Effect of Backing Plate in Laser Treatment

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Effect of backing plate on thermal cycles in laser surface

treatment: Theoretical and Experimental study

Thesis submitted to Indian Institute of Technology Kharagpur for the award of the

degree of

Master of Technology

in

Mechanical Engineering with Specialization in

Manufacturing Science and Engineering

by

Mohit Goenka

(10ME31001)

Under the guidance of

Prof. A. K. Nath

Department of Mechanical Engineering

Department of Mechanical Engineering

Indian Institute of Technology Kharagpur

2014-2015


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INDIAN INSTITUTE OF TECHNOLOGY

KHARAGPUR

CERTIFICATE

This is to certify that the thesis entitled, Effect of backing plate on thermal cycles

in laser surface treatment: Theoretical and Experimental study submitted by

Mr. Mohit Goenka (10ME31001) as a part of Master of Technology Project in

Indian Institute of Technology, Kharagpur is a bonafide work completed under my

supervision and guidance.

He has been sincere, diligent and eager to grasp more knowledge in his field of work.

I wish him good luck in his future endeavours.

Date: May 31, 2015

Prof. A.K Nath

Place: IIT Kharagpur


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CERTIFICATE OF EXAMINATION

This is to certify that we have examined the thesis entitled Effect of backing plate

on thermal cycles in laser surface treatment: Theoretical and Experimental

study submitted by Mohit Goenka and hereby accord our approval of it as a work

carried out and presented in a manner required for its partial fulfillment for the degree

of Master of Technology in Manufacturing Sciences for which it has been submitted

.This approval does not necessarily endorse to or accept every statement made,

opinion expressed or conclusion as recorded in the thesis. It only signifies the

acceptance of the thesis for the purpose for which it is submitted.

External Examiner

Date: May 2015

Place: Kharagpur


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DECLARATION

I certify that

a. The work contained in this report is original and has been done by me under

the guidance of my supervisor.

b. The work has not been submitted to any other Institute for any degree or

diploma.

c. I have followed the guidelines provided by the Institute in preparing the

report.

d. I have conformed to the norms and guidelines given in the Ethical Code of

Conduct of the Institute.

e. Whenever I have used materials (data, theoretical analysis, figures, and text)

from other sources, I have given due credit to them by citing them in the text

of the report and giving their details in the references. Further, I have taken

permission from the copyright owners of the sources, whenever necessary.

Mohit Goenka


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v

ABSTRACT

An analytical solution for the variation in thermal cycles in a finite thickness

workpiece, kept on different semi-infinite backing materials and irradiated by a

stationary and moving laser beam has been derived. The effects of laser beam

diameter, scan speed and backing material with heat sink compound in between on

thermal cycles have been investigated experimentally. The thermal cycles are

recorded using a non-contact type IR pyrometer. Mild steel, stainless steel and

aluminium are used as backing materials, considering their heat conduction capacity.

The effect of these backing materials on cooling rate, affected heat region and

solidification time are studied. The cooling trend from analytical model and

experiment has been compared. For experiment, a 1 mm finite AISI 1020 sheet has

been used and it is irradiated with a stationary laser beam for 0.9 sec for stationary

laser beam by varying spot diameters and keeping the power density constant. For

moving laser beam, sample has been irradiated with 3 mm spot diameter by varying

scan speed. The study shows that the cooling rate at surface i.e. at z=0, for a sample

decreases with increase in laser spot diameter and this trend is maintained for all the

six samples considered. Cooling is faster as the thermal conductivity of the backing

material, with heat sink compound, increases but for a same backing material, without

heat sink compound, it decreases. Cooling rate at z=0 for a finite mild steel sheet is

minimum and for semi-infinite mild steel sheet it is maximum. Solidification time or

melt pool life time follows the same trend as above, viz. for a given sample it

decreases with the decrease in spot diameter. For a given spot diameter, with increase

in thermal conductivity of backing plate it decreases. With increase in scan speed the

effect of backing plate decreases viz. for higher scan speed value of 3500 mm/mincooling rate across all samples are nearly close by and consecutively the effect of

backing plate is not observed. For a range of ~0.7-0.75 Crvalue thermal cycle plot

from analytical model is in good agreement with the experimental graphs for a

moving heat source at non-melting condition. All these have been demonstrated using

thermal cycle plots, cooling rate bar plots, and heat affected region plots generated

using experimental data.


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ACKNOWLEDGEMENT

I would like to express my deep sense of gratitude and profound thanks to Prof. A.K

Nath, Department of Mechanical Engineering, IIT Kharagpur for providing me with

this wonderful opportunity to work as a part of the team under his guidance. I am

greatly thankful to him for encouraging us to come up with innovative solutions.

I am also indebted to Mr Muvvala Gopinath for patiently mentoring and helping me

out with project. I would like to credit Mr Shitanshu Shekhar Chakraborty for writing

the MATLAB programme.

Mohit Goenka

10ME31001


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vii

LIST OF FIGURES

Fig. No. Title Page No.

3.1

Schematic representation of an infinite sheet subjected to uniform

heat flux at the top surface. 4

3.2 Laser irradiation on a finite sheet of thickness h unit 5

3.3 Schematic representation of heat partitioned at the z=0 interface 8

3.4(i) Radial conduction for stationary laser beam, (ii) Radialconduction for moving laser source beam

8

4.1.1 2 kW Ybfiber laser used 9

4.1.2 laser on time pulse for 0 sec input interaction time 10

4.1.3 laser on time pulse for 0.5 sec input interaction time 10

4.2.1

(a) Schematic representation of a stationary laser beam falling on asemi-infinite mild steel plate for 0.9sec, (b) Schematic representationof a stationary laser beam falling on finite mild steel sheet placed ona backing material with heat sink compound applied

12

4.2.2

(c) Schematic representation of a stationary laser beam falling onfinite mild steel sheet for 0.9sec, (b) Schematic representation of astationary laser beam falling on finite mild steel sheet placed on abacking material with no heat sink applied

12

4.3.1(a) Power meter, model-COMET-10K-V1 ROHS OPHIR make,accuracy 5% (b) Laser head (c) Pyrometer (d) Mild steel, AISI-1020 sample placed at an angle of 450with the vertical

13

4.3.2Reading for laser power absorptivity for AISI-1020 at varied laser

powers 14

5.1.1

Thermal plot for top surface i.e. z-=0 for different samples on beingirradiated with a 2mm stationary laser spot diameter for 0.9sec fromAnalytical Model using MatLab

15

5.1.2

Thermal plot for top surface i.e. z-=0 for different samples on beingirradiated with a 3mm stationary laser spot diameter for 0.9sec from

Analytical Model using MatLab15

5.2.1Experimental thermal cycle at z-=0 for samples on being irradiatedwith a 4mm laser spot diameter for 0.9sec 16

5.2.2

Cooling plot for top surface i.e. z-=0 for different samples on beingirradiated with a 2mm laser spot diameter for 0.9sec usingexperimental data

16

5.2.3


17

5.2.4


17

5.2.5Cooling rate for samples at z = 0 on irradiation with stationary source

of different spot diameters 18


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viii

5.2.6

(a) Intensity distribution for different spot radius (b) Olympus ModelSZ 1145TR PR zoom sterio microscope (c) 3X Magnification imageof affected region for 3mm spot on finite MS sheet

20

5.3.1

(a) Heat affected region on the finite mild steel sheet for differentlaser spot diameter, (b) Affected region on the semi-infinite mild

steel sheet for different laser spot diameter21

5.3.2Plot of heat affected region on sample surface; 2mm spot diameter, P= 300W, V=0 and t= 0.9 sec 21

5.3.3Plot of heat affected zone on sample surface; 3mm spot diameter, P =675W, V=0 and t= 0.9sec 22

5.3.4Plot of heat affected zone on sample surface; 4mm spot diameter, P =1200W, V=0 and t = 0.9 sec 22

5.4.1Cooling curve for different samples; 3mm spot diameter, P=675W,V=0(scan speed) and t = 0.9 sec 23

5.4.2Cooling curve for different samples; 4mm laser spot dia, P=1200W,V=0(scan speed) and t = 0.9sec 23

5.5.1Cooling trend at z=0 for semi-infinite mild steel sheet with differentlaser spot diameters 24

5.5.2Cooling trend at z=0 for finite mild steel sheet with different laserspot diameters 24

