Design Customization and Development of Split Hopkinson Pressure Bar for Light and Soft Armour

16 Pages·2014·1.01 MB·English

Global Journal of Researches in Engineering: A
Mechanical and Mechanics Engineering
Volume 14 Issue 7 Version 1.0 Year 2014
Type: Double Blind Peer Reviewed International Research Journal
Publisher: Global Journals Inc. (USA)
Online ISSN: 2249-4596 & Print ISSN: 0975-5861

Design Customization and Development of Split Hopkinson
Pressure Bar for Light and Soft Armour Materials
By Shishay Amare Gebremeskel, Neelanchali Asija, Aryan Priyanshu,
Hemant Chouhan & Naresh Bhatnagar
Indian Institute of Technology Delhi, India
Abstract- In order to face the grand challenge of characterizing soft and light armour material
system shaving polymers and shear thickening fluids under impacts at high strain rates lead to
design and development of this particular SHPB set up. The developed set up is designed for a
maximum firing pressure of 300 bar of nitrogen gas and it comprises automated gas filling and
firing, striker bar velocity recording and data acquisition system. Pressure bars are made of
titanium alloy due to its high yield strength and reasonably lower density which could protect
plastic deformation, wave dispersion and reduces impedance mismatch with the intended soft
specimens, unlike maraging steel bars. The maximum stresses on the critical parts of the setup
are crosschecked with simulation results and compared with corresponding yield strengths.
Velocity-pressure calibration of the developed setup shows higher velocities can be achieved at
any particular pressure, when it is compared with the existing public domain velocity calibration
of SHPB setup.
Keywords: split hopkinson pressure bar, high strain rate impact, armour, customized design,
simulation.
GJRE-A Classification : FOR Code: 091399p

DesignCustomizationandDevelopmentofSplitHopkinsonPressureBarforLightandSoftArmourMaterials

Strictly as per the compliance and regulations of:

© 2014. Shishay Amare Gebremeskel, Neelanchali Asija, Aryan Priyanshu, Hemant Chouhan & Naresh Bhatnagar. This is a
research/review paper, distributed under the terms of the Creative Commons Attribution-Noncommercial 3.0 Unported License
http://creativecommons.org/licenses/by-nc/3.0/), permitting all non commercial use, distribution, and reproduction inany medium,
provided the original work is properly cited.
Design Customization and Development of Split
Hopkinson Pressure Bar for Light and Soft
Armour Materials

Shishay Amare Gebremeskel α, Neelanchali Asija σ, Aryan Priyanshu ρ, Hemant Chouhan Ѡ
& Naresh Bhatnagar ¥
4
1
0
Abstract- In order to face the grand challenge of characterizing SHPB Split Hopkinson Pressure Bar 2
soft and light armour material system shaving polymers and STF Shear Thickening Fluids ear
shear thickening fluids under impacts at high strain rates lead Y
to design and development of this particular SHPB set up. The I. Introduction
developed set up is designed for a maximum firing pressure of 62
300 bar of nitrogen gas and it comprises automated gas filling An increasing demand of high strength, lightweight

and firing, striker bar velocity recording and data acquisition and soft armour material systems, especially for I
n
shyigshte myie. ldP rsetsresnugreth b aanrsd arerea smonaadbel yo lfo wtitearn iduemn saitlylo yw hdicuhe ctoo uiltds military applications, resulted in interesting rsio
research challenge to characterize possible materials at e
V
protect plastic deformation, wave dispersion and reduces
ballistic impacts. Nowadays FRPs and STFs are the
impedance mismatch with the intended soft specimens, unlike main materials of emphasis as a solution for the VII
maraging steel bars. The maximum stresses on the critical
parts of the setup are crosschecked with simulation results mentioned challenge. Thus, their high strain rate impact e
u
and compared with corresponding yield strengths. Velocity- behaviours need to be studied, since their properties at ss
pressure calibration of the developed setup shows higher static loadings could not be employed for dynamic I
V
velocities can be achieved at any particular pressure, when it designs. For this reason, having an appropriate test XI
is compared with the existing public domain velocity setup is significant and SHPB is a potential set up to be

