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International Journal of Mechanical Sciences 61 (2012) 1–7
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International Journal of Mechanical Sciences
0020-74
http://d
n Corr
E-m
srnaga@
journal homepage: www.elsevier.com/locate/ijmecsci
Investigations on micro-blast wave assisted metal foil formingfor biomedical applications
S.R. Nagaraja a,n, S.G. Rakesh a, J.K. Prasad b, P.K. Barhai b, G. Jagadeesh c
a School of Engineering, Amrita Vishwa Vidyapeetham, Bangalore, Indiab Birla Institute of Technology, Mesra, Ranchi, Indiac Indian Institute of Science, Bagalore, India
a r t i c l e i n f o
Article history:
Received 25 March 2011
Received in revised form
8 December 2011
Accepted 17 April 2012Available online 24 May 2012
Keywords:
Metal forming
Micro-blast waves
Explicit dynamic analysis
FEM
Biomedical applications
03/$ - see front matter & 2012 Elsevier Ltd. A
x.doi.org/10.1016/j.ijmecsci.2012.04.004
esponding author.
ail addresses: [email protected],
yahoo.com (S.R. Nagaraja).
a b s t r a c t
The deformation dynamics of metal foils (o0.25 mm thick) subjected to micro-blast wave are
presented in this paper. The energy of micro-blast wave emanating from the open end of a polymer
tube is used to deliver micro-particles for bio-medical applications. In these experiments metal foils are
used to transfer the energy of the micro-blast wave to the micro-particles. Using cubic root scaling law
the over pressure of the blast wave at the open end of the polymer tube is estimated and using this peak
plate over pressure is estimated. The finite element analysis is used to estimate the velocity profile of
the deforming metal foils. The finite element analysis results are compared with experimental results
for the maximum deformation and deformed shape. Based on the deformation velocity, metal foil to be
used for experiments is selected. Among the materials investigated 0.1 mm thick brass foil has the
maximum velocity of 205 m/s and is used in the experiments. It is found from finite element analysis
that the particles deposited within a radius of 0.5 mm will leave the foil with nearly equal velocity
(error o5%). The spray cone angle which is the angle of deviation of the path of particles from the axis
of the polymer tube is also estimated and found to be less than 71 up to a radius of 0.75 mm. Illustrative
experiments are carried out to deliver micro particles (0.7 mm diameter tungsten) into plant tissues.
Particle penetration depth up to 460 mm was achieved in ground tissue of potato tuber.
& 2012 Elsevier Ltd. All rights reserved.
1. Introduction
The occurrence of shock waves is commonly associated withsupersonic flight and is an integral part of high-speed flowanalysis. Shock waves can also be used for innovative applicationsin various fields such as medicine, biological sciences and indus-try. Menezes et al. [1] have developed a device to deliver microparticles using shock waves generated by laser ablation for biomedical applications. Recently Jagadeesh [2,3] has used thinmetal foils (�100 mm) to transfer the momentum from shockwave loading to carry out very interesting bio-medical applica-tions including needleless drug delivery and DNA transfer inbiological targets. High strain rate forming of metal plates (fewmm thickness) using explosives has been studied by manyresearchers, but on the other hand, not much data is availableon shock wave assisted metal forming of thin metal foils in theopen literature. Some of the important literature in the area ofhigh strain rate forming and biomedical applications of shock
ll rights reserved.
waves is briefly reviewed here followed by the motivation andobjectives of the present study.
