EXPERIMENTAL INVESTIGATION AND NUMERICAL SIMULATION … · Analytical and Numerical Tools -30- The literature review on the subject showed that numerical simulation of friction drilling

Proceedings of the 6th International Conference on Mechanics and Materials in Design,

Editors: J.F. Silva Gomes & S.A. Meguid, P.Delgada/Az

PAPER REF: 5371

EXPERIMENTAL INVESTIGATION ANDOF THE EXTRUSION DRILLING AND TAPPING PROCESS

Sigitas Kilikevičius1(*), Ramūnas Česnavičius1Department of Mechanical Engineering, Kaunas University of Technology, Kaunas, Lithuania

2Department of Production Engineering, Kaunas University of Technology, Kaunas, Lithuania

(*)Email: [email protected]

ABSTRACT

This paper presents an experimental investigation and numerical simulation of holes drilling

and threads tapping in thin-walled plates by using special tungsten carbide and HSS tools.

This technique is called as extrusion drilling and tapping, because the hole and the thread are

formed without chip removal. A review of the literature dealing with the analysed problem

was conducted as well as the experimental setup for extrusion drilling and tapping

experiments was described. The experiments were performed on DC

Ti-6Al-4V alloy sheets along with a numerical simulations using finite element analysis

software ABAQUS.

Keywords: thin plate, friction, drilling, tapping, numerical simulation.

INTRODUCTION

Thread machining is widely used process in various industries; however, sometimes it is

complicated due to insufficient thickness of the blank, for example in thin

order to produce a required thread length, an additional insert wel

increase the overall thickness of the wall. For this reason, non

tapping methods are used. One of them is extrusion or friction drilling and tapping by using

special tungsten carbide and HSS tool

metal becomes plastic due to significantly increased temperature in the drilling zone caused

by the friction between the tool and the workpiece and, as a consequence, the tool penetrates

the workpiece material. At that time, the tool forms an additional molten flange like a neck on

the underneath side of the sheet, which later can be frictionally tapped using a special tapper.

The main stages of extrusion drilling and tapping are shown in Fig.

a b c d e f

Fig. 1 - Extrusion drilling and tapping stages: a

c – material flow and hole forming; d

f


Editors: J.F. Silva Gomes & S.A. Meguid, P.Delgada/Azores, 26-30 July 2015

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INVESTIGATION AND NUMERICAL SIMULATION OF THE EXTRUSION DRILLING AND TAPPING PROCESS

Ramūnas Česnavičius1, Povilas Krasauskas2,

Department of Mechanical Engineering, Kaunas University of Technology, Kaunas, Lithuania

Department of Production Engineering, Kaunas University of Technology, Kaunas, Lithuania


walled plates by using special tungsten carbide and HSS tools.

extrusion drilling and tapping, because the hole and the thread are



described. The experiments were performed on DC-06, AISI 304 steel and

alloy sheets along with a numerical simulations using finite element analysis

friction, drilling, tapping, numerical simulation.


complicated due to insufficient thickness of the blank, for example in thin

order to produce a required thread length, an additional insert welding operation is required to

increase the overall thickness of the wall. For this reason, non-traditional drilling and tread


special tungsten carbide and HSS tools without cutting edges. Applying this method, the



rial. At that time, the tool forms an additional molten flange like a neck on


The main stages of extrusion drilling and tapping are shown in Fig. 1.

a b c d e f

Extrusion drilling and tapping stages: a – initial contact; b – former-tip penetration into the material;

material flow and hole forming; d – former withdrawal; e – fast travel of the tapper to the workpiece;

f – extrusion tapping; g – tapper withdrawal

NUMERICAL SIMULATION OF THE EXTRUSION DRILLING AND TAPPING PROCESSES

Department of Mechanical Engineering, Kaunas University of Technology, Kaunas, Lithuania

Department of Production Engineering, Kaunas University of Technology, Kaunas, Lithuania


walled plates by using special tungsten carbide and HSS tools.

extrusion drilling and tapping, because the hole and the thread are



06, AISI 304 steel and

alloy sheets along with a numerical simulations using finite element analysis


complicated due to insufficient thickness of the blank, for example in thin-walled parts. In

ding operation is required to

traditional drilling and tread


s without cutting edges. Applying this method, the



rial. At that time, the tool forms an additional molten flange like a neck on


a b c d e f g

tion into the material;

fast travel of the tapper to the workpiece;