5.6.1Thermal cycle for 1mm MS plate at varying scan speed at z = 0, P =

400W and 3 spot diameter 25

5.6.2

Thermal cycle for 1mm MS plate at varying scan speed at z = 0, P =

600W and 3 spot diameter 25

5.7.1Cooling cycle at z = 0 for various samples with P = 600W, 3 spotdiameter and 2000mm/min scan speed as laser parameter 26

5.7.2Cooling cycle at z = 0 for various samples with P = 600W, 3 spotdiameter and 2500mm/min scan speed as laser parameter

26

5.7.3Cooling cycle at z = 0 for various samples with P = 600W, 3 spot

diameter and 3000mm/min scan speed as laser parameter 27


5.7.5Cooling rate for samples at z = 0 on irradiation with moving heatsource of different scan speed, P = 600W and 3mm spot diameter 28


5.7.7Cooling cycle at z = 0 for various samples with P = 400W, 3 spot

diameter and 1500mm/min scan speed as laser parameter 30

5.7.8Cooling rate for samples at z = 0 on irradiation with moving heatsource of different scan speed, P = 400W and 3mm spot diameter 31

5.8.1

Cooling cycle at z = 0 from IR pyrometer for 1mm MS sheet, P =

400W, 3 spot diameter and varying laser scan speed 32


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LIST OF TABLES

5.8.2Cooling cycle at z = 0 from Analytical model for 1mm MS sheet, P =400W, 3 spot diameter and varying laser scan speed, Cr= 0.7 32

5.8.3Cooling cycle at z = 0 from IR pyrometer for 1mm MS sheet, P =

600W, 3 spot diameter and varying laser scan speed 33

5.8.4 Cooling cycle at z = 0 from Analytical model for 1mm MS sheet, P =600W, 3 spot diameter and varying laser scan speed, Cr= 0.7 33

5.8.5Cooling cycle at z = 0 from Analytical model for 1mm MS sheet, P =600W, 3 spot diameter and varying laser scan speed, Cr= 1 34

Table No. Title Page No.

4.2.1 Laser parameters for stationary heat source, interaction time keptconstant at 0.9s

11

4.2.2Laser parameters for Moving heat source, laser spot diameter

constant at 3mm 11

4.2.3Materials used for the experiment and their properties. (source:

EES and wikipidea)11

4.3Reading for laser power absorptivity for AISI-1020 at varied laserpowers

14

5.2 Temperature at two fixed interval for different spot diameter 18

5.3 Radius of the heat affected region on the samples surface 20

5.7.1Temperature at two fixed interval for a given laser scan speed, P =

600W28

5.7.2Temperature at two fixed interval for a given laser scan speed, P =

400W31


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TABLE OF CONTENTS

ABSTRACT.............................................................................................................................. v

ACKNOWLEDGEMENT...................................................................................................... vi

LIST OF FIGURES............................................................................................................... vii

LIST OF TABLES.................................................................................................................. ix

1. INTRODUCTION................................................................................................................ 1

2. LITERATURE SURVEY.................................................................................................... 2

3. ANALYTICAL MODELLING.......................................................................................... 4

4. EXPERIMENTAL DETAILS............................................................................................ 9

4.1. Specifications of Laser used...................................................................................... 9

4.2. Experiment Procedure and Laser Parameters.......................................................... 10

4.3. Absorptivity of Mild Steel (AISI-1020):................................................................. 13

5. RESULTS AND DISCUSSION.................................................................................... 15

5.1. Thermal cycle plot from Analytical Modelling....................................................... 15

5.2. Cooling plots of thermal cycle by IR sensor Stationary Heat Source................... 16

5.3. Effect of laser spot diameters on affected region..................................................... 20

5.4. Effect of backing on solidification time................................................................... 23

5.5. Effect of laser spot diameter on solidification time................................................. 24

5.6. Thermal Cycle for 1mm mild steel plate Moving Heat Source............................ 25

5.7. Effect of backing plate on cooling rate Moving Heat Source............................... 26

5.8. Cr, effective radial heat conduction: Moving Heat Source...................................... 32

6. CONCLUSION.............................................................................................................. 35

7. REFERENCES............................................................................................................... 36

8. APPENDIX..................................................................................................................... 37


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1. INTRODUCTION

Modification of surface properties over multiple length scales plays an important role

in optimizing a materials performance for a given application. Lasers provide the

ability to accurately deliver large amounts of energy into confined regions of a

material in order to achieve a desired response. For opaque materials, this energy is

absorbed near the surface, modifying surface chemistry, crystal structure, and/or

multiscale morphology without altering the bulk.

Cooling rate during laser treatment plays a crucial role in material surface properties.

Cooling time for a finite mild steel sheet on irradiation with laser beam is slow as heat

gets accumulated in it. So the study of backing plate and laser spot diameter effect on

the cooling rate becomes useful to control the cooling trend. Analytical Modelling

becomes important in such case to understand the process and control it. The target

with modelling is:

i. Semi quantitative understanding of the process mechanisms for the design of

experiments and display of results dimensional analysis, order of magnitude

calculations.

ii.Parametric understanding for control purposes empirical and statistical charts,

analytic models.

iii.Detailed understanding to analyse the precise process mechanisms for the

purpose of prediction, process improvement and the pursuit of knowledge

analytic and numeric models.

The analytical model for semi-infinite composite body considers both the body to be

semi-infinite [1]. Later a partitioning function was established to take into account the

laser treatment of finite sheet kept on a semi-infinite sheet [2]. It tries to quantify the

fraction of heat flow from top body to the bottom body at the interface. Clearly it now

helps to understand the cooling trend for a finite sheet irradiation by laser beam for

parameters like spot diameter, scan speed, power, backing material etc.


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2. LITERATURE SURVEY

Mathematical modelling is a tool to understanding and control of a process. There are

many research papers depicting the shear importance of this tool to analyse a process

undertaking certain assumptions. Steen and Mazumder [3]have discussed quite a few

analytical models:

i. Analytic models in 1-d heat flow.

a. Assumption: Heat flows in 1 direction and there is no convection or heat

generation. Equation:

T(z, t) = 2Fo(t)0.5/K ierfc{z/2(t)0.5}, = thermal diffusivity, Fo = absorbed intensity, t = interaction timeii. Analytical models for a stationary point source.

a. The instantaneous point source

b. The continuous point source: Since heat is not a vector quantity the effects

from different heat sources can be added [4].

c. Source other than point source: By integrating point source solution over an

area it is possible to calculate the heating from line sources, disc sources or

Gaussian sources. Carslaw and Jaeger [1] discusses solutions for nearly anygeometry.

iii. Analytical models for a moving point source: By integrating the point

solution over time and moving it by making x= (xo+vt). Rosenthal [5]

developed the well-known fundamental welding equations.

iv. Analytical keyhole models-Line source solution: Assumed that energy is

absorbed uniformly along a line in the depth direction.

Carslaw and Jaeger [1] discussed the analytical modelling for semi-infinite

composite solid. It considers that suppose the region x>0 is of one substance, K1,

1, k1 and x0 and K1T1/x = K2T2/x , at x=0,

t>0 where T1is for the temperature in the region x>0, and T2for that in the region

x


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i. The initial temperature T, constant, in x>0 and zero in x 0 at the constant rate

Foper unit time per unit area in the plane x=0. Solving gave:

T2 = 2Fo(k1k2t)0.5K1k20.5 + K2k10.5 ierfc z , = 2k2t

Both the above analytical model was derived assuming the composite body is of semi-

infinite length.

Duley [2]presented, in his book, the concept of partitioning function. The book

discusses the effect of semi-infinite body on analytical model of finite thickness

composite body; here the semi-infinite body act a base material for a finite body. It

says that when a finite body with K1, 1, k1 is kept on a semi-infinite body with

material property K2, 2and k2, where K, and k are thermal conductivity, density

and thermal diffusivity of the respective bodies, the heat partitioned at the interface is

given by a partitioning function:

Pr = K1k2 K2k1K1k2 + K2k1

Cooling rate plays an important role in deciding the microstructure of the material.

The rate with which solidification occurs is equally important and controlling it by

changing various parameters can be achieved. Laser surface processing has been a

key element in a number of large-scale industrial manufacturing operations, yet at the

same time it continues to reinvent it-self and find ever new uses in emerging areas.