High strain rate metal forming can be achieved using shockwaves generated either explosively or non explosively. Kosingand Skews [4,5] have used liquid shock tube to generate shockwaves non explosively for metal forming applications. Morerecently Stoffel et al. [6] and Stoffel [7] have used the conven-tional shock tube to study the response of shock wave loadedplates. Florence [8] conducted experiments on explosive formingof circular aluminium and steel plates of thickness 6.25 mm usingsheet explosives. The central deflections were measured andexperimental results were compared with theoretical valuesusing bending theory assuming the material as rigid—plasticmaterial. The differences in experimental and theoretical resultswere explained by an insufficient plate theory not taking mem-brane forces into account. Wierzbicki and Florence [9] modifiedthe constituent model by using visco-plastic law for large dis-placements. These studies showed that strain rate sensitivity andmembrane forces have equally important strengthening effect.Johson et al. [10] have conducted experiments to plasticallydeform clamped mild steel circular plates using underwaterexplosive charge. They have investigated the effects of chargeshape, eccentricity of the charge from the axis of the die and,
Nomenclature
I0 Primary inertiak Material constantm Hardening coefficientNxx, Nyy, Nxy Forces per unit lengthn Strain rate sensitivity coefficientP Shock wave pressurePr Peak plate over pressure (reflected pressure)Ps Peak over pressure of the blast wavePo Atmospheric pressureR Distance from the center of chargeuo Radial displacement of a point on the mid plane of
the plate
vo Angular displacements of a point on the mid plane ofthe plate
Vr Resultant velocity of the particleVx Velocity of particle parallel to the shock tube axisVz Velocity of particle perpendicular to the shock
tube axisW TNT equivalent weight of explosive under
considerationwo Transverse displacement of a point on the mid plane
of the plateZ Scaled distance| Rotation of transverse normalE StrainA Strain rated Angle of deviation (spray cone angle)
S.R Nagaraja et al. / International Journal of Mechanical Sciences 61 (2012) 1–72
eccentricity of the charge and die assembly from the axis of thewater tank in which the experiments are performed. They con-cluded that spherical charges produce larger midpoint deflections.Symonds and Weirzbicki [11], Perrone and Bhadra [12] havedeveloped empirical/theoretical relations to predict the deflectionof plates subjected to impulsive loads. Most of these relations area function of the imparted impulse, the plate thickness and radius,the density and the static yield stress of the material in combina-tion with an empirical factor.
Jiang et al. [13] have developed a device to generate micro-shock waves in ambient air by focusing the energy from a pulsedlaser beam into small spherical volumes. Once the depositedenergy of the focused laser beam exceeds the threshold value foroptical breakdown, ambient air breaks down with subsequentformation of laser plasma. The energy deposition immediatelycreates a primary spherical micro-shock wave travelling outwardsfrom the focal point. Jagadeesh and Takayama [14] have usedNd:YAG glass laser beam to generate spherical shock waves withtypical radius of few millimetres both in ambient air as well as inwater and typically the energy expended in this process is �1.38 J,which is equivalent to 0.3 mg of conventional TNT explosive.Miller [15] has used shockwave technology for the destruction ofrenal calculi through an endoscope. Shock waves are also used forsubcutaneous drug delivery into human skin. Possibility ofdestruction of E-Coli bacteria subjecting them to shock waveshas been explored by Jagadeesh [16] and the preliminary resultshave shown that there is a substantial reduction in the number ofE-Coli cells after subjecting them to repeated shock wave loading.Klein et al. [17] have reported delivery of nucleic acids into plantcells using high velocity micro projectiles. Small tungsten particlesof 4 mm diameter are coated with RNA or DNA and are acceleratedusing the device, called ‘particle gun’, so that the particles (microprojectiles) pierce cell walls and membranes and enter into plantcells without killing them. This method is used to study thetransient expression of foreign genes in an intact tissue. YokoYoshida et al. [18] have used Helios Gene Gun system to accelerateDNA coated gold particles to deliver genes into cell. For introduc-tion of genes into the liver of living rats, the best results wereobtained with this hand-held gene delivery system. The b-galac-tosidase gene introduced into rat liver with gold particles byhelium at 17.5 bar was expressed in a limited area of the liversurface (8�8 mm, depth 0.5 mm). Distribution and also the actualamount DNA delivered into the cells have been examined in thisstudy. M.A.F. Kendall et al. [19] have used Dermal Powder Jectdevice to deliver gold particles into excised human skin. Penetra-tion depth of 75 mm has been achieved with gold particles of2.24 mm diameter entering the skin with a velocity of 640 m/s.
These results have indicated that the penetration depth of the goldparticles into the skin is a strong function of the particle density,velocity and radius. Lee et al. [20] have used a shock tube fortransdermal delivery in fuzzy rats. Rhodamine-B dextran, 10 kDamolecular weight, was used as the probe molecule. Shock waveswere generated by a two-stage shock tube. Matsumi Nakada et al.[21] have used this device for invivo DNA transfer by deliveringplasmid DNA coated, 1-mm size gold particles into onion scale,tobacco leaf and soybean seed cells.