calibration of SHPB setup. used, Jadhav [1]. Since available SHPB setups are me
Keywords: split hopkinson pressure bar, high strain rate u
designed for particular challenges in terms of capacity, ol
impact, armour, customized design, simulation. material type and other requirements, design V
Highlights cmuastteormiailsza isti ofonu anndd t od beev enloecpemsesnatr yo. f own setup for soft () A
• Particular SHPB is developed for impact g
characterization of soft and light materials. Thus, studying the historical background in rin
advancements of SHPB set up starting from its first e
e
• FEM simulation is done for the critical parts of the n
setup. innovation up to the latest customizations is important ngi
for this particular design. According to studies in [2-5] E

• Hydraulic momentum arrest is provided to avoid Bertram Hopkinson primarily developed a set up called n
i
repeated loading of specimens. HPB in 1914 using a single bar and its modification was es
h
• Isolation of launching unit vibration is provided to made in 1948 in which electrical equipment was rc
a
eliminate noise signals. incorporated to record the stress waves. Following this se
e
modification, Herbert Kolsky split the HPB in to incident R
• Velocity-pressure calibration is performed.
and transmission bars in 1949 and hence the name of
Abbreviations SHPB. It is this Split Hopkinson Pressure Bar set up that al
n
CAE Computer Aided Engineering has been widely used in many research studies to ur
o
characterize materials at dynamic loadings. Articles [6- J
DFBADQ DFraetea BAcoqduy isDitiaiognr am 1c3u]s toamdidzaretisosne do f a SHcPomB mdoens igdne stihgant tchoeuoldry refosru lta niny Global

FEM Finite Element Method acceptable calibration curves and stress wave shapes.
T he customization made by Robertson et al. [14] is one
FOS Factor of Safety
of the advancements that enabled the setup to test
FRP Fibber Reinforced Polymers
materials at strain rates ranging 50 to 104 s-1. In a more

HPB Hopkinson Pressure Bar suitable approach, Haines et al. [9] followed two design

PLC Programmable Logic Control phases as mechanical system and DAQ system. The
mechanical system includes the launching unit which
Author α σ ρ Ѡ ¥:Department of Mechanical Engineering, Indian
has the high pressure cylinder as a main part, the
Institute of Technology Delh i, Hauzkhas, New Delhi, India.
e-mail: [email protected] pressure bars (striker bar, incident bar and transmission

©2014 Global Journals Inc. (US)
Design Customization and Development of Split Hopkinson Pressure Bar for Lightand Soft Armour
Materials
bar) and the momentum arrest. The DAQ system propagated through and the following governing
includes the strain gauges, oscilloscope and computer equations for strain rate (ε ̇), strain (ε) and stress (σ) on
as per Guedes et al. [15]. specimen to be tested on the setup are used, Akil [2]
To design the pre ssure bars, more emphasis and Song &Chen [16]:
should be given to the extent of stress waves to be
(t), , and
2Cb 2Cb t EbAb
Where, is εtḣ(et) el=as−tic wLsavεer velocεi(tyt) in= th−e bLasr, ∫0 εr(t)dtThe σcu(rtr)en=t dAessigεnt( t)has the following
is the sample length and and are the specifications that made it suitable to test softer
spe cimen and Cbbar cross-sectional a reas respectively. materials at higher strain rates; (a) Pressure cylinder
14 Ls, and are incident, reflecAtesd and Atrbansmitted designed to accommodate extreme pressure up to 300
0 bar of nitrogen gas. (b) Automated control of gas filling,
2 strains measu red from strain gages on the bar,
ear r𝜀𝜀e𝑖𝑖spεe𝑟𝑟ctively.𝜀𝜀 T𝑡𝑡he pressure bars are of the same material firing and instantaneous striker bar velocity recording.
Y (c) Separate foundation and construction of the
having elastic modulus E, density ρ, same cross
6 3 sectional area Ab, and hence same elastic wave pgreet strsaunres mciyttliendd etor tthoe i sboalarste w thhiec hv iobtrhaetirownis ien woordueldr cnroeta ttoe
more noise signals. (d) Complete arrest of momentum
I velocity .
n using hydraulic momentum trapping system. (e) Slender
o
sier CSbinc=e �thEe� cρonventional SHPB setup has been titanium alloy (ASTM Grade-5) bars with diameter of 12
V mm having reasonably lower acoustic impedance
designed for testing hard and metallic materials it is not
suitable for high strain rate impact testing of softer
VII suitable for softer materials like polymers and STFs. materials. (f) Negligible friction between bars and
Thus, newly customized SHPB setup has to be