Track_A

Analytical and Numerical Tools

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The literature review on the subject showed that numerical simulation of friction drilling is

conditioned by a lot of conventionalities and uncertainties as well as highly depends on

various factors such as material properties, cutting regimes, geometrical parameters of tools,

etc. (Lee, 2008; Miler, 2007; Krasauskas, 2012). Therefore, a numerical simulation of

extrusion drilling for each new material is complicated and specific. Since this method is a

recently new metal machining method, the extrusion drilling process still is not investigated

deep enough. In the time, the chipless tapping process of threads in holes formed by extrusion

drilling has not been investigated yet using numerical methods. Therefore, the purpose of this

work was to carry out an extrusion drilling and tapping experiment along with a numerical

simulation, as well as to verify the results.

EXPERIMENTAL TECHNIQUE OF THE EXTRUSION DRILLING AND TAPPING

DC-06, AISI 304 steel and Ti-6Al-4V alloy plates with 1.5 mm in thickness, which were cut

from sheet metal, were used for the experimental investigation of the extrusion drilling and

tapping processes. The mechanical properties of the materials are presented in Table 1.

Table 1 - Mechanical material properties

Material

Tensile strength,

ultimate, MPa

Tensile strength,

yield, MPa

Elongation at

break, %

Modulus of

elasticity, GPa

DC-06 370-350 170-180 41 201

AISI304 515-708 205-340 40 193

Ti-6Al-4V 1170 1100 10 114

The experiments were carried out on a CNC milling machine “DECKEL MAHO DMU-35M”

with a “Sinumerik 810D/840D” controller and “ShopMill” software using a tungsten carbide

fluteless drill with a diameter of 5.2 mm and an M6×1 HSS fluteless tapper. The experimental

setup is shown in Fig. 2.

a b c

Fig. 2 - Experimental setup of the friction drilling and tapping experiments: a – general view of the setup;

b – hole drilling experiment; c – tapping experiment

The axial force and torque were measured using a universal laboratory charge amplifier

Kistler type 5018A and a press force sensor Kistler type 9345B mounted on the CNC table.

Measuring ranges of the sensor: -10…10 kN for force, -25...25 Nm for torque; sensitivity: ≈-

3.7 pC/N for force, ≈-200 pC/Nm for torque. The amplifier converts the charge signal from

the piezoelectric pressure sensor into a proportional output voltage. The variation of the axial

drilling force and torque was recorded to a computer using a “PICOSCOPE 4424”



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oscilloscope and “PicoScope 6” software. The drilling temperature on the upper side of the

plate at the contact zone was measured using a “Fluke574” optical pyrometer (measuring

range: -30…900°C; accuracy: ±0.75% of reading; response time 250 ms) and recorded to the

computer as well.

The matrix of the drilling and tapping experiments is presented in Table 2.

Table 2 - Matrix of the drilling and tapping experiments

Material

Plate

thickness,

mm

Drilling Tapping

Spindle speed,

rpm

Tool feed rate,

mm/min

Spindle speed,

rpm

Tool feed

rate, mm/rev

Mild steel DC-06

1.5

2000/2500/3000 140

100

1

2000/2500/3000 100

2000/2500/3000 60

AISI304 stainless steel 1.5 2000/2500/3000 100

Ti-6Al-4V titanium alloy 1.5 2000/2500/3000 100

RESULTS AND DISCUSSION OF THE EXPERIMENTAL INVESTIGATION

The experiment showed that drilling parameters, such as the tool rotational speed and the feed

rate have a significant influence on the axial force and torque variation.

In order to investigate the influence of feed rate on the drilling force, DC-06 steel plates were

drilled under feed rates of 60, 100 and 140 mm/min. The results showed that an increase in

the feed rate results an increase in the axial force (Fig. 3).

Fig. 3 - Experimental drilling axial force and torque variation when spindle speed is

2000 rpm under different feed rates

The results of the investigation under different spindle speed are presented in Fig. 4. An

analysis of the experimental results showed that the axial force, during the drilling process

(from the initial contact until the end of the hole forming) varies in a very wide range. It was

defined, that the axial force reaches its maximum value when the conical part of the tool fully

penetrates into the plate. When the sheet is pierced, the axial force drastically decreases,

meanwhile the torsion moment increases. The maximum torque is reached when the conical

part of the tool is fully penetrated into the plate. It is seen from the figure that an increase of

the spindle speed leads to a decrease of both the axial force and the torque.