From the above discussion, it is very clear that in recent time,many innovative inter disciplinary applications of shock waveshave emerged. Shock wave assisted techniques are increasinglybeing used for many industrial and biomedical applications. Inmany of these devices metal foils (diaphragms) are used fortransferring the shock wave energy to the micro particles. Thedeformation and velocity vector of the metal foil governs thedirection of motion of particles and energy they carry till theyreach the target. Therefore, understanding the deformation andvelocity distribution is important for efficient design and optimi-sation of the diaphragm in terms of its diameter and thickness inthese systems. This has necessitated the study of behaviour ofthin metal foils when subjected to blast waves. Numerical solu-tions using finite element method provide a cost effective andreliable procedure to carry out parametric sensitivity study andhelp in selection of appropriate diaphragm. In this paper themethod of generation of micro blast waves, finite elementmodelling of the foils subjected to blast wave loading, analysisof deformation velocities, particle spray cone angle and selectionof metal foil are explained.
2. Generation of micro blast waves
A polymer tube coated with explosives acts like a shock tube togenerate micro blast wave. Small amounts (�18 mg/m length) ofmicro explosive (High Melt Explosive (HMX) and traces of Alumi-nium) is uniformly coated on the inner wall of this polymer tube(1 mm inner diameter; wall thickness 1 mm). When the microexplosive is electrically triggered from one end of the polymertube, a detonation wave is generated inside the tube. When thisdetonation front is allowed to escape from the open end of thepolymer tube, a micro-blast wave is generated. The schematicrepresentation of formation of micro blast wave at the open end ofthe polymer tube is shown in Fig. 1. Since the amount of energyexpended in the generation of the blast wave from the open end ofthe polymer tube is very small (�8.7 J; TNT equivalent �1.63 mg)they are referred here as micro-blast waves. The ignition of the
Fig. 1. A pictorial representation of micro-blast wave emanating from the open
end of the polymer tube followed by combustion products.
Fig. 2. Extrapolated values of peak side-on overpressure using cubic root
scaling law.
100
150
200
ssur
e (b
ar)
S.R Nagaraja et al. / International Journal of Mechanical Sciences 61 (2012) 1–7 3
reactive explosive compound (HMX) is done from one end of tube.The reactive explosive compound when initiated propagates a lowenergy signal along the length of the tubing with minimaldisturbance outside of the tube. The ignition of the reactivematerial coated on the inner surface of the shock tube results inthe formation of a shock front. As a result of the shock frontstreaming past the material on the tube walls, the reactivematerial is assumed to undergo a turbulent dispersion towardsthe centre of the tube. The shock front also heats up the gas in thetube. The dispersed energetic material is heated and then combustto release energy which supports the shock front at a typical rateof 2000 m/sec. The combustion reaction thus would resemble thatof a dust explosion. The detonation is confined to the tube alongits length and the products of combustion escape from the openend. The resultant output is characterised as a high pressureimpulse along with hot burning particles.
Thin metal foils placed at the open end of this polymer tubealong with appropriate mechanical fixtures is used to transfer theimpulse-momentum generated by micro-blast wave to appropri-ate medium.
0
50
0 100 10 10-6 20 10-6 30 10-6 40 10-6
Pre
Time (s)
Fig. 3. Pressure profile showing the plate peak over pressure.
3. Peak plate over pressure
The peak pressure at any distance for any size of any explosivecan be quite accurately estimated based upon scaling experimentsusing TNT. It is customary to plot the blast property of interest(in the present case overpressure) against the scaled distance Z.
Z ¼R
W ð1=3Þð1Þ
where R is the distance from the centre of charge and W is the TNTequivalent weight of the explosive under consideration.
Experiments were conducted using polymer tubes to measurethe pressure behind the micro-blast wave in open domain. Sideon overpressure behind the micro-blast wave is measured atdifferent distances from the blast source by sensors placed side onto the flow. PCB Piezotronics pressure transducers are used formeasuring the overpressure levels in open domain. Assuming thatthe micro-blast wave emanating from the open end of thepolymer tube follows the cubic root scaling law, the scaleddistance for an experimentally observed value of overpressurewas calculated from the scaling curve. From this scaled distanceand actual distance the weight of explosive in TNT equivalentweight was estimated to be 1.63 mg. Based on this energy levelsubsequent peak overpressures were estimated from the scalinglaw and was found to be matching very well with the experi-mental values of overpressures obtained at different lengths fromthe micro blast. Fig. 2 shows the plot of peak overpressure versusscaling distance for TNT blasts along with the values obtainedfrom the micro blast studies (marked in black spots). The valuesused are average of 12 firings.
