to design the tanker but sloshing analysis is also one of the prominent aspects for reducing its
detrimental effects over structure of tanker.

Sloshing can be the result o
f external forces due to
acceleration/deceleration of the containment body. Of particular concern is the pressure distribution on the wall

of the container reservoir and its local temporal peaks that can reach as in road tankers twice the rigid load
value.

In road tankers, the free liquid surface may experience large excursions for even very small motions of
the container leading to stability problems. Analysis of the sloshing motion of a contained liquid is of great
practical importance. Motion of a fluid
can persist beyond application of a direct load to the container; the
inertial load exerted by the fluid is time
-
dependent and can be greater than the load exerted by a solid of the
same mass. This makes analysis of sloshing especially important for transp
ortation and storage tanks. Due to
its dynamic nature, sloshing can strongly affect performance and behavior of transportation vehicles, especially
tankers filled with oil. In fact, a significant amount of research has gone into developing numerical models

for
predicting fluid behavior under various loads.

Hence liquid sloshing is a practical problem with regard to the safety of transportation

systems, such
as oil tankers on highways, liquid tank cars on railroads, oceangoing vessels with liquid cargo, prop
ellant tank
used in satellites and other spacecraft vehicles, and several others


II.

L
ITERATURE
R
EVIEW

Many researchers are studying the sloshing phenomena since 1950 for transportation of fluids as well
as gases for better national communication. Here, in th
is chapter we reviewed some literature regarding

sloshing and analyzing method.

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Donald Liu
[
1
]

has reported that t
he normal practice is to base the tanker's design on engineering analysis, and
to use rule equations only as a check, for guidance and control.

The potential benefit from utilizing
engineering analysis is stress verification and rational distribution of steel, which results in steel weight
optimization without sacrificing strength. Also it has been suggested the different types of engineering ana
lysis
required to design the tanker which are mentioned as below:



Ship Moment: The first step in the analysis consists of calculating the hull girder longitudinal vertical
bending moment, for all anticipated loaded and ballast conditions.



Ship Motion:

The
next step in the analysis is to calculate the vertical, lateral and torsional dynamic
components of the hull girder bending moments, as well as the motions, point accelerations and pressure
distribution along the vessel's length.



3
-
D Global 3
-
D Finite Elem
ent Analysis (FEM): The data obtained from ship moment and ship motion
above are used to carry out a three
-
dimensional global FEM analysis for the entire vessel, or for a portion
of the hull girder. This analysis gives the overall structural response in th
e form of element stresses and
displacements.



Sloshing Analysis: This analysis is used to determine the dynamic loads on the tank boundaries from the
motion of the fluid within the tank due to ship movements in a seaway.



Thermal Stress Analysis: This analy
sis provides the distortions and stresses in the hull structure induced
by non
-
linear temperature differentials in vessels carrying hot cargoes.



Fatigue and Fracture Mechanic Analysis: Based on the combined effect of loading, material properties and
flaw c
haracteristics, this analysis predict the service life of the structure, and determine the most effective
inspection plan.



Vibration Analysis: This analysis is used to determine the extent of vibrations in the ship structure induced
by the interaction of f
luids, structure, machinery and propellers.


Jean Ma and Mohammad Usman Jean

[
2
]

presented that, the sloshing phenomenon in partially filled fuel tanks
is more pronounced when vehicle experience a sudden start or stop. Sloshing is undesired because it prod
uces
noise, high impact force on the tank walls and the challenge of low fuel handling. Today the solution for
containing sloshing is to incorporate baffles inside the tank. The presence of baffles dissipates the energy that
is induced by the fuel motions.

Design of baffles is necessary step during the design of a fuel tank to meet
required perform
ance specification in service.

After literature review it can be seen that, this problem is having FSI nature so the
modeling

and
analyzing method should be susc
eptible to adopt such nature of problem. Here, in this chapter we will see
different approaches to solve FSI problem along with explanation about FEA code useful for analysis.


Approaches to solve FSI problem:

This type of problem can be modeled in basic f
our approaches which are used for fluid structure
interaction problem

a.

Lagrangian approach

b.

Euler approach


Lagrangian approach

Lagrangian formulation is usually used for describing a solid mechanics problem. The problem is
described with a high number of ma
ss particles, where the motion of every single particle is being observed in
space and time. The problem is exactly defined when the motion of all the particles is known. The Lagrangian
formulation is very simple and easy to use for one or only a few mass
particles. However, the method becomes
very complicated and complex for description of high number of mass particles.
(Fig.1)

In the Eulerian formulation the problem is being observed at one point in space which does not follow
the motion of the single par
ticle. In one time step
t

several mass particles may pass the observed point. Their
motion is exactly determined in the moment of passing through that point. In the observed point the field
variables are time dependent.

