Simulation Study of Carbon Steel Phase Transformation ......Submitted to Department of Laser and...
Transcript of Simulation Study of Carbon Steel Phase Transformation ......Submitted to Department of Laser and...
Ministry of Higher Education and Scientific Research
University of Technology
Department of Laser and Optoelectronic Engineering
Simulation Study of Carbon Steel
Phase Transformation using Nd:YAG
laser Pulse A Thesis
Submitted to Department of Laser and Opto-Electronic Engineering of the University of Technology in Partial Fulfillment of the Requirements for the Degree of Master of Science in Laser
Engineering
By Eng. ALAA FATHEL EDAN
(B.sc. 2001)
Supervised by
Assistant Prof
Dr. Kadhim A. Hubeatir
March 2008
ربيع االول 1428
جمھورية العراق وزارة التعليم العالي والبحث العلمي
الجامعة التكنولوجية قسم ھندسه الليزر والبصريات االلكترونية
التحول الطوري للحديد دراسة الكاربوني باستخدام الليزر النبضي
Nd:YAG
رسالة مقدمة إلى ر والبصريات االلكترونيةقسم ھندسة الليز
في الجامعة التكنولوجية و ھي جزء من متطلبات نيل ھندسة الليزر علوم درجة الماجستير في
من قبل عالء فاضل عيدان
( )الميكانيكيةعلوم في الھندسة سبكالوريو
إشراف
كاظم عبد حبيتر. د.م.أ
ربيع االول -ه1428 م2008 -اذار
Abstract
In this study, a mathematical model for the hardening process by the phase
transformation , is performed on the wrought iron with nickel alloy by using
matlab program(6.5). The metal surface temperature was calculated depending on
the alloy parameters which are thermal conductivity, thermal diffusivity,
reflectivity to the used laser wavelength and original surface temperature , which is
room temperature in addition to the values of power density , which were
calculated in previous step , and the used pulse duration ..
The proper sample thickness was calculated to get the self-quenching
which is the proper condition for the complete phase transformation from austenitc
to martensite phase which is the hardening phase.
The distribution, of the residual thermal stresses at the sample surface , is
calculated by using the linear expansion coefficient and the modulus of elasticity.
The laser energy distribution inside the alloy was calculated , this helps to find out
the penetration depth of the laser radiation inside the alloy by using the alloy
surface reflectivity and energy in addition to the absorption coefficient was
plotted .The graph of the distribution of the residual surface thermal stresses by
using Matlab. Temperature distribution, at alloy surface and inside the sample
(along the thermal penetration depth of laser radiation ), was calculated and plotted
in two graphs for the two thermal distributions by using Matlab.
Introduction
Chapter one
Introduction
1-1 GGeenneerraall Introduction
The twentieth century has witnessed many inventions and
discoveries, the mankind was unable through its long centuries to reach
these inventions and discoveries. May be one of the most important
inventions among these inventions is the laser radiation invention. Laser
radiation has great importance in many applications such as the scientific
and industrial applications. The invention of laser has led to a scientific
and technological revolution which included the conventional and
modern industries, laser helped in bring about tremendous developments
for many sciences and application fields and has become one of the
modern science achievements.
Laser is distinguished by several properties which are not available
in any other optical source, these properties are : high intensity,
coherence, monochromatic and little divergence, laser travels in a very
narrow beam for long distances . So, for all the above mentioned
properties of laser, laser technology has a big and important role in
processes connected to laser. Surface treatment of materials has been
used in industry for several years to improve some of the mechanical
properties of materials. Most failures, which may take place at material
surface as a result of lassitude , erosion and corrosion,are because of the
stresses which mostly take place at the surface and material exposure to
environment conditions. So the solution is to make the material acquire
surface properties which differ from the inner part. There are several
ways to change the surface structure for example by carburizing, nitriding
1
Introduction
and phase transformation hardening using flame, electrical inducation,
electron beam or plasma. Because of the advantages that laser has, it has
been used in surface thermal processes to change the microstructure of
the surface layers to improve the surface properties in comparison with
the material original properties . Using laser in surface hardening of
metals is regarded very important in several industries[1].
The advantages of laser hardening can be summarized as follows[2]:
• Selected areas can be hardened without affecting the surrounding
material.
• Minimal heat input causes little macro distortion and reduces the
need for additional machining.
.Treatment depth is accurately controlled and highly reproducible.
• Superior hardness, strength, lubrication, wear resistance and fatigue
properties can be obtained compared to conventional processes. • It can often be used without external quenching.
• No geometry specific tools such as that required for induction
hardening is necessary. • It can be integrated as an inline computer controlled process. • Time saving (no heating-up or soaking time is required). • Minimal environmental impact.
2
Introduction
1-2 Literature Survey
The heat treatment operations have got a lot of attention in researches
and studies since the laser was invented. This attention has become wider
and entered the industrial field because of the multi-benefit of laser .