Matthew et al. [6] discusses some of the versatile capabilities of laser processing to

modify the surface properties of materials in order to enhance their performance for a

variety of applications.


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3. ANALYTICAL MODELLING

For an infinitely thick sheet subjected to uniform heat flux at the entire top surface as

shown in Fig. 3.1 solution of temperature field can be obtained by solving the

following equation:

Fig 3.1. Schematic representation of an infinite sheet subjected to uniform heat flux at the top

surface.

2T(z, t)z2 = 1K T(z, t)t , K Tzz=0 = H,T|z= = T0 T|t=0 = T0 z (3.1)

Here, T, z, t, k, K, H and T0 denote temperature, depth from the top surface, time,

thermal diffusivity, thermal conductivity, magnitude of heat flux and initial sheet

temperature respectively. Now, a moving laser beam takes d/v time to move over a

point on its scan path where the laser beam diameter is d and v is the scans peed. If

the laser spot diameter d and the sheet thickness h are much larger than the thermal

diffusion length, given by 2kd/v corresponding to the time, d/v the sheet can beconsidered to be semi-infinite and this heat transfer problem can be approximated to

be similar to the situation depicted in Fig. 1. In that case the temperature as a function

of z and t can be obtained as follows [3]:

For t

d/v (i.e during heating),

T = T0 + HK ierfcz , = 2kd/vFor td/v (i.e during cooling), (3.2)T = T0 + H

Kierfcz ierfc z , = 2k(t d/v)

Here, H is taken as absorbed laser power intensity at the top surface (z = 0), 4 / (d2),

A and P being absorptivity and laser power respectively. Considering semi-infinite

sheet but adding a correction term for radial heat conduction loss the solution givenby Eq.(3.2) can be modified as the following [2]:

H

Z = 0

Z


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For td/v (i.e during heating),T = T

0+

HK

ierfc

z

ierfc

z2 + (d2/4)1/2

,

= 2

kd/v

For td/v (i.e during cooling), (3.3)T = T0 + H

Kierfc z ierfcz2 + (d2/4)

1/2

ierfc z ierfcz2 + (d2/4)1/2

, = 2k(t d/v)Considering the sheet to have finite thickness the solution of temperature field without

radial heat conduction loss can be obtained as follows [4]:

Fig 3.2. Laser irradiation on a finite sheet of thickness h unit

For td/v (i.e during heating),T = T0 + H

Kierfc|2(i 1) h+ z| + ierfc|2ih z| ni=1

For td/v (i.e during cooling),(3.4)

T = T0 +H

Kierfc|2(i

1) h+ z|

+ ierfc|2ih

z|

ni=1 ierfc|2(i 1) h+ z| + ierfc|2ih z| , = 2k(t d/v)

Here, theoretically the value of n should be infinite but practically this solution

converges rapidly with increasing value of n. Thus, combining the approaches used

for obtaining Eqs. (3.3) and (3.4) a solution of temperature for finite sheet thickness

with radial conduction loss can be arrived at as given by [7],

2h-Z

h

Z = 0

Z

Laser beam


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For td/v (i.e during heating),T = T0 + HKierfc|2(i 1 )h+ z|

ierfc(2(i 1)h+z)2 + (d2/4)1/2

n

i=1+ ierfc|2ih z| ierfc(2ih z)2 + (d2/4)1/2

For td/v (i.e during cooling), (3.5)T = T

0+

H

K

ierfc |2(i 1)h+z| ierfc(2(i 1)h+z)2 + (d2/4)

1/2 +ierfc |2ih z| ierfc

(2ih

z)

2+ (d

2/4)

1/

2

n

i=1

ierfc |2(i 1)h+z| ierfc(2(i 1)h+z)2 + (d2/4)1/2 +ierfc |2ih z| ierfc(2ih z)2 + (d2/4)1/2

A plate with finite thickness is kept over a substrate of semi-infinite length. (K1, k1, 1,

Cp1) and (K2, k2, 2, Cp2) denotes the thermal conductivity, thermal diffusivity, densityand specific heat capacity of the top plate and substrate respectively.

Now for material properties and scan speed such that the diffusion length > h ,where = 2k1d/v, h is the plate thickness, d is beam diameter and vis scan speed,a partitioning function Prcomes into equation 5 accounting for the heat partitioned by

the substrate top surface.

For t

d/v (i.e during heating),

T = T0 + HKPri ierfc|2(i 1) h+ z| ierfc(2(i 1)h + z)2 + (d2/4)

1/2

ni=0

+ ierfc|2ih z| ierfc(2ih z)2 + (d2/4)1/2

For td/v (i.e during cooling), (3.6)


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T = T0 + HK Pri

ierfc |2(i 1)h+z| ierfc(2(i 1)h + z)2 + (d2/4)1/2 +ierfc |2ih z| ierfc(2ih z)2 + (d2/4)1/2

ni=0

ierfc |2(i 1)h+z| ierfc(2(i 1)h+z)2 + (d2/4)1/

2 +ierfc |2ih z| ierfc(2ih z)2 + (d2/4)1/2

Where partitioning function is given as [2]:

Pr = K1k2 K2k1K1k2 + K2k1

During laser processing, for a stationary heat source, radial heat conduction takes

place in all direction i.e. effectiveness of radial heat conduction Cr= 1. For a moving

heat source Cr< 1 as radial heat conduction along the scan direction is negligible. So

this factor Crwas multiplied to the radial part of the equation 3.6.

For td/v (i.e during heating),T = T

0+

HK

P

ri

ierfc

|2(i 1 )h+ z|

C

r ierfc

(2(i 1 )h+ z)2 + (d2/4)1/2

n

i=0+ ierfc|2ih z| Cr ierfc(2ih z)2 + (d2/4)1

/2 For td/v (i.e during cooling), (3.7)T= T0

+

H

KPri ierfc

|2(i 1)h + z|

Cr ierfc

(2(i 1)h + z)2 + (d2/4)1/2

+

ierfc |2ih z| Cr ierfc(2ih z)2 + (d2/4)1/2

ni=0

ierfc |2(i 1) h+ z| Cr ierfc(2(i 1)h + z)2 + (d2/4)1/2 +ierfc |2ih z| Cr ierfc(2ih z)2 + (d2/4)1/2


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Fig 3.3. Schematic representation of heat partitioned at the z=0 interface

Here in the above figure 3.3, heat gets partitioned at the interface of the two body at Z

= 0. This partitioning is represented in the figure.

E2 = Pr E1, where Pr = K1k2 K2k1K1k2 + K2k1

Fig.3.4. (i) Radial conduction for stationary laser beam, (ii) Radial conduction for moving

laser source beam

The above figure 3.4 represents the schematic for radial heat conduction in two cases,

i.e. for stationary heat source and moving heat source respectively. For stationary heat

source since heat conduction is in all the direction Cr = 1is applied and for movingheat source since there is no conduction along the scan speed direction Crvalue has to

be less than 1.

Cr(i) = 1Cr(ii) < Cr(i)

Z = 0

ZE1

E3

E2

Semi-infinite body

K1, k

1,

1,C

p1

K2, k

2,

2, C

p2

Finite, h mm

Laser beam

V=0

Scan Speed, V mm/min

iii

Laser beam


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4. EXPERIMENTAL DETAILS

4.1.Specifications of Laser used

The experiments were carried out with a 2 kW Ybfiber laser (IPG photonics, Model

no. YLR - 2000) operating at 1.07 m wavelength. This can be operated in CW and

pulsed-mode in 501000 Hz frequency range with 5100% duty cycle. The laser

beam delivery system is mounted on a 5-axis CNC machine capable to move at

speeds up to 20 m/min scan speed effectively.

Fig. 4.1.1.2 kW Ybfiber laser

The actual power of this laser is not same as the power set. This laser was capable of

providing power upto 1280 W.

During the experiments it was observed that the laser on time for 0.5 sec input on time

was more than this. A diode oscilloscope setup was used to find the machines

actual on time. It was found that the laser on time for 0 sec input laser interaction time

was 0.9 sec and for 0.5 sec input time it was ~ 1.4 sec. Below fig. 4.1.2. and fig. 4.1.3.

represents the pulse on time generated using oscilloscope. The extra 0.85 sec without

any input on time is the time taken by the machine to read the programm lines. For fig

4.1.2 each division represents 200ms and so total pulse on time is 4.5 times 200ms

which is ~ 0.9 sec. Similarliy for fig 4.1.3 each division is 197ms and so total pulse on

time is 7 times 197ms which is ~ 1.4 sec.