(Fig.
2)

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Fig.

1
Langrangian Formula
tion


Fig.

2
Eulerian Formulation

The basic difference between the Lagrangian and the Eulerian formulation is that at the Lagrangian
formulation the magnitudes
x
,

y
and
z
are variable coordinates of a moving particle. At the Eulerian
formulation those coo
rdinates represent steady coordinates of the defined field point

A Lagrangian mesh should be used to model structural parts of a problem.

In the Lagrangian
formulation one finite element represents the same part of the material throughout the course of the

analysis.
The fluid domain can be described with a material model which skips the calculation of deviatoric stresses. By
defining a low bulk modulus for fluids such as water, the elastic shear forces become negligible, and by using a
low yield stress, fas
t tran

sition to plasticity can be achieved (e.g. by only considering the gravitation). Under
high dynamic loading, the shear forces and any unreal introduced forces become negligible in comparison to
the inerti
al forces of the fluid. (Fig.3
) illustrates t
he solution process of a simple fluid problem using the
Lagrangian formulation. It is presumed that the loading influences only the central node. The result of the
loading is the shift of that node in a computational time step. If the influence of the load
ing does not stop or
change, the node takes a new position in the next time step and the mesh deforms even more, since the
mesh
follows the material flow.



Fig. 3

Mesh Deformation in Langrangian Formulation


Eulerian
Approach
:

It is also possible to appl
y the Eulerian formulation for fluid flow analyses, where the fluid flow
through the fixed mesh in a space is observed. The material point moves from one finite element to another
and the finite element mesh does not move or deform. Although the Eulerian m
esh in appears not to move or
deform during the analysis, it does actually change its position and form only within the single time step. The
reason for this is the use of Lagrangian formulation in single time steps, which is much more advanced in. The
Eul
erian mesh is treated in a special way (Fig.3.4). To illustrate the use of an Eulerian mesh the same example
is used as in the previous chapter. Because of the central node loading, the observed node changes its position
during one computational time step
(mesh deforms). After the time step the analysis stops and the following
two approximations are performed:

-

Mesh smoothing: all the nodes of the Eulerian
mesh that have been displaced due to loading

are, moved to
their original position;

-

Advection: the
internal variables (stresses, flow fields, velocity field) for all the nodes that have been moved
are recomputed (interpolated) so that they have the same spatial distribution as before the mesh smoothing. In
this way the mesh smoothing does not affect the

internal variable distribution.

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The described
procedure is being repeated for each time step of the analysis and provides the analyst with a
non
-
movable and undeforms able
Eulerian mesh.



Fig.
4 Mesh Deformation in

Eulerian Formulation



Fig.
5

Aligning

Euler and Langrangian Elements



Fig.
6

Tanker Mesh


Fig.
7

Meshing of LPG in Unbaffled Tank


Fig.
8

Meshing of LPG Tank w
ith Full Enclosed Baffle at the


Fig.
9

Meshing of LPG Tank with Two Modified

Baffles


Fig.
10

Eulerian and Langrangian Meshing of LP
G in a

Tank with Modified Baffles



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Simulation of sloshing:

Simulation results are involving different iterations in

that first iteration is Sloshing of LPG without
baffle.

After taking possible iterations graphs are plotted to show the pressure and veloci
ty developed during
respective condition of sloshing
.

Simulation results are involving different iterations in that first iteration is Sloshing of LPG without
baffle which includes various stages of sloshing simulation at start which shown in Fig.
11

and Fi
g.
12

respectively. Similarly, disturbance in fluid is clearly shown in Fig.
13

and Fig.
14

Fig.
15

to Fig.
19
shows the
gradually increasing of LPG sloshing amplitude with enclosed full baffle inserted in a tanker. Similarly, Fig.
20

to Fig.
24

shows the simulat
ion of LPG sloshing with one modified baffle at the
center

of tank with various
views. Then, simulation result of LPG sloshing with two modified baffles is given in Fig.
25

to Fig.
29

with
various stages of sloshing phenomena.