It was observed that the tapping force values are very low (less than 90 N), therefore these

results were not presented and discussed. The variation of the tapping torque is presented in

Fig. 5. The negative value of the torque starting at about 7 s represents the tapper withdrawal

stage when it is rotating in the reversed direction. When the spindle speed is 2000 m, the

0

200

400

600

800

1000

1200

0 1 2 3 4 5 6 7 8 9 10

Axi

al d

rillin

g f

orc

e,

N

Drilling time, s

F60 mm/min

F100 mm/min

F140 mm/min

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maximum torque is obtained between 1 and 2

torque was several times higher than the drilling torque.

a b

Fig. 4 - Experimental drilling axial force and torque variation during hole forming when feed rate

100 mm/min: a

Fig. 5 - Experimental tapping torque variation during thread tapping of

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maximum torque is obtained between 1 and 2 s, after that it gradually decreases. The tapping

torque was several times higher than the drilling torque.

a b

c

Experimental drilling axial force and torque variation during hole forming when feed rate

a – DC-06 steel; b – AISI 304 stainless steel; c – Ti-6Al

Experimental tapping torque variation during thread tapping of steel DC-06,

AISI 304 and Ti-6Al-4V alloy

s, after that it gradually decreases. The tapping

Experimental drilling axial force and torque variation during hole forming when feed rate is

6Al-4V alloy

06, stainless steel



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MATHEMATICAL BACKGROUND OF EXTRUSION DRILLING AND TAPPING SIMULATION

During friction drilling and tapping, heat is generated from two sources: plastic energy

dissipation due to the shear deformation and heating due to the friction in the tool and

workpiece contact zone.

The heating from the friction between the tool and the workpiece is the main heat source and

comprises 98-99% of the total heat, therefore the heat transfer during tool penetration into

workpiece is described (Miler, 2007):

2 2 2

2 2 2x y z f

T T T Tc k k k q

t x y zρ

∂ ∂ ∂ ∂= + + + ∂ ∂ ∂ ∂

& , (1)

where ρ is the material density; c is the specific heat, T is the temperature, t is the time, k is

the heat conductivity in x, y, and z are the coordinates; fq& is the heat generated by the friction

between the tool and the workpiece, it is expressed:

0

fT

f fq dTω= ∫& , (2)

where ω is the angular velocity of the tool and Tf is the friction moment in the contact zone.

For the finite element method simulation the temperature and strain rate dependent Johnson-

Cook model was used (Johnson, 1983). In this case, the flow stress is expressed:

( )( )0

1 1

mn pl tran

pl

melt tran

A B Clnε θ θ

σ εε θ θ

− = + + − −

&

&, (3)

where parameter A is the initial yield strength of the material at room temperature, B is the

hardening modulus; C is the parameter representing strain rate sensitivity; plε is the effective

plastic strain; plε& is the effective plastic strain rate 0ε& is the reference strain rate; n is the strain

hardening exponent; m is the parameter which evaluates thermal softening effect, θ is

temperature, meltθ and tranθ are material the melting and transition temperatures.

A failure criterion is required to characterize the material properties degradation due to the

tool penetration into the material. The Johnson–Cook failure model based on the plastic strain

was used in this study. In this model, failure occurs when the parameter D reaches a value of

1:

1

pl

f

D d .εε

= ∫ (4)

The equivalent strain to fracture fε is defined by (Johnson, 1985):

( )3

1 2 4 5

0

1 1

pd

pl

f d d e d ln dσε

ε θε

− = + + +

&

&, (5)

where d1 to d5 are material constants, which can be determined from experiments, p is the

hydrostatic pressure, i.e. the third of the trace of the Cauchy stress tensor.