e bearings, by using custom designed adjustable three-
u designed depending on the nature of the planned test
ss point miniature ball bearings. (g) Simplified axis
I specimen and expected maximum impact velocity. As
alignment provisions. The overall work is presented in
V part of the customization process, selection of material
XI for the pressure bars is very important as the stress the following chapters.

em wave transmission is highly dependent on it. Even II. Materials and Methods
u though polymeric and aluminium bars are found to be
Vol suitable for the stated softer materials in terms of a) Design of launching unit, the b ars and mom entum
trapping
impedance matching as per Meng & Li [17] and Butt &
)
A Xue [18], the viscoelastic beha viour causing wave i. Design o f high pressure gas cylinder
(
ng dispersion and plastic deformation of both these bar Using the design procedures of pressure
ri materials made them unfit for higher velocity impacts. vessel:
e
ne To overcome the stated drawbacks of polymer and From theory of elasticity according to Budynas
ngi aluminum bars, titanium bars are employed in this & Nisbett [19], a pressure vessel experienc es three
E
n particular design as it has higher yield strength with high si multaneous principal stresses as shown in Fig. 1. The
i elastic deformation behavior at impacts of extreme stresses over the pressure vessel wall are function of
s
he speeds. This study presents the mechanical design radius.
c
ear analysis of main parts of customized SHPB, where the Principal stresses; σ1 = σt (tangential stress or
Res critical ones are supported and validated by FEM hoop stress), σ2 = σr (ra dial stress), σ3 =
simulation using Abaqus CAE. (longitudinal stress).
of
al σl
n
r
u
o
J

al
b
o
Gl
Fig.1: Schematic drawing of cylinder under pressure and its principal stresses

© 2014 Global Journals Inc. (US)
Design Customization and Development of Split Hopkinson Pressure Bar for Lightand Soft Armour
Materials
Thick-wall theory is considered, as it is used for
any wall thickness-to-radius ratio. Cylinder geometry ; (3)
2 2
includes r, r and L (internal radius, outer radius and Piri−Poro
length resipeoctively). Cylindrical stresses representing Two mechanicalσ dle=signro2 c−ari2sesr ic≤anr b≤e rcoonsidered as;
the principal stresses,σt, σr and , can be calculated at Case-1: internal pressure only(Po=0)
any radius ‘r’ in the range of wall thickness betweenr Case-2: external pressure only (P=0)
and ro. σl i This particular design iof high pressure gas
container corresponds to the first case, where P =0;
Tangential or hoop stress can be given as; o
therefore, the critical section exists at r = r, for which the
i
; (1) hoop stress can be evaluated as;
2 2 2 2 2
Piri−Poro−riro(Po−Pi)/r 4
andσ ts=imilarly the rro2a−dri2ial stress crai n≤ bre≤ girvoen; (4) 01
2 2 2 2
ro+ri ζ +1
; (2) Whereσ,t(r=ri)=σt,max =Piro2−ri2 =Piζ2−1=PiCti ear
Y
2 2 2 2 2
Hσrow=ePvierir−, Ptohreo+rloo2ri−nrrgoi2(itPuod−iPnia)/lr strrie≤ssris≤ arpoplicable to ro (5) 64
cases where the cylinder carries longitudinal load, such ζ = ri
as in capped ends and in boiler vessels, valid where ζ2+1 (6) n I
bending, nonlinearity an d stress concentrations are not are function of cylinder Cgteio=mζe2t−ry1 only. rsio
significant and can be estimated as; And the radial stress will become; e
V