Fig.
11

Iteration 1 Sloshing
of LPG without Baffle



Fig.
12

Iteration 1 Sloshing of LPG without Baffle in Front View



Fig.
13

Iteration 1 Sloshing of LPG without Baffle showing Side View



Fig.
14

Iteration 1: Sloshing of LPG without Baffle showing Disturbance of Fluid


Fig.
15

Iter
ation 2: Sloshing of LPG in a Tank with Enclosed Full Baffle


Fig.
16

Iteration 2: Sloshing of LPG in a Tank with Enclosed Full Baffle at Initial Stage

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Fig.
17

Iteration 2: Sloshing of LPG in a tank with enclosed full baffle at final stage



Fig.
18

Itera
tion 2: Sloshing of LPG in a tank with enclose
d full baffle showing side view



Fig.
19

Iteration 2: Sloshing of LPG in a tank with enclosed full baffle showing disturbance



Fig.
20

Iteration 3: Sloshing of LPG in a tank with one modified baffle



Fig.
21

Iteration 3: Sloshing of LPG in a tank with one modified baffle showing lift of fluid along baffle



Fig.
22

Iteration 3: Sloshing of LPG in a tank with one modified baffle showing peak amplitude



Fig.
23

Iteration 3: Sloshing of LPG in a tank with one m
odified baffle with side view

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Fig.
24

Iteration 3: Sloshing of LPG in a tank with one modified baffle showing disturbance of fluid in side view



Fig.
25

Iteration 4: Sloshing of LPG in a tank with two modified baffle



Fig.
26

Iteration 4: Sloshing of LP
G in a tank with two modified baffle showing lift of fluid along baffle



Fig.
27

Iteration 4: Sloshing of LPG in a tank with two modified baffle showing peak amplitude of fluid



Fig
.28

Iteration 4: Sloshing of LPG in a tank with two modified baffle in s
ide view



Fig.
29

Iteration 4: Sloshing of LPG in a tank with two modified baffle showing disturbance of fluid


Graphs:

After taking possible iterations graphs are plotted to show the pressure and velocity developed during
respective condition of sloshing

Revie
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Fig.
30
Sloshing of LPG without baffle


Fig.
31

Sloshing of LPG in a tank with one modified baffle


Fig.
32
Sloshing of LPG in a tank with two modified baffle


Fig.
33

Sloshing of LPG without baffle



Fig.
34

Sloshing of LPG in
a tank with one modified ba
ffle


Fig.
35

Sloshing of LPG in
a tank with two modified baffle

Revie
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Fig.
36

Sloshing of LPG in a tank with two modified baffle



Fig.
37

Comparison of LPG sloshing without baffle and with enclosed full baffle


Fig.
38

Comparison of LPG sloshing with one modi
fied baffle and two modified baffles


Fig.
39

Comparison of velocity variations of four iterations


Findings:

From the simulation result of
every iteration it can be found that, sloshing is reduced in considerable amount
with the help of two modified baffl
es located at 2500 mm apart from each other. Also the maximum pressure
generated in various iterations due to s
loshing of fluid is as follows:


Table.
1 Maximum pressure generated in various cases

Iteration
No.

Case Name

Time in
(
sec
)

Pressure in
(
N/m
2
)

1

LPG sloshing without
baffle

0.00189

2.58 x 10
9

2

LPG sloshing with enclosed

full baffle

0.00200

1.17 x 10
9

3

LPG sloshing with one

modified baffle

0.0020

9.88 x 10
6

4

LPG sloshing with two

modified baffles

0.0050

2.87 x 10
6

Revie
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Similarly the maximum veloci
ty developed in various iterations because of s
loshing of fluid is as follows:


Table.
2 Maximum velocity developed in various cases

Iteration
No.

Case Name

Time in
sec.

Velocity in
m/s

1

LPG sloshing
without baffle

0.049

62.13

2

LPG sloshing with
enclose
d

full baffle

0.045

53.48

3

LPG sloshing with
one

modified baffle

0.0475

43.85

4

LPG sloshing with
two

modified baffles

0.058

35.8



Therefore, from Table 1 and
2 we can say that, more time is required to generate maximum pressure and
velocity in the c
ase of two modified baffles compared to other cases. Also the maximum stress developed in
modified baffle having 20 mm thickness is 2.20 x 10
8

Pa which is lower than the yield strength of baffle
material (ASTM A576). Similarly, stress on wall of tanker is
2.05 x 10
8

Pa lower than yield strength o
f tanker
material (AISI 1040).


III.

C
ONCLUSION

Analysis of cylindrical liquid carrier tanker is carried out using the finite element method. Studies of
various methods in FEA are done and one particular method is selec
ted to model fluid
-
structure interaction
problem. These interaction problems are quite complex and they have been challenging as well.