In the nineties witnessed a tremendous expansion in researchs and
applications to heat treatment various Ferro-alloys. In 1990
(H.J.M.Geijselaers & J.Huetink)[3] set up a finite element model to
determine temperatures, phase compositions and stresses during a thermal
hardening cycle used (steel CK45). In 1996 (K.G.Watkins, et al)[4]
studied microstructural evolution in a range of laser surface treated
aluminum alloys including laser surface melting of Al-Cu, Al-Si, Al-
Zn,Al-Fe, laser surface alloying of Al-Ni, Al-Cr & Al-Mo. The
improvements in hardness and critical pitting potential compared with
conventional alloys by CO2 laser.
At the end of years of 2001 (K.G.Watkins , et al) [6] studies the
forming of 2D sheet materials on aluminum alloys and titanium alloys by
CO2 laser. In 2003 (Geijselaers,H.J.M)[7] set up simulation of laser
hardening consists of two parts. In the first part algorithms and methods
are developed for simulating phase transformations and the stresses
which are generated by inhomogeneous temperature and phase
distributions. The second part is concerned with simulation of steady state
laser hardening (usedsteel Ck45).In same year (P .T .Mannion et al)[8]
studied the effect of damage accumulation behavior on ablation
thresholds and damage morphology in ultrafast laser micro-machining of
common metals in air the observed morphologies seem to suggest that
normal vaporization is the most probable physical mechanisms
responsible for material removal during ablation (used titanium –
3
Introduction
sapphire laser and stainless steel). In 2005 (Haitham El Kadiri, et al) [9]
studied the creep and tensile behaviors of Fe-Cr-Al foils and laser micro
welds at high temperature by Co2 laser and they noticed no yield point
effect and the work hardening persists at all temperatures. In the same
year (Alexander.G.P)[10] studied feasibility investigation of laser
welding aluminum alloy 7075-T6 through the use of A 300w, single-
mode,ytterbium fiber optic laser and he noticed due to their high
reflectivity and complexity in heat treatment, aluminum alloys are some
of the hardest metals to be laser welded successfully and very high laser
power is usually required . In 2005 (L .Costa.et al)[11] set up a finite
element analysis model was applied to the study of the influence of
substrate size and ideal time between the deposition of consecutive layers
on the microstructure and hardness of a ten-layer AISI 420 steel wall built
by laser powder deposition. In same year (V. Ocelik , et al) [12] studied
sliding wear resistance of SiC/Al-8Si,WC/Ti-6Al-4v & TiB2/Ti-6Al-4v
layers by Nd:YAG laser , the observed wear mechanisms are summarized
and related to detailed micro structural observations. The layers have
been found to show excellent interfacial bonding , coupled with
dramatically improved tribological properties expressed through a
relative wear resistance value ranging from 30 to 1500. In 2006
(kennth.L) [2] studied the industrial applications and practical problems
encountered with laser transformation hardening by Co2 laser and
Nd:YAG laser and he noticed the maximum hardened with near surface
hardness values of 700-150 HV . In 2004 ( Peng . C, et al) [13] studied
laser forming of complex structures by Co2 laser and used low carbon
steel AISI-1010 and they noticed that the peak temperature drop on the
unscanned surface is much larger than that of the scanned surface, and
thus the temperature gradient through the thickness direction increases
with the increasing plate thickness. In 2007 (Milton .S.F
4
Introduction
,Flavia.A.G,Rudimar.R,Ana.M.d)[5] studied laser surface remelting and
hardening of an automotive shaft sing a high-power fiber laser used AISI
1040 steel and they noted that during heating , the eutectoid structure of
pearlite quickly changes to austenite when the temperature rices above
Ac1.In same year (Dennis .Ket al) [14] set up model which is applied to
photo thermal measurements ,leading to depth profiles of steel hardness,
which are compared with data , destructively obtained from the same
samples using Vickers indentation techniques. In same year (David
.H.P)[15] studied the effect of the surface hardening on the microstructure
and mechanical properties as wear resistance of silicon alloyed steel and
used 55Si7 steel alloy,50CrV4 chromium steel alloy, hardened by Nd:
YAG high power laser and he noticed that ausferritic structure has an
excellent tempering resistance, and that laser hardening treatment greatly
improves wear resistance of ausferritic steels. In same year
(M.Marticorena, et al)[16] noticed that the formation of layer of Tin on
the surface and the obtained roughness, have been demonstrated to
improve bone response by using a pulsed Nd:YAG laser. (G.Labeas et
al)[17] set up the finite element code ANSYS model to calculated the
residual stresses of the paint removal process by using laser radiation
(carbon dioxide & excimer) . The material used is aluminum alloy 2024-
T3,in sheet from of 1mm thickness.
1-3 Aim of the Work
The aim of this work aims to study the surface hardening by using
laser which is known analytically by using a Matlab software to find the
used laser data and the sample . For this purpose an alloy has been
selected which is difficalt to harden by the conventional ways because it
5
Introduction
6
has alow carbon ratio. The mathematical model used in this thesis put the
essential bases for the perfect choice of the laser and the material.
14 Outline of Thesis
Chapter one of this thesis gives introduction to laser hardening. Laser
transformation hardening will be presented in chapter two. The
parameters effect surface hardening process, types of laser used in
industrial applications, comparison between laser hardening with other
technologies, laser-material interaction, residual stresses, wear
resistance, Nickel-alloy wrought iron, the phases of the alloy, self-
quenching condition are two as well.