(7) VII

The longitudinal stress depeσnrd(sr o=n rei)nd= cσorn,mdaixtio=ns−: Pi(whichisanaturalbou ndarycondition) sue
(8) W h e r e , t=SE−Pi0r. i6Pi (10) XIV Is
Where, σl =�PiCli,cappedends� e
0,uncappedends (11) m

(9) σyt olu
ThSe( aldloimweanbsleiodness igonf sttrhees s)d=esFiOgSned pressure V
For calculatingC tlhie= thζ2i1−c1kness ‘t’of the cylindrical cylinder are given in Fig. 2. () A
s h e ll [ 2 0 ] , the following equation can be used. g
n
ri
ee
n
gi
n
E

n
i
es
h
c
r
a
se
e
R
of

al
n
our
J

bal
o
Gl

Fig. 2:High pressure gas cylinder (all dimensions in mm)

©2014 Global Journals Inc. (US)
Design Customization and Development of Split Hopkinson Pressure Bar for Lightand Soft Armour
Materials
ii. Design of column for the pressure cylinder
The high pressure gas cylinder is subjected to Using the formula for design or allowable
thrust force generated after each firing process. This bendAinbogr estirsecsrsoss:s ectionalareaofthecylinderbore
thrust force will be transmitted to its column. Fig. 3
shows the dimensions of the column and point of σb (13)
M
application of the transmitted thrust force.
W h e r e , M = b e n dσinbg= mZoment and Z= section
modulus
, length L of the column is fixed by
the axis height of the set up to be 800 mm.
Internal dMia=meFtte∗r LID of the column is fixed by the swivel
of the thrust bearing seat to be 75 mm and the outer
4
1 diameter OD to be calculated.
0
2
r iii.Design of bars and barrel
a
e
Y Titanium alloy is considered to design the bars
as it reasonably satisfies the following criteria:
6 5
 Bars must remain elastic after impacts (higher

I modulus of elasticity E)
n
o  Bars should neither breakdown nor plastically
si
Ver deform (higher yield str ength )

 Bars should have less density to reduce mismatch
VII of acoustic impedance Z witσhy soft specimens like
e Polymers.
u
s
Is Fig. 3 :FBD of pressure cylinder column b) Striker B arZ= ρC
XIV The maximum thrust force Ft that this part can From conserva tion of energy:
face is dependent on the net drop of the cylinder Potential energy of the striker bar = kinetic
e
m pressure after single firing. energy of the striker bar
u
Vol (12) (14)

) A W h e r e , Ft =Pnet ∗Abore PEs =KEs (15)
(ring WPhneetreis,thenetdropofthepressureatsinglefiring ,P iAslb =12msVs2 .
ee
n
gi The d Aimse=nsciroonsss soef ctthioen satlriakreera boafrt haes satr irkeesru lbt aorf, lb =c)le nDgethsigonft ohfe inbcairdreenlt mansd= trmana sssmoisf sthioens briakresr bar
n
E the above assumption are given in Fig. 4. To avoid buckling of the bars in between the

in supports, most literatures recommend that th eir aspect
es ratio (L/D ratio) should be limited to 100, however with
h
rc three-point contact miniature ball bearings (floater
a
se bearings) having low coefficient of friction can be used
e
R to increase the L/D ratio. As shown in Fig. 5, the length L
of of the barsis maintained to be 1200 mm while their

nal di ameter is fixed by striker bar to be 12mm.
r
u
o
J
al
b Fig. 4 :Striker bar (all dimensions in mm)
Glo

Fig. 5 :Incident and Transmission bars (all dimensions in mm)