Using MSc
-
Dytran software defined problem has been modelled which uses Arbitrary Langrangian
Eulerian method (ALE). Eleme
nts depicting the properties of the tanker and the liquid are selected and
coupled. Water is selected first to see the nature of sloshing and to get the maximum pressure. Then iterations
are taken for real liquid in the problem i.e.
Liquefied

Petroleum Gas

(LPG). Analysis is done to obtain sloshing
patterns, pressure and velocity parameters in different cases. From the results that obtained in analysis
fol
lowing conclusions can be drawn

We can accept the challenge for transportation of liquid in partially f
illed tankers by using baffles in
proper shape, numbers and location. In this problem sloshing of LPG is reduced in half filled cylindrical tanker

at the speed of 40kmph by using two modified baffles. Also effect of sloshing over tanker and baffles are
dec
reased with proper thickness. The pressure and velocity developed in two baffled condition is lower than
unbaffled, one baffled and enclosed baffled condition. So it is recommended to use two modified baffles,
2500mm apart from each other with thickness 20

mm which can decrease the sloshing considerably an
d
sustain the sloshing pressure

R
EFERENCES

[1].

Donald Liu “Tanker Spills Prevention By Design”

National academic

Press,

Publication Year1991

ISBN
-
10: 0
-
309
-
04377
-
8
,pp.208 to
213

[2].

Jean Ma and Mohammad Usman Jea
n

“Modeling of Fuel Sloshing Phenomenon Considering Solid
-
Fluid Interaction” 8
TH

International LS
-
DYNA Users Conference Fluid/Structure

[3].

Ranjit Babar and V.Katkar “Simulation of Fuel Tank Slosh Test
-
Coupled Eulerian
-
Langrangian Approach” Tata Technologies,
TATA
motors Ltd. Pimpri, Pune

[4].

Kim

Hyun
-
Soo and Lee

Young
-
Shin “Optimization design technique for reduction of sloshing by evolutionary methods” Journal of
Mec
hanical Science and Technology
,Number1/January 2008
,Vol.22


[5].

Jang
-
Ryong Shin and Kyungsik Choi and
Sin
-
Young Kang “An Analytical Solution to Sloshing Natural Periods for a Prismatic Liquid
Cargo Tank with Baffles” Proceeding of Sixteenth International Offshore and Polar Engineering Conference, California, USA, Ma
y 28
-
June 2, 2006



.



IOSR Journal of Mechanical and Civil E
ngineering (IOSR
-
JMCE)

e
-
ISSN: 2278
-
1684,p
-
ISSN: 2320
-
334X,

Volume 6, Issue 3 (May.
-

Jun. 2013), PP
2
5
-
36

www.iosrjournals.org

www.iosrjournals.org


25

| Page


D
etermination of
Mechanical Properties of Different Materials
Using
Inverse Finite Element Procedure for the
Miniature
Specimen

Test

Simulation


Dr. V Chitti Babu, Mr. Bade Venkata

Suresh, Sri P. Govinda Rao,

Associate Professor,
Department Of Mechanical Engineering

Gmrit, Rajam, Srikakulam,Ap

Pg Student,
Department Of Mechanical Engineering

Associate Professor,Department of Mechanical Engineering

GMRIT, RAJAM,

Srikakulam,AP


Abstract
:

Determination of mechanical properties of operating components is a key element in defining the
strategies for maintenance and repair for extending component life. The assessment of the present health has to
be done without disturbing the struct
ural integrity and functional capabilities of the plant components. To
achieve this, a miniature specimen can be extracted from an in
-
service component and its properties can be
evaluated. This helps in avoiding the removal of large size samples from the

in
-
service component for the
evaluation of current material properties. The miniature specimen also has an advantage in finite element
modelling

with respect to computational time and memory

space.


An inverse finite element simulation has also been carr
ied out on t
he miniature specimens of different
varieties of steels
.

Inverse finite element simulated load
-
displacement curve has been compared with

the
experimental results taken from the literature. Properties of different varieties of steels are obtaine
d when a
perfect match is found between inverse FE and experimental results.
Inverse finite element simulation
procedure helps in finding the constitutive
behaviour

of the unknown material in combination with experimental
output of miniature test.

The ap
proach seems to have potential to predict the mechanical properties of the in
-
service components.

Keywords


Modelling, FEM
,
Miniature Specimen



I.