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Fig. 4.1.2.laser on time pulse for 0 sec input interaction time

Fig. 4.1.3.laser on time pulse for 0.5 sec input interaction time

4.2.Experiment Procedure and Laser Parameters

For a stationary heat source mild steel plate of finite thickness with various backing

plates was irradiated with a staionary laser beam for 0.9sec. It was carried out to see

the affect of thermal conductivity of the backing plates on temperature behavior or the

cooling trend of the heat affected zone at Z=0 or in other words to observe the effect

of partitioing fucniton used in the anlytical model of the same. Also, the affected

region on the top surface of the mild steel due to laser irradiation gives us an idea

about radial and vertical conduction of heat for different backing plates. For this 3

different laser spot diameters were used and the laser power was changed accordingly

to maintain effective power density constant.


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For moving heat source case similar procedure was followed with keeping spot

diameter constant at 3mm and changing the scan speed for a given power.

Table 4.2.1.Laser parameters for stationary heat source, interaction time kept constant at 0.9s

Laser Spot diameter (mm) 2 3 4

Laser Power (W) 300 675 1200

Table 4.2.2.Laser parameters for Moving heat source, laser spot diameter constant at 3mm

Laser Scan Speed (mm/min)

400W 1000 1500 2000 2500 3000

600W 2000 2500 3000 3500 4000

Table 4.2.3.Materials used for the experiment and their properties. (source: EES and wikipidea)

Conductivity (W/m/K) Density (Kg/m3) Specific heat (J/kg/K)

Mild Steel (AISI-1020) 43 7850 620

Stainless Steel 16 7873 504.8

Aluminum 205 2688 936.6

Laser parameters are so selected such that the thermal diffusion length is always much

greater than the thickness of the top mild teel plate. From above thermal diffusivity of

mild steel is

k = K/Cp, 8.810-6m2/s = 2kt, where t interaction time is ~0.9sec. Hence, the thermal diffusion lengthis 5.6mmwhich is much more than 1mmmild steel plate.Mild steel with finitte thickness was kept on different material of semi-inifinite

thickness. In this experiment mild steel was irradiated with stationary laser beam for

six different samples and for each sample three laser spot diameters were used.

Inorder to improve the contact between the 2 plates, a heat sink compound was

applied in between the plates. For moving heat source the case with mild steel

backing without heat sink compound was not carried out. Below mentioned are the six

samples:


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12

Mild Steel of finite

thickness (1mm)

Semi-Infinite Mild Steel

Plate

Mild Steel (1mm) + Mild

Steel backing (13mm)

Mild Steel (1mm) + Heat

Sink + Mild Steel backing

(13mm)


Sink + Stainless Steel

backing (10mm)


Sink + Aluminium backing

(12.5mm)

To avoid repetition in the paper, following short forms have been used ahead:

MS: Mild Steel; SS: Stainless Steel; Al: Aluminium; HSC/HS: Heat Sink Compound

Below schematics represent the laser irradiation on MS plate for different samples:

(a) (b)

Fig 4.2.1(a) Schematic representation of a stationary laser beam falling on a semi-infinite mild steel

plate for 0.9sec, (b) Schematic representation of a stationary laser beam falling on finite mild steel

sheet placed on a backing material with heat sink compound applied

(c) (d)

Fig 4.2.2. (c) Schematic representation of a stationary laser beam falling on finite mild steel sheet for

0.9sec, (b) Schematic representation of a stationary laser beam falling on finite mild steel sheet placedon a backing material with no heat sink applied

Z = 0

Z

Z = 0

Z

Al or SS or

Z = 0

Z

Z = 0

Z


24/51

13

Temperature was measured with the help of a non-contact infrared (IR) sensor

(Micro-Epsilon make, model no. CTLM-2HCF3-C3H, temperature range=385 C to

1600 C, response time=1ms) during the heating process of the workpiece. All the

readings of the plots generated using pyrometer is to be multiplied with a calibration

factor of 2.3. So for this experiment the minimum temperature measure was 885.5 C.

4.3.Absorptivity of Mild Steel (AISI-1020):

The absorptivity of the 1mm mild steel surface was estimated by measuring the

incident and reflected laser powers from the surface with a laser power meter (model-

COMET-10K-V1 ROHS OPHIR make, accuracy 5%). The power meter needs a

continuous laser exposure of 10 s for each measurement. The average value of

absorptivity was estimated to be ~75%. Below fig. 4.3 shows the instruments used to

find the AISI-1020 absorptivity.

Fig. 4.3.1.(a) Power meter, model-COMET-10K-V1 ROHS OPHIR make, accuracy 5%(b) Laser

head (c) Pyrometer (d) Mild steel, AISI-1020 sample placed at an angle of 450with the vertical

To find absorptivity of AISI-1020 laser power was increased from 200W to 600W insteps of 100W and resulting absorptivity value from each has been averaged.

a

b

c

d


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14

Mild steel sample was kept at an angle of 45o with the vertical. For a given laser

power and 16mm laser spot diameter 3 readings T1, T2and T3were taken. Table 4.3

below shows the data from the experimental values obtained from the power meter.

AISI-1020 was irradiated with laser beam and the reflected laser power was captured

by the power meter.

Both the average laser power reflected and % absorptivity has been depicted through

Table 4.3 and fig 4.3.2 histogram plot below.

Table 4.3.Reading for laser power absorptivity for AISI-1020 at varied laser powers

Laser Power

(W)

Reflected Power (W)AVG.

%

AbsorptivityT1 T2 T3

200 116.8 106.3 116.3 113.1333 43.43

300 147 121.9 136 134.97 55.01

400 98.6 95.8 102.1 98.83 75.3

500 89.2 87.3 92 89.5 82.1

600 86.4 83.2 89 86.2 85.63

Fig. 4.3.2.Plots representing the laser power absorptivity for AISI-1020 for varied laser power ranging

from 200W to 600W in steps of 100W

0

20

40

60

80

100

200 300 400 500 600

%A

bsorptivity

Laser Power (W)


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15

5. RESULTS AND DISCUSSION

Analytical plots for Stationary heat source:

5.1.

Thermal cycle plot from Analytical Modelling

Fig. 5.1.1.Thermal plot for top surface viz. z-=0 for different samples on being irradiated with a 2mm

stationary laser spot diameter for 0.9sec from Analytical Model using MatLab

Fig. 5.1.2.Thermal plot for top surface viz. z-=0 for different samples on being irradiated with a 3mm

stationary laser spot diameter for 0.9sec from Analytical Model using MatLab

0

200

400

600

800

1000

1200

1400

1600

1800

0 0.5 1 1.5 2

Temp(C)

Time (sec)

Analytical Model: Temp vs Time, stationary heat source of 2mm spot diamater,P=300W

Finite MS sheet

AL backingMS backing

SS backing

0

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

2400

2600

0 0.5 1 1.5 2

Tem

p(C)

Time (sec)

Analytical Model: Temp vs Time, stationary heat source of 3mm spot diamater,P=675W

Finite MS Sheet

AL backing

MS backing

SS backing


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16

Experimental plots for stationary heat source:

5.2. Cooling plots of thermal cycle by IR sensor Stationary Heat Source

Fig. 5.2.1.Experimental thermal cycle at z-=0 for samples on being irradiated with a 4mm laser spot

diameter for 0.9sec

Fig. 5.2.2.Cooling plot for top surface i.e. z-=0 for different samples on being irradiated with a 2mm

laser spot diameter for 0.9sec using experimental data

0 500 1000 1500 2000 2500

400

500

600

700

800

900

1000

Time (millisec)

Temp(C)

Finite MS Sheet

Semi-Infinite Sheet

Thermal cycle for stationary laser beam of 4mm spot diameter, P=1200W

885

1085

1285

1485

1685

1885

2085

2285

0 50 100 150 200 250

Temp(C)

Time (millisec)

Experiment: Stationary heat source, 2mm spot diameter, P=300W

1mm MS

Semi-Infinite MS

12.5mm Al backing

13mm MS backing

10mm SS backing

MS backing without Hsink


28/51

17


laser spot diameter for 0.9sec using experimental data.


laser spot diameter for 0.9sec using experimental data.