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FINITE ELEMENT SIMULATION OF THE EXTRUSION DRILLING AND TAPPING PROCESSES

The simulation of the extrusion drilling and tapping was carried out on a Ti-6Al-4V alloy

plate with a thickness of 1.5 mm and an AISI 304 steel plate with the same thickness, using

ABAQUS/EXPLICIT finite element analysis software. The computational model

incorporating the workpiece, the former and the tapper is shown in Fig. 6. The workpiece was

created as a disk of 18 mm diameter and 1.5 mm thickness.

a b

Fig. 6 - Computational model of drilling (a) and tapping (b)

One of the primary difficulties in the simulation is the excessive mesh distortion in the plunge

phase, so ABAQUS/EXPLICIT finite element code based on the adaptive mesh technique,

allows automatically regenerate the mesh when the elements due to large deformation are

distorted. The adaptive meshing technique in ABAQUS/ EXPLICIT creates a new mesh and

remaps the solution parameters from the existing mesh to the newly created mesh. In this

study, the adaptive meshing was carried out for every three increments and five mesh sweeps

per adaptive mesh increment was performed. The drill and the workpiece was meshed using

element type C3D8RT, which has 8-node tri-linear displacement, temperature and reduced

integration with hourglass control. A global element size of 0.3 mm was used to mesh the

workpiece. An element size of 0.15 mm was used in the centre of the workpiece where the

tool penetrates the material. 10 layers of elements through the thickness were generated in the

workpiece. The mesh of the workpiece contained 89710 elements. The tapper was meshed

using element type C3D4T due to its complex shape.

In order to save computational time, the mass scaling technique that modifies the densities of

the materials in the model and improves the computational efficiency was used. In this study,

mass scaling was performed every 10 increments to obtain a stable time increment of at least

0.0001 s step time.

It was assumed that the drill and the tapper are rigid and adiabatic, the frictional contact is

described by Coulomb’s friction law with the constant coefficient of friction and 100% of

dissipated energy caused by the friction between the parts was converted to heat. The

coefficient of friction was set to 0.05.

The boundary conditions (Fig. 6) were set as follow: the outer surface of the workpiece was

fixed in all degree of freedom; the top and bottom surfaces of the workpiece were under free

convection with the convection coefficient of 30 W/m2K; the ambient air temperature and the

initial temperature of the workpiece were set to 295 K (22ºC).

Material properties and the Johnson-Cook parameters used for the simulation of the drilling

and tapping processes are presented in Table 3 (Frontań, 2012; Lesuer, 2000).

f1

ω2

ω1

f2



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The Jonson-Cook material damage parameters used in the simulation for AISI 304 were as

follow: d1 = 0.69, d2 = d3 = d5 = 0, d4 = 0.0546 (Frontań, 2012). Accordingly, for Ti-6Al-4V:

d1 = -0.09, d2 = 0.25, d3 = -0.5, d4 = 0.014, d5 = 3.87 (Lesuer, 2000).

Table 3 - Material properties and the Johnson-Cook parameters

Parameter Units AISI 304 Ti-6Al-4V

Young modulus, E GPa 207.8 113.8

Poisson‘s ratio, ν - 0.3 0.342

Density, ρ N/m3 8000 4430

Melting temperature,meltθ K 1673 1878

Specific heat capacity J/(kgK) 452 526.3

Thermal expansion, L

α 10-6

K-1

17.8 10.6

Initial yield strength A MPa 280 1098

Hardening modulus B MPa 802.5 1092

Strain hardening exponent n - 0.622 0.93

Thermal softening exponent m - 1.0 1.1

Strain rate constant C - 0.0799 0.014

Reference strain rate 0ε& 1/s 1.0 1.0

RESULTS OF THE SIMULATION AND COMPARISON TO THE EXPERIMENTS

The simulation showed that the maximum temperature is reached during the drilling stage

when the conical part of the tool penetrates the workpiece (Fig. 7c), it reaches up to 1642 K

(1369ºC) at that moment for Ti-6Al-4V alloy, when ω1=3000 rpm, feed ratio f1=100 mm/min,

and 1180 K (907ºC) for AISI 304 steel. The temperature is up to 1270 K (997ºC) in the final

stage of the drilling (Fig. 7d) for Ti-6Al-4V alloy and 969 K (696ºC) for AISI 304 steel.

a b

c d

Fig. 7 - Workpiece temperature (units are in K) drilling Ti-6Al-4V alloy at various distances of tool travel:

a – 1.5 mm; b – 3 mm; c – 7.86 mm; d – 12 mm

The temperature variation on the upper side of the workpiece at the contact zone is shown in

Fig. 8.

Track_A


Fig. 8 - Temperature on the upper side of the workpiece at the contact zone drilling AISI

The surface temperature variation of the simulation was obtained from the identical position

where the surface temperature was measured in the experiments. T

value on the upper side of the workpiece at the contact zone obtained by simulation was

589ºC. The simulation and the experiments both showed very similar results.