The over pressure value near the open end of the blast tubecannot be measured due to high temperature of the debris gas.
It is estimated by extrapolation from graph of peak over pressureversus scaling distance for TNT blast as depicted in Fig. 2 and it isfound to be �24 bar. The actual pressure (peak plate overpressure or reflected pressure) felt by the metal foil which isplaced normal to the polymer tube near the open end can becalculated using Rankine–Hugoniot relations as ([22])
Pr ¼ 2Psð7P0þ4PsÞ
ð7PoþPsÞð2Þ
where
Pr-Peak plate over pressure (reflected pressure)Ps-Peak over pressure of the blast wavePo-Atmospheric pressure
For peak over pressure of Ps¼24 bar and Po¼1 bar, the peakplate over pressure Prffi160 bar. After calculating the peak plateover pressure, pressure profile with exponential decay as shownin Fig. 3 is assumed. This pressure profile is used as an input to thefinite element analysis.
Fig. 4. Computational domain used in the finite element analysis.
Fig. 5. A photograph of the device used micro particle delivery into soft targets.
S.R Nagaraja et al. / International Journal of Mechanical Sciences 61 (2012) 1–74
4. Finite element analysis
Thin metallic plates/foils are used to transfer impulse momen-tum of the micro blast wave to the micro particles to be deliveredinto soft targets. These micro particles (0.7 mm diameter tungsten)are deposited on the posterior side of these metal foils. The velocityof these particles depends on the velocity of metal plate/foil whichdepends on the type of material, thickness and amount of deflec-tion. A number of empirical relations are available in openliterature to predict midpoint deflection of plates subjected toimpulse loading. A review of these relations is done by Nurick andMartin [23]. Most of these relations are based on experimentalinvestigations on thick plates (thickness in excess of 2 mm)subjected to shock wave loading generated using explosives andcannot be used in the present study on thin plates. Moreover theseempirical relations are functions of exponentially decayingimpulse, yield stress, radius and thickness of the specimen. In caseof thin plates/foils considerable plastic deformation takes place andstrain hardening and strain rate sensitivity of the material play animportant role. Also these relations do not provide any informationon the dynamics of deformation. Hence finite element method isused to determine dynamic deformation of a these foils.
The dynamic deformation equations of a circular plate/foilsubjected to axisymmetric time varying pressure load P based onthe Mindlin plate theory and using principle of virtual displace-ments is [24]
�@Nxx
@xþ@Nxy
@y
� �þ I0
@2u0
@t2¼ 0
�@Nxy
@xþ@Nyy
@y
� �þ I0
@2v0
@t2¼ 0
�@
@xNxx
@w0
@xþNxy
@w0
@y
� �þ@
@yNxy
@w0
@xþNyy
@w0
@y
� ��
þ@|x
@xþ@|y
@yþ I0
@2w0
@t2¼ P
)ð3Þ
After expressing the above Eq. (3) in the weak form and using aninterpolation function they can be expressed in the matrix form as
½M�uþ½C� _uþ½K�u¼ ½F� ð4Þ
where [M], [C] and [K] are mass, damping and stiffness matrices, {u}displacement vector and [F] externally applied force vector. Eq. (4)can be solved using finite element analysis solvers, which incorpo-rate both geometric non-linearities and material non-linearities. Theexplicit dynamic analysis is carried out using ANSYS with LS-DYNAsolver. The boundary condition used is—all degrees of freedom arefixed at the outer periphery of the plate (fixed plate). It is assumedto have biaxial stress system, which is valid since thickness of theplate is very small. Hence the SHELL 163 element with fiveintegration points is used. It is a 4 node element with both bendingand membrane capabilities. Both in-plane and normal loads arepermitted. The element has 12 degrees of freedom at each node, i.e.,translations, accelerations and velocities in the nodal x, y, and z
directions and rotations about the nodal x, y, and z axes. Fully-integrated Belytschko-Tsay shell element formulation (KEYOPT(1)¼12) which is generally used for metal forming applicationshas been used (ANSYS reference manual). It uses a 2�2 quadraturein the shell plane. Non linear strain rate dependent plasticitymaterial model generally used in metal forming applications isselected. This material model follows constitutive relationship of theform
s¼ kAm _A n ð5Þ
where e is the strain, _A is the strain rate, k is the material constant,m is the hardening coefficient, and n is the strain rate sensitivitycoefficient.