885

1085

1285

1485

1685

1885

2085

0 200 400 600 800

Temp(C)

Time (millsec)


1mm MS

Semi-infinite MS

12.5mm Al backing

13mm MS backing

10mm SS backing


885

1085

1285

1485

1685

1885

2085

2285

0 500 1000 1500

Temp(C)

Time (millisec)


1mm MS

Semi-Infinite MS

12.5mm Al backing

13mm MS backing

10mm SS backing



29/51

18

From the above cooling plots from the experimental data, cooling rate trend is plotted

to analyse the variation in the cooling rate within a sample for different laser spot

diameters and also compare the cooling rates for a same spot diameter for different

samples.

Fig. 5.2.5.Cooling rate for samples at z = 0 on irradiation with stationary source of different spot

diameters

The above cooling rate bar graphs have been generated considering the time taken for

different sample to cool down from a particular temperature to another at z=0.

Suppose the temperature at time t1 is T1 C and at time t2 is T2 C where t2 > t1,

cooling rate is given by (T1 T2)/(t2 t1)C/sec. For our calculation below are theT1and T2considered for plotting cooling rate bar graphs:

Table 5.2.Temperature at two fixed interval for different spot diameter:

Spot dia T1, C T2, C

2mm 1345 885.5

3mm 1345 885.5

4mm 1288 885.5

From both the plots i.e. cooling curves from experimental data fig. 5.2.2 - 5.2.4 and

0

2000

4000

6000

8000

10000

12000

14000

16000

Finite MSsheet

MS backingwithout HS

SS backing MS backing Al backing Semi-InfiniteMS sheet

CoolingRate(C/sec)

Cooling Rate of samples for different laser spot diameters at z=0

2mm

3mm

4mm


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19

cooling rate bar graph fig. 5.2.4, it is observed that:

1. Cooling rate, at z=0, for a sample decreases with increase in laser spot diameter

and this trend is maintained for all six samples. This may be due to the difference

in temperature gradient for varying spot diameters. The radial temperature

gradient decreases with increase in spot diameter. Now as radial conduction will

be higher for higher temperature gradient hence cooling for 2mm spot diameter

will be faster than the 3mm and 4mm spot diameters.

2. Cooling rate, at z=0, for a given spot diameter is minimum for finite mild steel

sheet, maximum for semi-infinite mild steel sheet and lies in between for rest

samples.

3.

Cooling rate with Al backing, MS backing and SS backing were in decreasingorder respectively for a given spot diameter. Reason for such trend can be argued

with their respective thermal conductivity which is also in decreasing order.

4. Although theoretically cooling rate for sample with Al backing should have been

higher than that of semi-infinite mild steel sheet but experimentally it didn't

follow the trend. This shows that even the application of heat sink compound

couldn't create a proper contact between mild steel and aluminium creating

resistance.

5. Cooling rate of mild steel backing with heat sink compound at z=0 is more than

that of mild steel backing without heat sink compound because of the presence of

air gap layer in the latter. Conductivity of air is very low and hence heat gets

accumulated rather being conducted.

Decrease in cooling rate with increase in laser spot diameter can be explained through

the following reasoning:

i.

It is known that the thermal conduction is higher for high temperature

gradient. Radial temperature gradient dT/dX decreases with increase in spot

diameter, hence cooling for a 2mm laser spot is faster than a 3mm laser spot

diameter and so on.

ii. = L2/ k, where is thermal diffusion time, L is thermal diffusion length and

kis thermal diffusivity. is defined as the time it takes for heat to travel over a

distance L. Following this it is clear that energy travel in 2mm spot diameter is

faster than 3mm and so on.


31/51

20

Fig. 5.2.6.(a) Intensity distribution for different spot radius (b) Olympus Model SZ 1145TR PR zoom

sterio microscope (c) 3X Magnification image of affected region for 3mm spot on finite MS sheet

5.3. Effect of laser spot diameters on affected region

To have a better understanding of radial heat conduction vs heat conduction along the

depth considering variation in laser spot diameters and 0.9 sec interaction time,

circular plots of the affected region is generated for different samples.

Fig. 5.3.1 shows the samples which are irradiated with a stationary laser beam varying

the spot diameter as 2mm, 3mm and 4mm respectively keeping the power density

constant. The above fig.5.2.6 (b) and (c) represents the images of those affected

region on the material surface taken using a high resolution optical microscope. To

plot the schematic of affected region, the images from optical microscope was

measured using software ImageJ.

Table 5.3.Radius of the heat affected zone on the samples surface:

Radius of the affected region for different Laser spot diameters (mm)

Samples For 2mm spot For 3mm spot For 4mm spot

Finite MS sheet 2.718 3.875 5.264

MS backing without HS 2.651 3.655 4.394

SS backing 2.412 3.271 4.349

MS backing 2.257 3.169 4.224

Al backing 1.818 3.073 4.043

Semi-Infinite MS sheet 1.526 2.306 3.132

The above table 5.3 shows radius of the affected region on the sample surface for

different laser spot diameter. All the measurements are in mm.

r1=2mm

r2=3mm

r

r2

r1Spot dia 3mm, Finite

MS sheet

, 3X Magnification

ab

c


32/51

21

Fig. 5.3.1. (a) Heat affected region on the finite mild steel sheet for different laser spot diameter, (b)

Affected region on the semi-infinite mild steel sheet for different laser spot diameter

Fig. 5.3.2. Plot of heat affected region on sample surface; 2mm spot diameter, P = 300W, V=0 and t=

0.9 sec, laser interaction time

For all the three cases with different laser power and spot diameters such that the laser

power intensity remains to be a constant, in MS plate with backing condition with

heat sink the affected region radius increases as the thermal conductivity of the

backing plate decreases. For finite MS sheet the radius is maximum as in this case

radial heat conduction is maximum and heat gets accumulated. Comparing affected

region for MS backing with and without heat sink, the backing condition with heat

sink compound has smaller affected region as the heat sink compound creates a better

contact improving the thermal conduction along the depth as compared to the other

situation.

4mm 3mm

2mm

(a) (b)

mm

mm

-3 -2 -1 0 1 2 3

2.5

-2

1.5

-1

0.5

0

0.5

1

1.5

2

2.5

1mm MS

Bulk MS

AL backing

MS backing

SS backing

MS without HS

2mm spot dia


33/51

22

Fig. 5.3.3. Plot of heat affected zone on sample surface; 3mm spot diameter, P = 675W, V=0 and t=

0.9sec, laser interaction time

Fig. 5.3.4. Plot of heat affected zone on sample surface; 4mm spot diameter, P = 1200W, V=0 and t =


mm

mm

-4 -3 -2 -1 0 1 2 3 4

-4

-3

-2

-1

0

1

2

3

4

1mm MS

Bulk MS

AL backing

MS backing

SS backing

MS without HS

3mm spot dia

mm

mm

-6 -4 -2 0 2 4 6

-5

-4

-3

-2

-1

0

1

2

3

4

5

1mm MS

Bulk MSAL backing

MS backing

SS backing

MS without HS

4mm spot dia


34/51

23

5.4. Effect of backing on solidification time

Fig. 5.4.1. Cooling curve for different samples; 3mm spot diameter, P=675W, V=0(scan speed) and t =


Fig. 5.4.2. Cooling curve for different samples; 4mm laser spot dia, P=1200W, V=0(scan speed) and t

= 0.9sec laser interaction time

In Fig. 5.4.1 and 5.4.2 the duration of horizontal trend during cooling or the durationbetween the changes in slopes depict the solidification time.

885

1085

1285

1485

1685

1885

2085

0 200 400 600 800 1000 1200

Temp(C)

Time (millisec)

Cooling curve for staitionary heat source of 3mm spot diameter

Finite MS sheet

MS backing without HS

10mm SS backing

13mm MS backing

12.5mm Al backing

Semi-Infinte MS

885

1085

1285

1485

1685

1885

2085

2285

0 400 800 1200 1600 2000

Temp(C)

Time (millisec)

Cooling curve for staitionary heat source of 4mm spot diameter

Finite MS sheet

MS backing without HS

10mm SS backing

13mm MS backing

12.5mm Al backing

Semi-Infinte MS


35/51

24

5.5. Effect of laser spot diameter on solidification time

Fig. 5.5.1. Cooling trend at z=0 for finite mild steel sheet with different laser spot diameters

Fig. 5.5.2. Cooling trend at z=0 for semi-infinite mild steel sheet with different laser spot diameters

In fig. 5.5.1 and 5.5.2 it can be observed that the solidification time increases with

increase in spot diameter because the cooling rate decreases with spot diameter

increment.