The shape of the neck and the equivalent plastic strain after the fin

shown in Fig. 9a, and the same after the thread is tapped

obtained on the Ti-6Al-4V alloy plate, under the following regimes:

mm/min for drilling and ω2=100 rpm and

information for the AISI 304 alloy plate is presented in Fig.

a b

Fig. 9 - Equivalent plastic strain in the final stag

Ti-6Al-4V alloy plate,

a b

Fig. 10 - Equivalent plastic strain in the final stage of drilling (a) and after the thread is ta

AISI 304 steel plate,

The shape of the workpiece deformation during drilling and tapping was close to the actual

one obtained by the experiment.

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Temperature on the upper side of the workpiece at the contact zone drilling AISI


where the surface temperature was measured in the experiments. The maximum temperature



The shape of the neck and the equivalent plastic strain after the final stage of drilling are

9a, and the same after the thread is tapped – in Fig. 9b. These results were

4V alloy plate, under the following regimes: ω1=3000 rpm,

=100 rpm and f2=1 mm/rev for tapping. Accordingly, the same

304 alloy plate is presented in Fig. 10.

a b

Equivalent plastic strain in the final stage of drilling (a) and after the thread is tapped (b) in the

4V alloy plate, ω1=3000 rpm, f1=100 mm/min, ω2=100 rpm and f2=1

a b

Equivalent plastic strain in the final stage of drilling (a) and after the thread is ta

304 steel plate, ω1=3000 rpm, f1=100 mm/min, ω2=100 rpm and f2=1


one obtained by the experiment.

Temperature on the upper side of the workpiece at the contact zone drilling AISI 304 steel


he maximum temperature



al stage of drilling are

9b. These results were

=3000 rpm, f1=100

or tapping. Accordingly, the same

e of drilling (a) and after the thread is tapped (b) in the

=1 mm/rev

Equivalent plastic strain in the final stage of drilling (a) and after the thread is tapped (b) in the

mm/rev




The comparison of the experimental an

Fig. 11, while for Ti-6Al-4V alloy

Fig. 11 - Comparison of the experimental and simulation results is presented for drilling (a) and tapping (b)



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The comparison of the experimental and simulation results for AISI 304 steel is presented in

4V alloy - in Fig. 12.

Comparison of the experimental and simulation results is presented for drilling (a) and tapping (b)

AISI 304 steel, f1=100 mm/min

4 steel is presented in


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Fig. 12 - Comparison of the experimental and simulation results is presented for drilling (a) and tapping (b)

The comparison of the experimental and simulation results for tapping is presented in Fig.

The profiles of the experimental and simulated force and torque variations were quite similar,

therefore it is possible to conclude that the presumptions taken in the simulation are correct

and realistically describe the extrusion drilling and tapping processes. The com

model could be useful for prediction of reasonable extrusion drilling and tapping regimes.

However, in order to get more precise results and a better agreement between the

experimental and simulation results, the computational model could be imp

more realistic friction model along with taking into account the tool temperature and

deformations.

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Ti-6Al-4V alloy, f1=100 mm/min

The comparison of the experimental and simulation results for tapping is presented in Fig.

f the experimental and simulated force and torque variations were quite similar,


and realistically describe the extrusion drilling and tapping processes. The com



experimental and simulation results, the computational model could be imp



The comparison of the experimental and simulation results for tapping is presented in Fig. 13.

f the experimental and simulated force and torque variations were quite similar,


and realistically describe the extrusion drilling and tapping processes. The computational



experimental and simulation results, the computational model could be improved by using a




Fig. 13 - Comparison of the experimental and simulation results

CONCLUSIONS

An experimental analysis and a numerical simulation of extrusion drilling and tapping plates

of various materials were carried out and the axial force and torque variations were measured

under different drilling and tapping regimes.

The analysis of the experimental results s

process (from the initial contact until the end of the hole forming) varies in a very wide range.

It was detected, that the axial force reaches its maximum value when the conical part of the

tool fully penetrates into the plate. When the plate is pierced, the axial force drastically

decreases, meanwhile the torsion moment increases. The maximum torque is reached when

the conical part of the tool is fully penetrated into the sheet. An increase of the spindle sp

leads to a decrease of both the axial force and the torque, while an increase in the feed rate

results an increase in the axial force. The tapping process experimental investigation showed

that the tapping torque is several times higher than the drilli

is very low compared to the drilling force.

