Laboratory for Laser Materials Synthesis & Fabrication Department of Materials Science & Engineering UNIVERSITY OF TENNESSEE, Knoxville, TN Ab-initio Computational

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Laboratory for Laser Materials Synthesis & FabricationDepartment of Materials Science & Engineering

UNIVERSITY OF TENNESSEE, Knoxville, TN

Ab-initio Computational Approach to Ab-initio Computational Approach to Laser Micro-machining of Laser Micro-machining of

Structural CeramicsStructural Ceramics

Anoop N. Samant, Anoop N. Samant,

Narendra B. DahotreNarendra B. Dahotre

Laboratory for Laser Materials Synthesis & Laboratory for Laser Materials Synthesis & FabricationFabrication

Department of Materials Science & Engineering,Department of Materials Science & Engineering,University of Tennessee,University of Tennessee,

Knoxville, TNKnoxville, TN

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OUTLINEOUTLINE

Objectives

Structural Ceramics

Methodology

Laser Machining of Structural Ceramics

Physical Phenomena in Machining

Data Analysis

Contribution of current work

Significance of research

Future Work

Conclusions

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OBJECTIVESOBJECTIVES

Demonstrate feasibility of laser machining of

structural ceramics.

Understand material removal mechanisms (MRM)

Develop an ab-initio computational model based on

MRM.

Use model for advance predictions of laser processing

conditions to attain desired attributes.

Save considerable energy and time.

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Properties Low thermal and electrical conductivity High hardness Chemical stability High thermal resistance

Applications Machine tools, valves, bearings, rotors Optical and Electronic devices Hazardous Waste Disposal

Examples Silicon Carbide, Alumina, Silicon Nitride, Magnesium Oxide,

Zirconia

STRUCTURAL CERAMICSSTRUCTURAL CERAMICS

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LASER MACHININGLASER MACHINING

An operation similar to laser drilling subsequently conducted on

neighboring locations.

Advantages :

Non contact processing

Capability of automation

Reduced manufacturing costs

Efficient material utilization

Reduced heat-affected zone (HAZ)

High productivity

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LASER MACHININGLASER MACHINING

Fig.3 Types of Laser Machining [2]

Fig.2 Laser Machining [1][1]Kalpakjian, Serope and Steven R. Schmid, Manufacturing Engineering

and Technology, Upper Saddle River, New Jersey: Prentice Hall, Inc, 2001.

[2]Samant and Dahotre, Journal of European Ceramic Society, 29(2009) 969.

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METHODOLOGYMETHODOLOGY Come up with optimum pulse width, pulse energy, and pulse

repetition rate to develop sufficient laser-ceramic interaction.

Vary processing parameters to machine cavities of different

dimensions.

Develop 3D-thermal model to generate temperature profiles.

Incorporate different physical phenomena into the developed

model.

Correlate predicted attributes of machined cavities with

observed features.

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Symbol Property Value

d Out of focus beam diameter 0.5 mm

λ Laser Wavelength 1,064 nm

δf Focal Length 120 mm

SILICON CARBIDE MACHININGSILICON CARBIDE MACHININGTable 1. Laser Parameters (JK 701 pulsed Nd:YAG laser )

Fig.4 Through holes in 2mm and 3mm SiC plates [1].

25 and 125 pulses machined 2 and 3 mm plates at 6 J, 0.5 ms and 50 Hz.

[1] Samant et. al., International Journal of Advanced Manufacturing Technology, in press.

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Fourier’s Second Law for maximum surface

temperature:

Radiation losses at the surface :

⎥⎦

⎤⎢⎣

⎡

∂∂

+∂

∂+

∂∂

=∂

∂2

2

2

2

2

2

z

t)T(z,

y

t)T(y,

x

t)T(x,á(T)

t

t)z,y,T(x,

( )404 Tt)0,y,T(x,åóäaIz

t)y,0,T(x,

y

t)y,0,T(x,

x

t)y,0,T(x,k(T) −−=⎟⎟

⎠

⎞⎜⎜⎝

⎛∂

∂+

∂

∂+

∂

∂−

( )0Tt)D,y,T(x, h(T)z

t)H,y,T(x,

y

t)H,y,T(x,

x

t)H,y,T(x,)T(k −=⎟⎟

⎠

⎞⎜⎜⎝

⎛∂

∂+

∂

∂+

∂

∂−

(1)

(2)

(3)

ε - emissivity , k(T) - thermal conductivity, T0- initial temperature, h(T) - heat transfer

coefficient, H – plate thickness, a – absorptivity (1 due to multiple reflections. [1]) [1] Mazumdar et. al., J.Appl.Phys., 51(2), 1980

Convection taking place at the bottom:

TEMPORAL EVOLUTIONTEMPORAL EVOLUTION

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Temperature during pulse OFF time [1] :

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−

⎥⎥⎦

⎤

⎢⎢⎣

⎡−−+=

)T(k

t)T()T(herf

)T(k

t)T(hexp)TT(TT

offoffii

'i

αα11

2

2

0

)T(k

/t)T(

d

PaTT on'ii

παπ 218

+= −

(4)

(5)

Ti - Temperature during heating of pulse i, toff - OFF period between

successive pulses, erf - error function, α(T) - thermal diffusivity

T’i-1 - temperature during cooling of the earlier pulse, ton - pulse duration,

P – incident beam power [1] Konstantinos et.al. , Journal of Materials Processing Technology 183 (2007), 96.