The computational domain used in the finite element analysisis shown in Fig. 4. The shock wave is treated as a slug force actinginstantaneously on the thin metallic plate constrained at theouter periphery. In order to validate the finite element modeldeveloped, experiments were carried out using a speciallydesigned holder shown in Fig. 5. The maximum (midpoint)deflection of the plate/foil obtained from the experiments iscompared with those values from the finite element simulations.The results are tabulated as shown in Table 1. The table also liststhe velocity values for aluminium, brass and copper foils of0.1 mm, 0.15 mm and 0.18 mm thickness obtained using finiteelement analysis. It can be observed that the experimental valuesfor the midpoint deflection closely agree with simulated values.
Fig. 6 shows the variation of velocity and midpoint deflectionof 0.1 mm brass foil. It is observed that peak velocity is reachedbefore the maximum deflection is reached and hence the particleswould have been ejected from the free surface of the foil beforethe completion of the deformation process. Fig. 7 shows thevariation of pressure and velocity with time for 0.1 mm thickbrass foil. It is observed that the velocity vector lags behindthe rate of application of pressure. The deformation of the foiland velocity are very slow compared to the rate of appliedpressure.
Table 1Values of midpoint deflection and midpoint velocity for various foils obtained
from finite element analysis and midpoint deflection from experiments.
Materialof the foil
Thickness(mm)
Midpointdeflection(mm)
Midpoint deflection(mm) (Experimental)
Midpointvelocity(m/s)
Brass 0.1 2.88 3.1 204.80
Brass 0.15 1.99 2.5 142
Brass 0.18 1.64 2.34 119.8
Copper 0.1 2.23 2.56 186
Copper 0.15 1.64 1.74 133.72
Copper 0.18 1.41 1.52 112.61
Aluminium 0.1 4.40 Fail (100% failure rate) 486.62
Aluminium 0.15 2.68 Fail (75% failure rate) 310.01
Aluminium 0.18 2.19 2.68 (17% failure rate) 252.91
0
1
2
3
4
5
0
50
100
150
200
250
0 100 10 10-6 20 10-6 30 10-6 40 10-6
Midpoint Deflection (mm)
Velocity (m/s)
Mid
poin
t def
lect
ion
(mm
)
Vel
ocity
(m/s
)
Time (s)
Fig. 6. Variation of midpoint deflection and velocity with time for a 0.1 mm brass
foil loaded with the blast wave.
0
50
100
150
200
250
0
50
100
150
200
250
0 100 10 10-6 20 10-6 30 10-6 40 10-6
Pressure (bar)
Velocity (m/s)
Pre
ssur
e (b
ar)
Vel
ocity
(m/s
)
Time (s)
Fig. 7. Variation of plate peak over pressure and velocity with time for a 0.1 mm
thick brass foil loaded with the blast wave.
Fig. 8. A schematic sketch showing velocity components at a point on the
diaphragm. Vz is parallel to the shock tube (polymer tube) axis.
0
20
40
60
80
100
120
140
0 0.5 1 1.5 2 2.5 3
2.5 microsecs7.5 microsecs12.5 microsecsMax velocity at 18 microsecs
Vel
ocity
(m/s
)
Radius of foil (mm)
Fig. 9. Variation of the resultant velocity along the radius of the foil at different
time intervals for brass foil of thickness 0.18 mm.
S.R Nagaraja et al. / International Journal of Mechanical Sciences 61 (2012) 1–7 5
5. Spray cone angle
Fig. 8 shows the components of deformation velocity vector atany point on the deforming metal foil. Vz is velocity componentparallel to axis of the shock tube (polymer tube) and d the spraycone angle or angle of deviation. As the applied pressure load isrotationally symmetric (or axisymmetric) and edge conditions
(boundary conditions) are also axisymmetric, all the variables(deformation, velocity, stress, strain) are functions of radius andtime only. The deformation velocity vector determines the angleof spray (d) i.e., angle of deviation from axis of the shock tube(polymer tube). Larger the value of d, greater is the distance aparticle deposited on the metal foil has to travel before it reachesthe target and smaller is the velocity at target surface. Thissmaller velocity of the particle results in smaller depth ofpenetration in the target material. Assuming the velocity ofparticles leaving the metal foil surface to be same as that of thefoil (Menezes et al.[1]), the magnitude and angle of deviation ofthe particles can be calculated.