© 2014 Global Journals Inc. (US)
Design Customization and Development of Split Hopkinson Pressure Bar for Lightand Soft Armour
Materials
To predict the Stress capability of incident and
(18)
transmission barsthe following equations are used;
Fd
Where, σmax = A
(16)
1 2 (19)
Where, KE=2msVs
KE
(17) Fd(MPaoxismitiuomn doyf nbameaicrinfogr cseuopnptohretsb aorfs )In=cidlse n t and
Transmission bars
T h e n t h e m a x mimsu=m ρsAtrselsss on the bars will be The number of bearing supports ‘n’ is fixed to
the maximum dynamic force divided by the cross
sectional area A of the bars. be two for each bar and their position is c alculated by
using Airy’s formula[21].
4
1
0
2
r
ea
Y

66

I
n
o
rsi
e
V

Fig. 6 :FBD of position of bearing supports of incident and transmission bars VII

As show n in Fig. 6, the distance betw een d) Design of the barrel (launching tube)
e
u
centers of the bearings ‘A’ has been calculated as Considering the barrel as a short time pressure s
follows; vessel with no welded joints; corresponding joint Is

V
(20) efficiency, E, is given as 1 and FOS is fixed to be 2.Its XI
thickness ‘t’ is calculated using the formula in equation

L (10) above as the internal radiu s o f the barrel ‘r ’ is fixed me
Where, L= 1200mm, n=A2=; �n2−1 bythe radius ofthe striker bar to be 6mm. ib olu
1200 The necessary dimensions are accordingly V
253.5 mmTh deirsetfaonrec,e tfhroem b beoaAtr hin= gen �sd2u2s−p o1pf=o trht6es9 b3aarmer. mplaced at calculated and given in F ig. 7. () A

g
n
ri
e
e
n
gi
n
E

n
i
s
e
h
c
r
a
e
s
e
R

of
al
Fig. 7 :Barrel or launching tube (all dimensions in mm) rn
u
Jo

e) Momentum Trapping al
b
o
i. Selection of hydraulic oil Gl
Selection of the right hydraulic oil should be
made based on its bulk modulus or compressibility. For
complete absorption of the kinetic energy KE ge nerated

at 300 bars of reservoir pressure and safe design, we
assume that the total KE of the striker bar at its
maximum velocity of 600m/s will be transferr ed to the
momentum trap.

©2014 Global Journals Inc. (US)
Design Customization and Development of Split Hopkinson Pressure Bar for Lightand Soft Armour
Materials

4
1
0
2
r
a
e
Y
6 7 Fig. 8 :schematic drawing of momentum trap hydraulic cylinder (all dimensions in mm)

From Fig.8 it is observed that the level H of oil

I responsible to absorb the momentum is made 160mm
n
sio and an initial volume Vo is calculated as;
r
e
V
π (21)
VII di2
A l l o w i n g 0 . V2o %= ch∗an4g∗e Hin volume of the oil,
e bulk modulus E of the hydraulic oil will be calculated as;
u
ss ∆V
I (22)
V
XI KE
According to the technical data in [22] the
E=∆V

e possible oil at 300 bar pressure is the petroleum based
m
u hydraulic oil with corresponding bulk modulus E of 1.6
ol Fig. 9 : FBD of mass attached to a spring and damper
V GPa is therefore selected.
representing the momentum trap
) Considering the momentum trap as a mass
A
( attached with a spring and damper as shown in Fig.9, it The stiffness K is calculated using the following

g is modeled and the stiffness and damping coefficient formula;
n
eeri are predicted as follow s; (24)
n
gi (23) 2
En Where, m is mKas=s mof∗ tωhen movable parts in the
in W h e r e , F d Fisd t+heK mx+axCimvu=m0 dyn amic force to be momentum trap (head+rod+piston), and
s trapped, K is the stiffness of the momentum trap, x is the
e
ch maximum axial displacement of the piston, C is the
r
ea damping coefficient of the momentum trap and v is ωn isthenaturalfrequency. (25)
s
Re velocity of the striker bar. Cst
of ωn =2∗Lt

al
urn m
Jo III. FwehmerSe iCmstuislsapteieodnof o sofuCndriinttihceablarPsagrivtesnas50E7le3msenatn tdypLet i=s lteentrgathheodfrtahle transmission bar.
al
b using Abaqus cae 6.10 Number of elements = 8908
o
Gl
a) Pressure Cylinder