Temperature during pulse ON time [1] :

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Fig.5 Heating curves for a) 2mm and b) 3mm thick SiC plate

Temperature drops during the OFF

time and rises during the ON time of

the laser giving the heating curve a

meandering nature.

Maximum surface temperature

reached while processing 3mm thick

plate is higher than that reached while

processing 2 mm plate.

High temperatures exist for extremely

short time and rapidly drops due to

self quenching.

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EVAPORATION LOSSESEVAPORATION LOSSES Rate of evaporation :

21

2

/

s

vsd kT

m)T(pj ⎥

⎦

⎤⎢⎣

⎡=

π

mv - mass of vapor molecule, Ts-surface temperature, k - Boltzmann

Constant , p(Ts) - saturation pressure, p0 – ambient pressure

Material loss : ρtimej

z deva

×=

Corresponding drop in temperature :

d

t)T(tgarc

d)T(k

LjT

/vd

eva

απ

4223=Δ

(6)

(7)

(8)

Lv - latent heat of evaporation

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DISSOCIATION ENERGY LOSSESDISSOCIATION ENERGY LOSSESPossible dissociation species :

Si(l), C(s), C(g), Si(g), Si3(g), Si2(g), SiC2 (g), Si2C(g) and Si(s)

Most likely reaction at 3103 K:

(9)

Volume of hole: 4

2avacyl zdπ

(10)

(assuming cylinder of diameter

zava = available melt depth = ztotal - zeva = melt depth from surface - evaporated depth Energy Loss :

310422 −××Δ.VolumeG

(11)

≈ (Volume/ 22.4 x 10-3) moles)3/d

)s()l( CSiSiC +=

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RECOIL PRESSURERECOIL PRESSURE

Cause : Evaporation of the melt surface exposed to laser.

Effective melt depth zeff: Portion remaining after expelling a

fraction of the total melt depth.

Recoil pressure pr : Is a function of the material properties,

maximum surface temperature and input energy [1] :

⎟⎠

⎞⎜⎝

⎛+

=2

2

221

691

4 b.

b

L

.

aP

pd

v

rπvvs LmTkb /=2

(12)

[1] Anisimov , Sov. Phys. JETP 27 (1968), 182

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Surface tension effect : Modifies pressure on melt, thus

affecting depth of machined cavity [1].

Effective beam radius: Beam radius changes with change in

machined depth [2] .

Velocity of expulsion [3]:

SURFACE TENSIONSURFACE TENSION

( ) 21

2

2

41

2/ft

eff d

zdr

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛ ++=

π

δλ

tr

r/p)t(v

eff

effrexp

τρ

−=

1

(13)

(14)

τ - surface tension coefficient of liquid Si , t – time, reff – effective beam

radius, ρ - density [1] Han et.al., Journal of Heat Transfer, 127 (2005),1005.

[2] Salonitis et.al., Journal of Materials Processing Technology 183 (2007), 96

[3] Matsunawa et.al., J. Phys. D: Appl. Phys. 30(1997),798.

(13)

(14)

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MACHINED CAVITYMACHINED CAVITY DEPTH DEPTHMachined cavity: Depth of

cavity formed due to expulsion of

available melt depth [1] :

∑=t

elledexpt zz0

dt)t(vzt

expelledexp ∫=0

Fig.6 Cavity Evolution

(15)

(16)

zexpelled – Depth expelled at different time instants

zt – Total cavity depth formed at a certain time instant

[1] Semak et. al., J. Phys. D: Appl. Phys. 39 (2006),590.

Predicted pulses: 21 and 103

pulses for machining through a 2

and 3 mm plate.

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MACHINED CAVITY DEPTHMACHINED CAVITY DEPTH

Fig.7 Stages of Cavity Evolution

Till t2, material expelled

in upward direction.

Around t3, direction of

material expulsion

reversed due to least

resistance to the recoil

pressure by small mass

of supporting material at

the bottom.

At t4, all the rest of

molten material expelled

and a clean through

cavity formed.

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ALUMINA MACHININGALUMINA MACHINING

Applications: Substrate in hybrid circuits, aerospace industry.