885

1085

1285

1485

1685

1885

2085

2285

0 200 400 600 800 1000 1200

Temp(C)

Time (millisec)

Cooling curve for stationary heat source on 1mm mild steel plate

2mm Spot Dia

3mm Spot Dia

4mm Spot Dia

885

1085

1285

1485

1685

1885

2085

0 50 100 150 200 250

Temp(C)

Time (millisec)

Cooling curve for stationary heat source on a semi-infinite MS plate

2mm Spot Dia

3mm Spot Dia

4mm Spot Dia


36/51

25

5.6. Thermal Cycle for 1mm mild steel plate Moving Heat Source

Experimental plots for Moving heat source:

Fig. 5.6.1. Thermal cycle for 1mm MS plate at varying scan speed at z = 0, P = 400W and 3 spot

diameter

Fig. 5.6.2. Thermal cycle for 1mm MS plate at varying scan speed at z = 0, P = 600W and 3 spot

diameter

885

1085

1285

1485

1685

1885

2085

0 100 200 300 400 500 600

Temp

(C)

Time (millisec)

Thermal cycle for 1mm MS plate, P=400W, 3mm spot diameter

1000 mm/min

1500 mm/min

2000 mm/min

2500 mm/min3000 mm/min

885

1085

1285

1485

1685

1885

2085

0 50 100 150 200 250

T

emp(C)

Time (millisec)

Thermal cycle for 1mm MS plate, P=600W, 3mm spot diameter

2000 mm/min

2500 mm/min

3000 mm/min3500 mm/min

4000 mm/min


37/51

26

5.7. Effect of backing plate on cooling rate Moving Heat Source

Cooling plots for moving heat source, P = 600W, 3mm spot diameter:

Fig. 5.7.1. Cooling cycle at z = 0 for various samples with P = 600W, 3 spot diameter and

2000mm/min scan speed as laser parameter



885

985

1085

1185

1285

1385

1485

1585

1685

1785

0 50 100 150 200

Temp(C)

Time (millisec)

P = 600W, V = 2000mm/min and 3mm spot diameter

1mm MS

Al backing with HS

MS backing with HS

SS backing with HS

Bulk MS

885

1085

1285

1485

1685

1885

2085

0 20 40 60 80 100

Temp(C)

Time (millisec)


1mm MS

Al backing with HS

MS backing with HS

SS backing with HS

Bulk MS


38/51

27





885

985

1085

1185

1285

1385

1485

1585

1685

1785

1885

0 10 20 30 40

Temp(C)

Time (millisec)


1mm MS

Al backing with HS

MS backing with HS

SS backing with HS

Bulk MS

885

985

1085

1185

1285

1385

1485

1585

1685

0 10 20 30 40

Temp(C)

Time (millisec)


1mm MS

Al backing with HS

MS backing with HS

SS backing with HS

Bulk MS


39/51

28


to analyse the variation in the cooling rate within a sample for different laser scan

speed and also compare the effect on cooling rates for a same scan speed for different

samples.

Fig. 5.7.5.Cooling rate for samples at z = 0 on irradiation with moving heat source of different scan

speed, P = 600W and 3mm spot diameter





Table 5.7.1.Temperature at two fixed interval for a given laser scan speed, P = 600W:

Scan Speed(mm/min) T1, C T2, C

2000 1480 885.5

2500 1400 885.5

3000 1500 885.5

3500 1400 885.5

0

5000

10000

15000

20000

25000

30000

1mm Sheet SS backing with

HS

MS backing with

HS

Al backing with

HS

Bulk MS

Cooling

Rate(C/sec)

2000 mm/min 2500 mm/min 3000 mm/min 3500 mm/min


40/51

29

While plotting the above cooling rate histogram plots, for a given scan speed, T1C

and T2 C temperature during the cooling cycle chosen was same across all the

samples so as to compare the cooling rates.

Observation:

i. For a given laser scan speed cooling rate is least for 1mm mild steel sheet, it

is maximum for bulk mild steel sheet and it ranges in between these two

extremes for the backing conditions. Cooling rate for a given scan speed

increases with the increase in thermal conductivity of the backing plate.

Reasoning for this observation remains same as discussed earlier in the case

of samples irradiation by a stationary heat source.

ii.

With the increase in laser scan speed the effect of backing plate decreases

i.e. for higher scan speed value of 3500 mm/min the cooling rate across all

samples are nearly close by and consecutively the effect of backing plate is

not observed. This may be because with the increase in scan speed laser

interaction time decreases and hence the thermal diffusion length also

decreases. Due to this for higher scan speed, as for above case, thermal

effect due to laser barely reaches the interface. As mentioned above the

thickness of mild steel sheet is 1mm. Now considering the above scan

speeds value, the theoretical thermal diffusion length = 2kd/vare:a) For 3500 mm/min, ~1.3mm

b) For 3000 mm/min, ~ 1.45mmc) For 2500 mm/min, ~ 1.6mmd) & For 2000 mm/min, ~ 1.8mm

Clearly for 2000mm/min,

~ 1.8mm is greater than the mild steel sheet

thickness of 1mm as compared to laser scan speed of 3500 mm/min for

which it is closer to the mild steel sheet thickness.

iii. For a given sample with increase in laser scan speed cooling rate increases.


41/51

30

Cooling plots for moving heat source, P = 400W, 3mm spot diameter





For both 600W and 400W cooling curves for varying scan speed at constant spot

diameter the cooling rate trend is in match with the trend observed for stationary heat

885

985

1085

1185

1285

1385

1485

1585

1685

1785

1885

0 100 200 300 400

Temp(C)

Time (millisec)

P = 400W, 3mm spot diameter and V = 1000 mm/min

1mm MS

Al backing with HS

MS backing with HS

SS backing with HS

Bulk MS

885

1085

1285

1485

1685

1885

2085

0 10 20 30 40 50 60 70 80 90 100 110 120 130

Temp(C)

Time (millisec)

P = 400W, 3mm spot diameter and V = 1500 mm/min

1mm MS

Al backing with HS

MS backing with HS

SS backing with HS

Bulk MS


42/51

31

source i.e. with the increase in backing plate thermal conductivity cooling rate also

increases.


to analyse the variation in the cooling rate within a sample for different laser scan

speed and also compare the effect on cooling rates for a same scan speed for different

samples.

Fig. 5.7.8.Cooling rate for samples at z = 0 on irradiation with moving heat source of different scan

speed, P = 400W and 3mm spot diameter





Table 5.7.2.Temperature at two fixed interval for a given laser scan speed, P = 400W:

Scan Speed(mm/min) T1, C T2, C

1000 1500 885.5

1500 1450 885.5

1931.42

5873.13

2227.71

6930.25

3863.11

7275.26

4783.64

8162.54

5825.94

9922.81

0

2000

4000

6000

8000

10000

12000

1000 mm/min 1500 mm/min

CoolingRate(C/sec)

Cooling Rate of samples for different laser Laser scan speed, P = 400W

1mm Sheet

SS backing with HS

MS backing with HS

Al backing with HS

Bulk MS


43/51

32

5.8. Cr, effective radial heat conduction: Moving Heat Source

Fig. 5.8.1. Cooling cycle at z = 0 from IR pyrometer for 1mm MS sheet, P = 400W, 3 spot diameter

and varying laser scan speed

Fig. 5.8.2. Cooling cycle at z = 0 from Analytical model for 1mm MS sheet, P = 400W, 3 spot diameter

and varying laser scan speed, Cr= 0.7

885

935

985

1035

1085

1135

1185

1235

1285

1335

0 20 40 60 80 100

Temp(C)

Time (millsec)

Experimenatal: P=400 W and 3mm spot diameter

2000 mm/min

2500 mm/min

885

935

985

1035

1085

1135

1185

1235

1285

1335

0 20 40 60 80 100

T

emp(C)

Time (millisec)

Analytical: P=400 W and 3mm spot diameter, Cr = 0.7

2500 mm/min

2000 mm/min


44/51

33

Fig. 5.8.3. Cooling cycle at z = 0 from IR pyrometer for 1mm MS sheet, P = 600W, 3 spot diameter

and varying laser scan speed


and varying laser scan speed, Cr= 0.7

885

985

1085

1185

1285

1385

1485

1585

1685

0 20 40 60 80

Temp(C)

Time (millisec)

Experimental: P=600 W and 3mm spot diameter

3500 mm/min

4000 mm/min

4500 mm/min

885

985

1085

1185

1285

1385

1485

1585

1685

0 20 40 60 80

Temp(C)

Time (millisec)

Analytical: P=600 W and 3mm spot diameter, Cr = 0.7

3500 mm/min

4000 mm/min

4500 mm/min


45/51

34


and varying laser scan speed, Cr= 1

At 400W and 600W thermal cycle plots from both experimental and analytical

modelling has been generated as shown in above fig 5.8.1 5.8.5. Laser spot diameter

was kept at 3mm and the laser scan speed was varied for a given laser power such that

the melting case do not occur. The analytical model developed earlier is based on non

melting condition. To get a match for the thermal cycle with the experimental plot,

parameters are such chosen so as to avoid melting. By keeping the laser absorptivity

for AISI 1020 at ~75% and changing the Crvalue manually, thermal cycle plot was

generated using MatLab programming.