The following input data are provided to
simulate the stress condition of the cylinder under
maximum nitrogen gas pressure and observation of the

maximum stress is taken, as shown in Fig. 10, to

compare with the yield strength of the selected material.

Material = AISI4130, steel
Load type = 300 bar uniformly distributed internal
pressure

© 2014 Global Journals Inc. (US)
Design Customization and Development of Split Hopkinson Pressure Bar for Lightand Soft Armour
Materials

4
1
0
2
r
ea
Y

68
Fig.10: Visualization of FEM simulation results of pressurized SHPB cylinder

I
b) Column of the pressure cylinder Load type = dynamic/explicit, due to the maximum net n
o
The following input data are provided to pressure drop of gas cylinder after single firing (20 bar rsi
e
simulate the stress condition of the column under of uniformly distributed pressure) V

dynamic loading and observation of the maximum
stress is taken, as shown in Fig. 11, to compare with the Element type = tetrahedral VII
Number of elements = 56091
yield strength of construction material. e
u
s
Material = AISI4130, steel Is

V
XI

e
m
u
ol
V
() A

ng
ri
e
e
n
gi
n
E

n
s i
e
h
c
r
a
e
s
e
R
Fig.11 :Visualization of FEM simulation results of the column
of

al
c) Pressure Bars Loading Duration = 60 μs (set to be two times period of n
r
The following input data is provided to simulate the wave to check for higher stress) ou
J
the one dimensional stress propagation in the pressure Since each bar of the assembly could not be al
bars during firing and observation of the maximum visually identified in a window at a time, the zoomed ob
compressive stress is taken, as shown in Fig. 12, to images of the interaction areas are displayed in Fig. 12. Gl
compare with the yield strength of the Titanium bar The first one is the interaction between striker bar and
material. incident bar while the second one is between incident
Material = Ti6Al4V, Titanium(ASTM Grade-5) bar, specimen and transmission bar. The results of
which are discussed later in the Results and Discussion
Load type = dynamic/explicit, due to the maximum net
section.
pressure drop of gas cylinder after single firing (20 bar

of uniformly distributed pressure)
Element type = tetrahedral
Number of elements = 103306

©2014 Global Journals Inc. (US)
Design Customization and Development of Split Hopkinson Pressure Bar for Lightand Soft Armour
Materials

4
1
0
2
r
a
e
Y
6 9

I
n
o
si
r
e
V
Fig.12 :Visualization of FEM simulation results of 1-D stress wave propagation through
VII pressure bars under impact

e
u d) Data Acquisition System (DAQ)
s
Is The instrumentation of the SHPB set-up typically

V comprises a velocity measurement system, strain
XI gauges, high speed strain gage input module with built-

e in signal conditioner and amplifier as well as voltage
m
u excitation source for powering the wheat stone bridge
Vol circuit, and oscilloscope for the display of acquired
strain signals in both the incident and transmission bars.
)
A
( The following section discusses each of the above