Dissociation at 3250K:

Machining mechanism: Dissociation, melt expulsion by recoil

pressure and evaporation.

Predicted pulses: 3, 7, 16 and 19 pulses for machining 0.26, 0.56, 3.23

and 4.0 mm respectively at 0.5ms, 4J and 20Hz.

232 512 O.AlOAl )s( += (17)

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ALUMINA MACHININGALUMINA MACHINING

Fig.9 Cavities in alumina [1]

Fig.10 Evolution of cavities [1]

[1] Samant and Dahotre, Int. Journal of Machine Tools and Manufacture, 48 (2008), 1345.

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MAGNESIUM OXIDE MACHININGMAGNESIUM OXIDE MACHINING

Applications: Refractory and brake linings, thin film semi-conductors.

Dissociation at 3123K:

Machining mechanism: Dissociation followed by evaporation.

Predicted machining times: 0.11, 0.2, 0.25 and 0.8 s for machining

0.25, 0.86, 1.54 and 3mm respectively at 0.5ms, 4 J and 20 Hz.

(19))g()s( OMgMgO +=

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MAGNESIUM OXIDE MACHININGMAGNESIUM OXIDE MACHINING

Fig.13 Cavities in

MgO [1]

Fig.14 Evolution of cavities with

time [1]

[1] Samant and Dahotre, Optics and Lasers in Engineering, 47(2009),570.

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PHYSICAL PHENOMENA IN PHYSICAL PHENOMENA IN DIFFERENT CERAMICSDIFFERENT CERAMICS

Melting Dissociation Evaporation

Silicon Carbide (SiC) Alumina (Al2O3) Magnesium Oxide (MgO)

Physical Process

Material

Table 2. Physical Phenomena Governing Machining in Different Ceramics [1]

[1] Samant and Dahotre, Ceramics International, in press.

Melting Dissociation Evaporation

Silicon Carbide (SiC) Alumina (Al2O3) Magnesium Oxide (MgO)

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Fig.8 Flowchart for computations

FLOW CHARTFLOW CHART

Stepwise procedure to

achieve final machining

parameters starting with

material properties and

process parameters.

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DATA ANALYSISDATA ANALYSISTable 3. Comparison between experimental and predicted attributes of machined cavities

CeramicDepth of machined

cavity (mm)Pulsesexperimental

(Time, sec)

Pulsespredicted

(Time, sec)

Al2O3

0.26 5 (0.25) 3 (0.15)

0.56 10 (0.5) 7 (0.35)

3.23 20 (1.0) 16 (0.8)

4 30 (1.5) 19 (0.94)

SiC2 25(0.5) 21(0.41)

3 125(2.5) 103(2.05)

MgO

0.25 3 (0.15) 2 (0.11)

0.86 6 (0.3) 4 (0.2)

1.54 9 (0.45) 5 (0.25)

3 20 (1) 16 (0.8)

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CONTRIBUTION OF CURRENT WORK CONTRIBUTION OF CURRENT WORK

Prior work conclusions: a) Machining comprises of melting

and material removal by expulsion [1].

b) Machining takes place by single step evaporation without

melting [2].

c) Effect of multiple reflections neglected.

Current work conclusions: a) Material removal occurs by a

combination of melt expulsion, dissociation and evaporation.

b) Multiple reflections affect the amount of absorbed energy.

[1] Salonitis et.al, Journal of Materials Processing Technology, 183(2007) 96.

[2] Atanasov et. al, Journal of Applied Physics, 89(2001) DOI: 10.1063/1.1334367

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SIGNIFICANCE OF RESEARCH SIGNIFICANCE OF RESEARCH

Proposed systematic approach is an advancement of

existing computational approach to ceramic machining.

Advance prediction of number of pulses/ pulse duration/

pulse energy possible.

Developed model can be extended to two and three

dimensional laser machining.

A system with optimum machining rate can be

generated.

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FUTURE WORKFUTURE WORK

Laser Machining in 2 D (Laser Cutting) and 3D

(engraving complex shapes).

Effect of multiple passes on machined depth by

considering preheating effect.

In-situ temperature measurements and

absorptivity predictions using thermocouples.

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SUMMARYSUMMARY Structural ceramics were successfully machined.

Theoretical model incorporating several vital effects encountered during machining was developed.

Model predictions compared well with experimental observations for machining.

Model aids to provide an advance estimate of number of pulses required for machining required depth or the depth machined after applying certain number of pulses.

Laser Fluence and machining time could also be predicted.

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THANK YOUTHANK YOU

Documents

Laboratory for Laser Materials Synthesis & Fabrication Department of Materials Science & Engineering UNIVERSITY OF TENNESSEE, Knoxville, TN Ab-initio Computational