The value for Crwas manually fed from 0.5 1.

Observation:

i. It was observed that for a range of ~0.7-0.75 Crvalue and keeping all other

parameters same, the thermal cycle plot from analytical model is in good

agreement with the experimental graphs.

ii. It is clearly seen from fig 5.8.5 that the C r= 1 incorporation to the analytical

model under predicts and is not in good agreement with the experimental

results observed in fig 5.8.3.

885

985

1085

1185

1285

1385

1485

1585

1685

0 20 40 60 80

Temp(C)

Time (millisec)

Analytical: P=600 W and 3mm spot diameter, Cr = 1

3500 mm/min

4000 mm/min

4500 mm/min


46/51

35

CONCLUSION

1. Cooling rate, at z=0, for a sample decreases with increase in laser spot

diameter and this trend is maintained for all the six samples considered.2. Cooling is faster as the thermal conductivity of the backing material, with heat

sink compound, increases but for a same backing material, without heat sink

compound, it decreases.

3. Solidification time follows the same trend as above, viz. for a given sample it

decreases with the decrease in spot diameter. For a given spot diameter, with

increase in thermal conductivity of backing plate it decreases.

4. Heat affected region for a given spot diameter decreases with increase in the

conductivity of the backing plate with heat sink compound. It is maximum for

finite MS sheet and minimum for semi-infinite MS sheet in the considered

sample range.

5. For a given laser scan speed cooling rate is least for 1mm mild steel sheet, it is

maximum for bulk mild steel sheet and it ranges in between these two

extremes for the backing conditions. Cooling rate for a given scan speed

increases with the increase in thermal conductivity of the backing plate.

6. With the increase in laser scan speed the effect of backing plate decreases viz.

for higher scan speed value of 3500 mm/min cooling rate across all samples

are nearly close by and consecutively the effect of backing plate is not

observed.

7. For a range of ~0.7-0.75 Crvalue thermal cycle plot from analytical model is

in good agreement with the experimental graphs for a moving heat source at

non-melting condition.


47/51

36

6. REFERENCES

[1] Carslaw.H.S., Jaeger.J.C. "Conduction of Heat in Solids" 2nd Edition Oxford

University Press, 1959.

[2] Duley, W.W., 1983. Laser Processing and Analysis of Materials. Plenum

Press, NewYork/London.

[3] Steen, W.M., Mazumder, J., 2010. Laser Material Processing, 4th ed.

Springer, London,pp. 256258.

[4] McBride, R., Bardin, F., Gross, M., Hand, D.P., Jones, J.D.C., Moore, A.J.,

2005. Modelling and calibration of bending strains for iterative laser forming.

J. Appl. Phys. D:Appl. Phys. 38, 40274036.

[5] Rosenthal. D. Trans ASME 849-866 1946.

[6] Matthew S. Brown, Craig B. Arnold Fundamentals of Laser-Material

Interaction and Application to Multiscale Surface Modification, 2010. 91-

120.

[7] Shitanshu Shekhar Chakraborty, Harshit More, Vikranth Racherla, Ashish

Kumar Nath, Modification of bent angle of mechanically formed stainless

steel sheets by laser forming, Journal of Materials Processing Technology,

Volume 222, August 2015, Pages 128-141, ISSN 0924-0136.


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7. APPENDIX

Matlab code for the Analytical Model:

% Funct i on t o comput e t emper ature vs t i me at Z = 0. % Anal yt i cal model used to comput e temper at ur e evol ut i on i n a f i ni t e% t hi ckness sheet , % wi t h a sheet at t he bott om at t ached, subj ect ed t o a st at i onar y heatsour ce of const ant wi dt h ( equal t o beamdi ameter) and% and uni f or m i nt ensi t y of magni t ude 4AP/ ( pi d 2) f or t i me d/ v( McBr i de et al . , 2006)

% I NPUT PARAMETER%% A - - > Absor pt i vi t y% d - - > Di amet er of l aser beam i n mm% P - - > Laser power i n W

% v - - > Scan speed i n m/ mi n% h - - > Sheet t hi ckness i n mm% zVec - - > Vect or cont ai ni ng di st ances f r om t op sur f ace i n mm wher et he t emper at ur e i s t o be est i mated. Fi r st poi nt shoul d be z=0% T0 - - > I ni t i al sheet t emper at ur e% n - - > No. of r ef l ect i ons consi der ed i n t he anal yt i cal expr essi onf or est i mat i on of t emper at ur e i n a f i ni t e thi ckness sheet % Tot al Ti me - - > Tot al t i me of anal yses i n seconds% Ti meI ncr ement - - > Ti me I ncr ement t o be used i n t he anal yses% TempRi seFor StepCal c - - > Temperature r i se f or t he St epTi mecal cul at i on% Cr - - > Ef f ect i veness of Radi al heat conduct i on, < or = 1% pr 1 - - > heat f l ow par t i t i oni ng i nt o subst r at e- 1 kept on a basemat er i al - 2

cl ear al l A = 0. 75; d = 3; P = 400. 0; v = 1; h=1; zVec=0: 0. 05: 1; n=50; Cr = 0. 7; T0 = 27; Ti meI ncr ement= ( pi *d*60) / ( 4*v*1000*80) ; Tot al Ti me=2;TempRi seWi t hi nTi meI ncr ement=10; I nt ensi t yMul t i Fact or = 1; Tmeanguess=500; TPropMax1 = 1200; k2 = 205; r ho2 = 2688; cp2 = 936. 6; % k2, r ho2 and cp2 ar e conduct i vi t y, densi t y and speci f i c heat of t he% bot t om mat er i al i n SI uni t q = I nt ensi t yMul t i Fact or *( A*P*1e6) / ( pi *d 2/ 4) ; %Aver age i nt ensi t y i nW/ m 2zVec = zVec/ 1000; %Dept h i n mh = h/ 1000; %Sheet t hi ckness i n md = d/ 1000; %Beam di amet er i n mv = v/ 60; %Beam vel oci t y i n m/ sTcond1 = [ 0; 100; 200; 300; 400; 500; 600; 700; 800; 1000; 1200] ; %Temperat ur esat whi ch conducti vi t y i s speci f i edcond1 = [ 51. 9; 50. 7; 48. 2; 45. 6; 41. 9; 38. 1; 33. 9; 31. 1; 24. 7; 26. 8; 29. 7] ;%Conduct i vi t y at speci f i ed t emper at ur esTdens1 = [ 0; 100; 200; 300; 400; 500; 600; 700; 800; 1000; 1200] ; %Temperat ur esat whi ch densi t y i s speci f i eddens1 =[ 7700; 7700; 7700; 7700; 7700; 7700; 7700; 7700; 7700; 7700; 7700] ; %Densi t y atspeci f i ed t emper atur esTspht 1 = [ 0; 100; 200; 300; 400; 500; 600; 700; 800; 1000; 1200] ; %Temperat ur esat whi ch speci f i c heat i s speci f i ed


