Table Of ContentMaterials Forming, Machining and Tribology
Bekir S. Yilbas
Ahmad Y. Al-Dweik
Nasser Al-Aqeeli
Hussain M. Al-Qahtani
Laser Pulse
Heating of Surfaces
and Thermal Stress
Analysis
Materials Forming, Machining and Tribology
Series Editor
J. Paulo Davim
For furthervolumes:
http://www.springer.com/series/11181
Bekir S. Yilbas Ahmad Y. Al-Dweik
•
Nasser Al-Aqeeli Hussain M. Al-Qahtani
•
Laser Pulse Heating
of Surfaces and Thermal
Stress Analysis
123
BekirS. Yilbas Ahmad Y.Al-Dweik
Nasser Al-Aqeeli Department of Mathematics andStatistics
Hussain M.Al-Qahtani KingFahdUniversityof Petroleum
Mechanical EngineeringDepartment and Minerals
KingFahdUniversityof Petroleum Dhahran
and Minerals SaudiArabia
Dhahran
SaudiArabia
ISSN 2195-0911 ISSN 2195-092X (electronic)
ISBN 978-3-319-00085-5 ISBN 978-3-319-00086-2 (eBook)
DOI 10.1007/978-3-319-00086-2
SpringerChamHeidelbergNewYorkDordrechtLondon
LibraryofCongressControlNumber:2013940306
(cid:2)SpringerInternationalPublishingSwitzerland2014
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Preface
High power lasers can be used as the tools to treat and machine the materials in
industry with precision of operation, high processing speed, and low cost.
Although laser processing of metallic materials has several advantages over the
conventional methods, the development of high temperature gradients in the
treatedregiongivesrisetotheformationofhighstresslevelsintheregiontreated.
In some instances, this limits the practical applications of the material processed
by a high power laser beam. Although considerable research studies were carried
out to examine the thermal stress developed during laser processing, the models
developed have short comings to reflect the actual physical problems. This is
mainly because of the complicated nature of the problem, which involves with
multi-physicsphenomena.Onlineexperimentationofthethermallyinducedstress
fieldisextremelydifficultandcostlybecauseofthelimitationsinsensingsystems,
which operate at tremendously elevated temperatures during laser processing.
Therefore, the model studies still satisfactorily provide physical insight into the
thermally induced processes enabling to understand the relations between the
process parameters and thermal response of the treated material.
Although the physical processes related to the laser heating and thermal stress
development are complicated, analytical solution to the problem is possible
through incorporating some useful assumptions in the analysis. Since the tem-
perature gradient along the absorption depth is much higher than that of the
direction normal to the absorption depth, heating situation may reduce to one-
dimensional problem. In addition, the assumption of heating of a semi-infinite
bodycanbejustifiedaftercomparingthedepthofabsorptionwiththethicknessof
the substrate material, which is significantly larger than the absorption depth.
Analyticalsolutiontothelaserpulseheatingproblemyieldsthefunctionalrelation
between the dependent and independent parameters, despite the unavoidable
number of assumptions, which may be reduced in the numerical solutions. Nev-
ertheless, validation through the experimentation of the findings is necessary to
fulfill the required accuracy of the solutions.
In this book, thermal stress development during laser pulse heating of metallic
surfaces is formulated for various laser pulse parameters and heating conditions
incorporating the temporal variation of laser pulse intensity, the convection
cooling of the surface resembling the assisting gas, and the consideration of
v
vi Preface
surfaceandvolumetricheatsources.Inaddition,equilibriumandnon-equilibrium
heating situations are classified presenting the closed formsolutions, accordingly.
Analyticalsolutionisalsopresentedfortwo-dimensionalheatingsituationfornon-
equilibriumenergytransferintheirradiatedregion.However,somecasespertinent
tolaserheatingandthermalstressdevelopmentarenotpresentedinthisbookdue
to space limitations and, therefore, these cases are left for the future treatments.
Acknowledgments
WewouldliketoacknowledgetheroleofKingFahdUniversityofPetroleumand
Mineralsinextendingastrongsupportfromthebeginningtoendfacilitatingevery
means during the preparation of this book. The author wishes to thank the col-
leagues who contributed to the work presented in the book through previous
cooperationoftheauthor.Inparticular,thankstoDr.MuammerKalyon,Dr.S.Z.
Shuja, Dr. Saad Bin Mansoor, and all our graduate students.