The simulation showed that the maximum temperature in the workpiece is reached during the

drilling stage when the conical part of the tool penetrates the workpiece. Under the fol

drilling regime: ω1=3000 rpm,

for Ti-6Al-4V alloy and 1180 K (907ºC) for AISI

(997ºC) in the final stage of the drilling for Ti

steel. The variation of temperature on the upper side of the workpiece at the contact zone

obtained by the simulation and the experiments was very similar.

The comparison of the experimental and simulation results leads to the conclusion that the

presumptions taken in the simulation are correct and realistically define the friction drilling



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omparison of the experimental and simulation results for tapping, ω2=100 rpm and

lysis and a numerical simulation of extrusion drilling and tapping plates


under different drilling and tapping regimes.

The analysis of the experimental results showed that the axial force, during the drilling



ates into the plate. When the plate is pierced, the axial force drastically


the conical part of the tool is fully penetrated into the sheet. An increase of the spindle sp



that the tapping torque is several times higher than the drilling torque while the tapping force

is very low compared to the drilling force.


drilling stage when the conical part of the tool penetrates the workpiece. Under the fol

=3000 rpm, f1=100 mm/min, it is up to 1642 K (1369ºC) at that moment

4V alloy and 1180 K (907ºC) for AISI 304 steel. The temperature is up to 1270 K

(997ºC) in the final stage of the drilling for Ti-6Al-4V alloy and 969 K (696ºC) for AISI


obtained by the simulation and the experiments was very similar.


ons taken in the simulation are correct and realistically define the friction drilling

=100 rpm and f2=1 mm/rev

lysis and a numerical simulation of extrusion drilling and tapping plates


howed that the axial force, during the drilling



ates into the plate. When the plate is pierced, the axial force drastically


the conical part of the tool is fully penetrated into the sheet. An increase of the spindle speed



ng torque while the tapping force


drilling stage when the conical part of the tool penetrates the workpiece. Under the following

mm/min, it is up to 1642 K (1369ºC) at that moment

304 steel. The temperature is up to 1270 K

4V alloy and 969 K (696ºC) for AISI 304



ons taken in the simulation are correct and realistically define the friction drilling

Track_A


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and tapping process. The computational model could be useful for prediction of rational

frictional drilling and tapping regimes in order to lower drilling forces and, as a consequence,

to decrease tool wear and extend the lifetime of tools.

REFERENCES

[1]-Frontań J. et all. Ballistic performance of nanocrystalline and nanotwinned ultrafine

crystal steel. Acta Materialia 60, 2012, p.1353-1367.

[2]-Johnson G, Cook W Constitutive Model and Data for Metals Subjected to Large Strains,

High Strain Rates and High Temperatures: Proceeding of the 7th Int. Symp. on Ballistics, The

Hague, 1983, p. 1-7.

[3]-Johnson G., Cook W. Fracture characteristics of three metals subjected to various strains,

strain rates, temperatures and pressures. Eng. Fract. Mech. 21, 1985, p. 31-48.

[4]-Lee SM, Chow HM, Huang FY, Yan BH. Friction drilling of austenitic stainless steel by

uncoated and PVD AlCrN- and TiAlN-coated tungsten carbide tools. International Journal of

Machine Tools and Manufacture, 2008, 49, p. 81- 88.

[5]-Lesuer D. Experimental Investigations of Material Models for Ti-6AL-4V Titanium and

2024-T3 Aluminum, U.S. Department of Transportation Federal Aviation Administration,

DOT/FAA/AR-00/25, 2000.

[6]-Krasauskas P, Keselys T, Kilikevičius S. Experimental Investigation and Simulation of

Stainless AISI 304 Steel Thermoplastic Drilling: Proceedings of 17th International

Conference, Kaunas, Mechanika, 2012, p. 150-154.

[7]-Miller SF, Shih AJ. Thermo-mechanical finite element modelling of the friction drilling

process. Journal of Manufacturing Science and Engineering, 2007, 129, p. 532 -538.

Documents

EXPERIMENTAL INVESTIGATION AND NUMERICAL SIMULATION … · Analytical and Numerical Tools -30- The literature review on the subject showed that numerical simulation of friction drilling