Introduction

Miniature specimen test techniques enable the characterization of mechanical properties using
extremely small volume of the material. Though they have their origin in materials development programmes in
industries. The miniature specimen test techniques fi
nd very promising applications in the field of remaining life
assessment, failure analysis, properties of weld
ments,

coatings

etc.
Determination of mechanical properties of
operating components is a key element in defining the strategies for maintenance an
d repair for extending
component life. The assessment of the present health has to be done without disturbing the structural integrity
and functional capabilities of the plant components.
To achieve this, a miniature specimen can be extracted from
an in
-
se
rvice component and its properties can be evaluated.

This helps in avoiding the removal of large size
samples from the in
-
service component for the evaluation of current material properties. The miniature
specimen also has an advantage in finite element
modeling with respect to computational time and me
mory
space.


II.

A
NALYSIS
O
F
M
INIATURE
S
PECIMEN
T
EST

1.1 Materials:

To study the effectiveness of the miniature specimen test simulation in getting the material properties
from miniature specimens, five
different materials have been selected. All these five materials show a broad
range in their mechanical behaviour. A brief description of the selected materials is given below:

ALUMINIUM ALLOY (AR66)

This is one of the aluminium alloys. Zinc is the princip
al alloying element in this group. When it is combined
with smaller percentages of magnesium and, in some cases copper, it results in heat
-
treatable alloys of very high
strength. This alloy is used in aerospace applications, automobile industries, railways
, shipping industry etc. and
in many other engineering applications.

DIE STEEL (D3)

This is high carbon chromium steel with 2% Carbon, 12% Chromium, 0.3% Manganese and 0.3% Silicon. This
type of steel has high dimensional stability with added wear resistan
ce

coupled with excellent edge holding qualities which are commonly applied in thread rolling dies, cold extrusion
tools and dies, draw plates and dies, cutters, measuring tools, pressure casting moulds, blanking tools, reamer,
finishing rolls for tyre m
ills and also for many applications in mechanical engineering.

Determination of Mechanical Properties of Different Materials Using
Inverse Finite Element

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26

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CHROMIUM HOT WORK STEEL (H11)

This is a low alloy steel with Manganese (0.4%), Silicon (1%), Chromium (5%) and Molybdenum (1.1%). It has
very good high temperature characteristics and excellent

toughness combined with receptivity to heat checking,
which is commonly used for extrusion dies, gripper dies, rams, drop forging dies, pressure casting moulds for
light alloys, metal track pressure tools, high stressed internal boxes, little tube pressin
g mandrels for water
-
cooling, die
-
casting tools etc. which are employed in many components and structures for various industries.


LOW CARBON STEEL (LC)

In this steel Carbon 0.19%, Manganese 0.44% and Silicon 0.14% are present. Other elements are
Copper, N
ickel, Chromium and Molybdenum etc. and their weight percentages are presented in Table. This steel
is highly versatile and useful. It can be machined and worked into complex shapes, has low cost and good
mechanical properties. It is widely used in automot
ive industries and in other areas where formability and
stiffness are sought.

MEDIUM CARBON STEEL (MC)

In this steel carbon .35%, manganese 0.68% and silicon 0.15% are present. This type of steel has high wear
resistance and can be used for components whic
h are subjected to severe abrasion, wear or high surface loading.
This steel is preferred for heat treated components having large sections and subjected to exacting requirements.


Table 1.1

Uniaxial properties of the above materials:

















III.

Finite Element Simulation Of Miniature Specimen Test

ABAQUS/CAE 6.12
-
2
Student Edition has

been used for the finite element modeling of the given problem.
The shell ty
pe finite element model has been created where in

a circular dumb
-
bell shaped miniature
specimen
with two circular pins

are

taken to model

the miniature specimen test

simulation
.


3
.1 Geometric m
odeling:

The test spe
cimen has been

modeled with 2
-
d four noded quad shell type element of plain stress
type
with thickness
0.5mm
because

of the shape of the body and convenience to mesh geometry
.
In order to represent
the situation exactly
similar to the experimental set up,

A circular section
of radius 5mm is taken to model. T
wo
circular
cut
sections of radius 0.5mm at a distance of 3 mm
from the center are modeled at the top and bottom of
the specimen

to grip the specimen
. Two more
cut
circular sections of radius 2mm at a distance of 2.5mm from
the center are modeled on left and right side of the specimen and two rectangular
cut
sections
of 3mm width and
2mm height are modeled at right and left side of the specimen at distance of 2mm from the center

to simulate

the actual geometry of the specimen
. Then the auto trim option is used to subtract the two circles of radius 2mm,
another two circ
les of radius 0.5mm and rectangles from the larger circle of radius of 5mm to obtain the
required model of circular dumb
-
bell shaped specimen.