Vr ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiV2
xþV2z
qð6Þ
d¼ tan�1 Vx
Vzð7Þ
where Vr Resultant velocity of the particle
Vz Velocity of particle parallel to the shock tube axis.Vx Velocity of particle perpendicular to the shock tube axis.d Angle of deviation (spray).
Fig. 9 shows the resultant velocity of various points along theradius of the foil at different time intervals. It is observed that allthe points along the radius initially have almost same velocity.The central portion accelerates and rapidly reaches the peak
0
4
8
12
16
20
0
Spr
ay C
one
Ang
le (d
egre
es)
Radius (mm)0.5 1 1.5 2
Fig. 10. Variation of the spray cone angle d along the radius of the foil for brass foil
of thickness 0.1 mm.
0
50
100
150
200
250
0 100 5 10-6 10 10-6 15 10-6 20 10-6 25 10-6
Copper 0.1 mm thickAluminium 0.22 mm thickBrass 0.1 mm thick
Vel
ocity
of f
oil (
m/s
)
Time (s)
Fig. 11. Variation of velocity for aluminium, brass and copper foils of different
thickness loaded with the blast wave.
Fig.12. A photograph showing penetrated tungsten micro particles in ground
tissue of potato tuber.
S.R Nagaraja et al. / International Journal of Mechanical Sciences 61 (2012) 1–76
velocity. In this case the maximum difference in the magnitude ofvelocity between the central point and a point at a distance of0.5 mm along the radius is o5%. Therefore, if the particles aredeposited over an area of radius 0.5 mm then all of them will havesame velocity when they leave the metal foil. Fig. 10 shows thevariation of the spray cone angle (angle of deviation-d) along theradius of the metal foil. The values plotted are over a radius of1.5 mm and at the time corresponding to maximum midpointvelocity. It is observed that spray cone angle increases withradius. The particles deposited nearer to centre of the metal foildeviate less from the axis of the shock tube (polymer tube) thanthose deposited far away from the centre. The spray cone angle inthis case is about 71 at a radius of 0.75 mm.
6. Selection of metal foil
The thickness and material of the metal foil selected is basedon the maximum velocity to be imparted to the particles. Thevelocity of the particles is assumed to be equal to the velocityof the foil. It was observed that for a given thickness aluminiumfoil has the maximum velocity compared to brass and copper.
But many (17%) of the aluminium foils of 0.18 mm failed whensubjected to blast wave loading. Fig. 11 shows velocity of foilswhich did not fail (0.1 mm brass, 0.1 mm copper and 0.22 mmaluminium). Among the foils which did not fail 0.1 mm brass foilshave the maximum velocity of deformation (�205 m/s) andhence they are selected to conduct particle penetration experi-ments into soft targets.
7. Bio-medical applications
Illustrative experiments were carried out to demonstrate the useof metal foil deformation (by blast wave loading) for bio-medicalapplications. For this a device has been built to deliver microparticles in to soft targets using the energy of the micro blast wave.This device uses the metal foils as energy transferring mechanismbetween the micro blast wave and micro particles. Using finiteelement analysis, it was concluded that brass foils of 0.1 mm thickare best suited to conduct these experiments. Fig. 6 shows aphotograph of the device used to deliver micro-particles. Experi-ments were carried out to deliver micro particles into the planttissue. Fig. 12 shows penetration of micro particle in the groundtissue of potato tuber. The depth of penetration up to 460 mm isachieved. In these experiments the micro particle (0.7 mm diametertungsten) are deposited on the posterior side of the brass foil.
8. Concluding remarks
�
The maximum midpoint deflection and the deformation velo-cities obtained from finite element analysis closely agree withthe measured values (error o13%). � Among the materials investigated (brass, aluminium, copper)for a particular thickness aluminium foils have maximumdeformation velocity.
� Brass foil of thickness 0.1 mm has maximum deformationvelocity (204 m/s) among those foils which did not fail.
� The angle of deviation from axis of penetration varies fromzero at the midpoint to about 71 at a radius of 0.75 mm forbrass foil of 0.1 mm thickness.
� The particles deposited over a radius of 0.5 mm will leave themetal foil with same velocity (maximum difference is o5%).
� Tungsten particles of 0.7 mm diameter were successfully deliveredin to plant tissue (potato tuber) with a depth of penetrationup to 460 mm.
S.R Nagaraja et al. / International Journal of Mechanical Sciences 61 (2012) 1–7 7
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