g components of DAQ system in detail.
n
eri i. Velocity Measurement System
e
n The main purpose of the velocity measurement
gi
n sy stem is to determine the impact v elocity of the striker
E
n bar. It comprises of two IR (Infra-red) sensors, KOYO Fig.13 :Schematic diagram of Velocity Measurement
s i PLC and high speed counter module (HO-CTRIO-2). As System
e
h
c soon as the striker bar is triggered, it passes in front of
r ii. Stress-Strain Measurement System
ea the IR sensors within a fraction of second.
s This system comprises of the strain gages,
Re Consequently, pulse state and stop is registered in the
signal conditioner cum amplifier and data acquisition
of PLC. The function of the high speed counter module is (DAQ) system. The selection of appropriate DAQ system
nal to determine the time duration between the consecutive is solely based upon the required sampling frequency
r pulse start and stop. By knowing the distance between
u (f) i.e. number of samples taken per second. The
Jo the speed sensors, the impact veloci ty of the striker bar s
sampling rate of the DAQ system must satisfy the
al is calculated. The schematic of the velocity-
b Nyquist criterion [23], which states that the signal must
Glo measurement system is illustrated in Fig.13. be sampled at a frequency which is greater than twice
the highest frequency component of interest in the
signal, otherwise, the high frequency content will alias at
a frequency inside the spectrum of pass-band. The

specific DAQ system used in this setup is based on NI

PXIe supported by Lab view software. Fig.14 shows the

photograph of the DAQ and analysis system including
the strain input card and the monitor.
Sampling rate f of the DAQsystem
s

© 2014 Global Journals Inc. (US)
Design Customization and Development of Split Hopkinson Pressure Bar for Lightand Soft Armour
Materials

( 2 6 )
Where, λ is the wave length and C is the wave
T=λ/C
speed with in the pressure bars. The wave length λ is

two times the length of the striker bar which comes out
to be 0.152m (2*0.076m). Period T is calculated to be
30 μs and the subsequent maximum wave frequency

f will be 1/T, which is nearly 34 KHZ. Thus, sampling
max
rate of DAQ system, according to Nyquist criteria;
f>2f , should at least be 70 Kilo samples per second
s max
(>2*34 KS/sec).
Whe atstone Bridge Configuration 14
0
2
diametricTawlloy opapcotisviete osnt rtahine bagrasg, ethsu s wcoenres titumtinogu nHteadlf Year
Fig.14 : Photograph of the D AQ and Bridge Type II co nfiguration.
70
analysis system

Calculation of loading duration T of pressure I
n
bars is essential to fix the minimum sampling rate o
required by the DAQ system. ersi
V

VII

e
u
s
s
I

V
XI

e
m
u
ol
V
Fig.15 :Half Bridge Type II Circuit Diagram
() A
In Fig. 15, R1 and R2 are the half bridge axial strain while rejecting the bending strain. The strain ng
completion resistors, R3 is the active strain gage gage output voltage was converted to corresponding eri
element measuring the compressive strain (-ε) and R4 is strain units by using the following equation. ne
the active strain gage element measuring the tensile gi
En
strain (+ε). This bridge configuration measures purely
n
i
s
S train (ε) = (27) che
r
−2𝑉𝑉𝑟𝑟 𝑅𝑅𝐿𝐿 ea
s
( 𝐺𝐺𝐺𝐺 )∗(1+𝑅𝑅𝑔𝑔) e
R
Where, V (the voltage ratio)= (28)
r 𝑉𝑉𝐶𝐶𝐶𝐶(𝑠𝑠𝑡𝑡𝑟𝑟𝑠𝑠𝑖𝑖𝑠𝑠𝑠𝑠𝑠𝑠 )−𝑉𝑉𝐶𝐶𝐶𝐶(𝑢𝑢𝑠𝑠𝑠𝑠𝑡𝑡𝑟𝑟𝑠𝑠𝑖𝑖𝑠𝑠𝑠𝑠𝑠𝑠 ) of
𝑉𝑉𝐸𝐸𝐸𝐸 nal
V is the excitation voltage,V is the measured r
EX CH u
signal voltage,GF is Gag e factor o f the strain gages and Jo

R R are lead resistanc e andnominal strain gage al
L& g b
resistance, respectively. Glo
e) Fabrication and Installation
Fabrication of the designed SHPB parts, their

assembly and the total installation is thereby
accomplished. The total setup assembly contains
different mechanical, electrical and ele ctromechanical
parts as tabulated in Table 1 below.

©2014 Global Journals Inc. (US)