vii
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Equilibrium Laser Pulse Heating and Thermal Stress Analysis . . . 5
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Step Input Laser Pulse Heating. . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.1 Stress Free Boundary at the Surface . . . . . . . . . . . . . . . 6
2.2.2 Stress Continuity Boundary at the Surface. . . . . . . . . . . 19
2.3 Time Exponentially Varying Laser Pulse Heating . . . . . . . . . . . 26
2.3.1 Stress Free Boundary at the Surface . . . . . . . . . . . . . . . 26
2.3.2 Stress Free Boundary and Convection at the Surface. . . . 36
2.3.3 Stress Boundary at the Surface. . . . . . . . . . . . . . . . . . . 54
2.4 Entropy Analysis Due to Thermal Stress Field . . . . . . . . . . . . . 64
2.5 Findings and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
2.5.1 Step Input Pulse Heating . . . . . . . . . . . . . . . . . . . . . . . 67
2.5.2 Time Exponentially Varying Laser Pulse Heating. . . . . . 71
2.5.3 Entropy Analysis Due to Thermal Stress Field. . . . . . . . 79
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3 Analytical Solution of Cattaneo and Thermal Stress Equations . . . 85
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.2 Surface Heat Source Consideration . . . . . . . . . . . . . . . . . . . . . 86
3.2.1 Step Input Pulse Heating . . . . . . . . . . . . . . . . . . . . . . . 87
3.2.2 Exponential Pulse Heating. . . . . . . . . . . . . . . . . . . . . . 92
3.3 Volumetric Source Consideration . . . . . . . . . . . . . . . . . . . . . . 95
3.3.1 Step Input Pulse Heating . . . . . . . . . . . . . . . . . . . . . . . 96
3.3.2 Exponential Pulse Heating. . . . . . . . . . . . . . . . . . . . . . 103
3.4 Entropy Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
3.5 Findings and Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
3.5.1 Surface Heat Source Consideration. . . . . . . . . . . . . . . . 110
3.5.2 Volumetric Heat Source Consideration . . . . . . . . . . . . . 114
3.5.3 Entropy Generation Rate . . . . . . . . . . . . . . . . . . . . . . . 117
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
ix
x Contents
4 Analytical Treatment of Hyperbolic Equations
for Stress Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.2 Formulation of Energy Transport in Metallic Substrates
at Microscopic Level. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.3 Thermal Stress Field: Consideration of Surface
and Volumetric Sources. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
4.3.1 Surface Heat Source Consideration. . . . . . . . . . . . . . . . 134
4.3.2 Volumetric Heat Source Consideration . . . . . . . . . . . . . 140
4.4 Thermal Stress Field: Two-Dimensional Consideration . . . . . . . 147
4.5 Findings and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
4.5.1 Surface Heat Source Consideration. . . . . . . . . . . . . . . . 154
4.5.2 Volumetric Heat Source Consideration . . . . . . . . . . . . . 158
4.5.3 Two-Dimensional Analysis. . . . . . . . . . . . . . . . . . . . . . 160
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
5.1 Equilibrium Heating. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
5.1.1 Step Input Laser Pulse Intensity . . . . . . . . . . . . . . . . . . 168
5.1.2 Exponential Laser Pulse Intensity. . . . . . . . . . . . . . . . . 168
5.2 Cattaneo Heating Model and Thermal Stresses . . . . . . . . . . . . . 170
5.2.1 Exponential Laser Pulse Intensity. . . . . . . . . . . . . . . . . 171
5.2.2 Step Input Laser Pulse Intensity . . . . . . . . . . . . . . . . . . 171
5.3 Non-Equilibrium Heating. . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
5.3.1 Surface Heat Source Consideration. . . . . . . . . . . . . . . . 173
5.3.2 Volumetric Heat Source Consideration . . . . . . . . . . . . . 174
5.3.3 Two-Dimensional Heating . . . . . . . . . . . . . . . . . . . . . . 174
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
Chapter 1
Introduction
Abstract Laser heating offers considerable advantages over the conventional
methodssuchasprecisionofoperation,localtreatment,andlowcost.Laserathigh
intensity when interacts with the solid surface, the absorption takes place. This in
turncausesinternalenergygainofthesubstratematerialandheatreleasefromthe
irradiatedregion.Sincetheprocess,ingeneral,isfast,temperaturegradientsremain
high in the irradiated region. This results in high thermal strain and thermally
inducedstressesinthisregion.Moreover,inlasertreatmentprocess,theendproduct
is important from the application point view. The high stress levels formed in the
irradiatedregionmaycausefailureofthesurfacethroughstressinducedcracking.
Consequently, a care needs to be taken during the laser treatment process. This
chapterprovidestheinformationabouttheimportanceandlimitationsofthelaser
treatmentprocessintermsofthethermalstressesformedintheirradiatedregion.
Lasersareconsideredtobeoneoftheeffectivetoolsforlasertreatmentofmetallic
surfaces.Highpowerlaser,whenfocusedatthesurface,generatesexcessiveheat,
which enables the surface to reach the melting temperature of the substrate
material.Insomecases,laserheatingisassociatedwiththephasechange,suchas
melting and evaporation at the surface. In this case the heating process becomes
complicated because of the size of the heated, which is in the order offraction of
millimeter. Therefore, controlling the phase process becomes necessary to avoid
surface asperities, such as cavities, which are formed during surface evaporation.
One of the methods to secure the control melting at the surface is to model the
physical processes involved during the laser interaction with surface. Although
model studies involve with assumptions simplifying the mathematical arrange-
ments,experimentingtheprocessisdifficult,timely,andexpensivebecauseofthe
high temperature involvement and small size of heated region during the short
time period. The time limitation in measurements is attributed to the laser pulse
length, which has to be shorter to be effective for the treatment of the surfaces.
Laser heating process can be classified into two categories. The first category
involves with the solid state heating without the phase change at the irradiated
surface. The heating is governed by the conduction process, which can be
B.S.Yilbasetal.,LaserPulseHeatingofSurfaces 1
andThermalStressAnalysis,MaterialsForming,MachiningandTribology,
DOI:10.1007/978-3-319-00086-2_1,(cid:2)SpringerInternationalPublishingSwitzerland2014