Sl.
No
.

Materia
ls

Di
fferent Mechanical Properties

Young’s
Mo摵d畳=
⡇maF
=
viel搠
=
strength=
⡍maF
=
qensile=
=
ptrengt

=
⡍maF
=
moisson
’s ratio
=
ν
=
=

=
Ao㘶S
alloy
=
㜰T㘹S
=
㔰㘮㤰
=
㔶㜮㤲
=
〮㈵
=

=

=
steel
=
㈰ㄮ〰
=
㐸㌮〰
=
㜴㔮㜱
=
〮㌰
=
P
K
=
eㄱN
steel
=
ㄹ㔮〰
=
㐷㐮〰
=
㘹㌮㐵
=
〮㌰
=
Determination of Mechanical Properties of Different Materials Using
Inverse Finite Element

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27

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TABLE 2
.1 TRUE STRESSES AND TRUE STRAINS




















TRUE STRESS (σt):

σ = P/Ai; Ai = AoLo/Li;

σ = PLi/(AoLo);

σt = P/Ao;


Li = Lo+ΔL;

σt = σ (1+
ε
)
Li/Lo =1+

ΔL
,


TRUE STRAIN (
ε
t
):

ε
t

= dLi/
Li;

Li = Lo+ ΔL;

ε
t

=
ln (
1+
ε
);



Ai = Instantaneous Cross Sectional Area;


A0 = Original Cross Sectional Area;


σ t = True Stress;





σ =

Nominal Stress;



ΔL=Change in Length;


3
.2 Material m
odeling:

In the elastic analysis of simulation, the material properties of column were defined by elastic modulus
and Poisson’s ratio. In the plastic analysis stage, material nonlinearity or pla
sticity was included in the
ABAQUS by incorporating the yield stress and plastic strain values. In the finite element simulation of
miniature dumb
-
bell specimen, the plastic properties are defined together with the isotropic hardening rule. It
means that t
he yield surface size changes uniformly in all the directions such that the yield stress increases in all
stress directions as plastic strain occurs. The curve of true stresses and true plastic strains were specified during
the tensile test defines the bas
ic flow characteristics of the material. The incremental plasticity model required
the true stress
-
strain curve to the ultimate point of the stress
-
strain curve.



Fig: 2.2
Finite element model of the miniature specimen

s.
no

AR66 alloy

D3 steel


H11 steel

True
stress

N/m2

True
plastic
strain

True
stress

N/m2

True

plastic
st
rain

True
stress

N/m2

True
plastic
strain

1.

506.90

0.0000

484.4

0.0000

474.2

0.0000

2.

512.32

0.0025

520.3
9

0.0056

518.8

0.0128

3.

520.04

0.0035

544.7

0.0094

573.4

0.0173

4.

526.58

0.0048

581.8

0.0153

633.3

0.0258

5.

537.57

0.0084

616.4

0.0213

672.1

0.0352

6.

552.50

0.0171

674.6

0.0335

697.6

0.0443

7.

568.66

0.0299

712.9

0.0438

720.2

0.0555

8.

591.39

0.0509

742.6

0.0541

734.6

0.0649

9.

606.47

0.0667

759.9

0.0613

748.0

0.0761

10

612.65

0.0737

778.5

0.0705

758.5

0.0866

11
.

620.25

0.0826

801.5

0.0844

764.1

0.0932

12
.

626.75

0.0908

826.9

0.1041

772.1

0.1438

Determination of Mechanical Properties of Different Materials Using
Inverse Finite Element

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als.org


28

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IV.

F
INITE
E
LEMENT
R
ESULTS
A
ND
D
ISCUSS
IONS

4
.1

AR
66

ALLOY
:

The load
-
elongation solution is plotted below


FIG.
3.1
:Displacement of AR66 miniature specimen


The stress distribution for AR66 is shown in below figure


FIG.3.
1.1

Stress distribution of AR66 miniature specimen


The experimental load
-
elongation curve is taken from
the literature

is shown in graph
2
.1


Graph
3.1.2

The Load

elongation curve from finite element
simulation is shown in graph 3.1.3

Determination of Mechanical Properties of Different Materials Using
Inverse Finite Element

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29

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Graph 3.1.3


Comparison of experimental results with finite element

result