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spht 1 = [ 486; 486; 550; 548; 586; 649; 708; 770; 624; 548; 548] ; %Speci f i c heatat speci f i ed t emper at ur es

t p = d/ v; %Heat i ng t i me i n seconds

zLength=l ength(zVec) ;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ANALYSES FOR THE TOPSURFACE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

z=zVec( 1) ; count =1; Temp( 1, : ) =[ 0, T0] ; %I ni t i al i zi ng count and Temper at ur eT( 1, 1) =0; T( 1, 2: ( n+1) ) =T0;

k=cond1( 1) ; r ho=dens1( 1) ; c=spht 1(1) ;

di f f use=k/ ( r ho*c); del =2*sqr t ( di f f use*t p) ; TRi se1=q*del / ( k*sqr t ( pi ) ) ; Tmean =( T0+TRi se1) / 2;

i f ( TRi se1>TPr opMax1) Tmean=TPr opMax1;

end

k1 = spl i ne( Tcond1, cond1, Tmean) ; %Thermal conduct i vi t y i n W/ m/ K atTmeanr ho1 = spl i ne( Tdens1, dens1, Tmean) ; %Densi t y i n kg/ m 3 at Tmeancp1 = spl i ne(Tspht 1, spht 1, Tmean) ; %Speci f i c heat i n J / kg/ K at Tmean

di f f usi vi t y1 = k1/ ( r ho1*cp1) ; %Di f f usi vi t y i n m 2/ sec at Tmeandi f f usi vi t y2 = k2/ ( r ho2*cp2) ;

pr 1=( ( k1/ sqr t ( di f f us i vi t y1) ) -(k2/ sqrt (di f f us i vi t y2) ) ) / ( (k1/ sqrt ( di f f us i vi t y1) ) +(k2/ sqrt ( di f f us i vi ty2)) ) ; pr1=1; %For wi t hout backi ng condi t i on

f or t = Ti meI ncrement : Ti meI ncrement : Tot al Ti mecount =count +1; i f t


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f 3 = 1/ exp( x3 2) / sqr t ( pi ) - x3*( 1- er f ( x3) ) ; f 4 = 1/ exp( x4 2) / sqr t ( pi ) - x4*( 1- er f ( x4) ) ;

f 3=Cr *f 3; f 4=Cr *f 4;

TempRi sez=TempRi sez+q*Di f f usi onLengt h1*( pr1 i ) *( f 1+f 2- f 3-f 4) / k1; %Temper at ur e ri se at dept h z t aki ng n r ef l ect i ons wi t h r adi alheat l oss

T( count , i +1) = TempRi sez+T0; %Temper at ure est i mat ed at zt aki ng i r ef l ect i ons

endx1 = z/ Di f f usi onLengt h1; x3 = sqr t ( z 2+d 2/ 4) / Di f f usi onLengt h1; f 1 = 1/ exp( x1 2) / sqr t ( pi ) - x1*( 1- er f ( x1) ) ; f 3 = 1/ exp( x3 2) / sqr t ( pi ) - x3*( 1- er f ( x3) ) ; f 3=Cr *f 3; TempRi sez1 = q*Di f f usi onLengt h1*( f 1- f 3) / k1;

Temp( count , 1) =t ; Temp( count , 2) =T0+TempRi sez+TempRi sez1;

el se %Bel ow i s t he t emperat ur e est i mat i on f or t he cool i ng per i od

Di f f usi onLengt h1=2*sqr t ( di f f usi vi t y1*t ) ; Di f f usi onLengt h2=2*sqr t ( di f f usi vi t y2*t ) ; Di f f usi onLengt hCool i ng1 = 2*sqr t ( di f f usi vi t y1*( t - t p) ) ; Di f f usi onLengt hCool i ng2 = 2*sqr t ( di f f usi vi t y2*( t - t p) ) ;

sum1=0; sum2=0;

f or i =1: nx1 = ( 2*i *h+z) / Di f f usi onLengt h1; x2 = ( 2*i *h- z) / Di f f usi onLengt h1; x3 = sqr t ( ( 2*i *h+z) 2+d 2/ 4) / Di f f usi onLength1; x4 = sqrt ( ( 2*i *h- z) 2+d 2/ 4) / Di f f usi onLengt h1;

f 1 = 1/ exp( x1 2) / sqr t ( pi ) - x1*( 1- er f ( x1) ) ; f 2 = 1/ exp( x2 2) / sqr t ( pi ) - x2*( 1- er f ( x2) ) ; f 3 = 1/ exp( x3 2) / sqr t ( pi ) - x3*( 1- er f ( x3) ) ; f 4 = 1/ exp( x4 2) / sqr t ( pi ) - x4*( 1- er f ( x4) ) ; f 3=Cr *f 3; f 4=Cr *f 4; sum1 = sum1+q*Di f f usi onLengt h1*( pr1 i ) *( f 1+f 2- f 3- f 4) / k1;

x11 = ( 2*i *h+z) / Di f f usi onLengt hCool i ng1; x22 = ( 2*i *h- z) / Di f f usi onLengt hCool i ng1; x33 = sqr t ( ( 2*i *h+z) 2+d 2/ 4) / Di f f usi onLengt hCool i ng1; x44 = sqrt ( ( 2*i *h- z) 2+d 2/ 4) / Di f f usi onLengt hCool i ng1;

f 11 = 1/ exp( x11 2) / sqr t ( pi ) - x11*( 1- er f ( x11) ) ; f 22 = 1/ exp( x22 2) / sqr t ( pi ) - x22*( 1- er f ( x22) ) ; f 33 = 1/ exp( x33 2) / sqr t ( pi ) - x33*( 1- er f ( x33) ) ;

f 44 = 1/ exp( x44 2) / sqr t ( pi ) - x44*( 1- er f ( x44) ) ; f 33=Cr *f 33;


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f 44=Cr *f 44;

sum2 = sum2+q*Di f f usi onLengthCool i ng1*( pr1 i ) *( f 11+f 22-f 33- f 44) / k1;

T( count , i +1) = sum1- sum2+T0; %Temper at ure est i mat ed at z

t aki ng i r ef l ect i onsendTempRi sez= sum1- sum2;

x1 = z/ Di f f usi onLengt h1; x3 = sqr t ( z 2+d 2/ 4) / Di f f usi onLengt h1; x11 = z/ Di f f usi onLengt hCool i ng1; x33 = sqr t ( z 2+d 2/ 4) / Di f f usi onLengthCool i ng1; f 1 = 1/ exp( x1 2) / sqr t ( pi ) - x1*( 1- er f ( x1) ) ; f 3 = 1/ exp( x3 2) / sqr t ( pi ) - x3*( 1- er f ( x3) ) ; f 11 = 1/ exp( x11 2) / sqr t ( pi ) - x11*( 1- er f ( x11) ) ; f 33 = 1/ exp( x33 2) / sqr t ( pi ) - x33*( 1- er f ( x33) ) ; f 3=Cr *f 3; f 33=Cr *f 33;

sum1 = q*Di f f usi onLengt h1*( f 1- f 3) / k1; sum2 = q*Di f f usi onLengt hCool i ng1*( f 11- f 33) / k1; TempRi sez1= sum1- sum2;

Temp( count , 1) =t ; Temp( count , 2) =T0+TempRi sez+TempRi sez1;

endendcount Max=count ; TMax=max( Temp( : , 2) ) ; %Maxi mum t emper at ur e

p = 1; TPrevi ous=T0; Resul t s( 1, 1) =0; Resul t s( 1, 2: ( zLengt h+1) ) =T0; f or i =1: count Max

i f ( ( abs( Temp( i , 2) - TPr evi ous) >=TempRi seWi t hi nTi meI ncr ement ) | | ( Temp( i , 2) ==TMax) )

p=p+1; Resul t s( p, 1) =i *Ti meI ncr ement ; Resul t s( p, 2) =Temp( i , 2) ; TPr evi ous=Temp( i , 2) ;

end

endp=p+1; Resul t s( p, 1)=countMax*Ti meI ncrement ; Resul t s( p, 2) =Temp( count Max, 2) ; pMax=p; del Tmax = max( abs( di f f ( Temp( : , 2) ) ) ) ;

Fi gName=spr i nt f ( ' Temper at uresDat a. emf ' ) ; h=f i gur e; pl ot ( Resul ts ( : , 1) , Resul ts ( : , 2) , ' Li neWi dt h' ,2 ) ; xl abel ( ' Ti me ( s) ' ) ; yl abel ( ' Temper at ure ( Deg C) ' ) ;t i t l e( ' Temperatur es vs t i me' ) ;

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