Chapter three provides the detailed description and analysis of laser
transformation hardening models. Chapter four provides the results and
discussion. Finally, the conclusions taken from this work in addition to
the suggested future work are given in chapter five.
Theory Background
Chapter Two Theoretical Background
2-1 IInnttrroodduuccttiioonn
The economics of different hardening processes can only be
compared on a case-by-case basis. Comparative costs of the hardening
processes cannot be considered separately from the comparative costs of
preparing the material for hardening and the cost of subsequent
operations. A negative cost consideration for laser hardening is the need
to pre-treat the surface with paint to enhance the absorption of the beam,
and the subsequent need to remove the remnants of the paint. A positive
cost consideration is the absence of any post-hardening machining
operation to correct for distortion.
For hardening of gears, cost comparisons between laser hardening
and gas carburizing are available. In an environment where the laser is
producing two shifts per day, laser treatment was shown to be cost
effective for large gears where a limited area was to be treated.
One manufacturer that replaced gas carburizing with laser
hardening cites the reasons as follows[2]:
��Reduced hardening time ��Reduced scrap rate ��Elimination of complex quenching, plating, masking,
stripping, and cleaning steps. ��Reduced work-in-progress inventory ��Quicker turnaround, less material handling ��Reduced floor space requirements
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Theory Background
��Reduced pollution by elimination of copper plating ��Reduced energy use
2-2 The parameters effect on the surface hardening
process
The parameters effects on the surface hardening process are:
1- Laser hardening is a rather modern technique , where the surface to be
hardened is heated by high density laser light [3].
The value of power density to raise the sample temperature to get the
value proper to the surface hardening by phase transformation is given
by:
(2‐1)
where:
E : the energy (J)
f : focal length (cm)
θ : divergence (rad)
t : pulse duration (μs)
I : power density (w/cm2)
2- Thermal conductivity values . which on this values the thermal flow
depends . Heating the material depends on the thermal flow thought.
3- The value of thermal diffusivity which indicates the speed of heat
diffusion through the material. Temperature rises a little in materials with
high thermal diffusivity with a good penetration to the materials surface a
contrary to low thermal diffusivity which suffer from a high rise in
temperature with a low thermal penetration through the material .
8
Theory Background
where :
To : initial surface temperature (K)
I : power density (w/cm2)
R : reflectivity (%)
K : thermal conductivity (W/cm.k)
N : thermal diffusivity (cm2/s)
t : pulse duration (s)
5-The reflectivity value which is one of the important properties
determines the proper wavelength. Most materials reflect a large portion
of the laser beam so, a high laser power system is needed to affect the
metal surface. The reflectivity is also a affected by the surface condition
like the presence of greases which affects the reaction between the laser
beam and the metal surface. The reflectivity of a metal can be reduced by
coating it with a material , however, the coating is not efficient always
because of the weakness of thermal coupling between the coat and
metal[1] .
9
Theory Background
2-3 Types of laser used in hardening process
Laser equipments operating with high power levels, the high power
lasers, can produce highly energetic and well focusable laser beams that
are usable in hardening . [28]
2-3-1 Carbon dioxide (Co2) lasers
The most traditional high power lasers which has very high power and
power density, Moderate efficiency, reliable operation and excellent
beam quality. But, the high wavelength of 10.6µm results in a relative
low absorption of the laser beam by metals. It is usual to apply an
absorption enhancing pretreatment like graphitizing.[18]
2-3-2 Nd:YAG Laser
The Nd ion when doped into a solid-state host crystal produces the
strongest emission at a wavelength just beyond 1µm. The two host
materials most commonly used for this laser ion are yttrium aluminum
garnate (YAG) and glass. When doped in YAG, the Nd:YAg crystal
produces laser output primarily at 1.064 µm, when doped in glass, the
Nd:glass medium laser at wavelengths ranging from 1.054 to 1.062 µm,
depending upon the type of glass used. Nd also lases at 0.94 µm and at
1.32 µm from the same upper laser level as the 1.064 µm transition,
although these transitions have lower gain.
The Nd laser incorporates a four-level system and consequently has
a much lower pumping threshold than that of the rube laser. The upper
laser level lifetime is relatively long (230 µs for Nd:YAG and 320µs for
Nd :glass), so population can be accumulated over a relatively long
10
Theory Background
duration during the pumping cycle when the laser is used either in the Q-
switching mode or as an amplifier. The emission and gain line width are
45 nm for YAG and 28 nm for glass. These lasers can be pumped either
by flashlamps or by other lasers. Diode pumping is a relatively recent
technique that has led to the development of much more compact Nd
lasers, both at the fundamental wavelength of 1.06µm and at the
frequency-doubled wavelength of 0.53µm.
The Nd:YAG crystal has good optical quality and high thermal
conductivity, making it possible to provide pulse laser output at repetition
rates of up to 100Hz. The crystal size is limited to length of
approximately 0.1m and diameters of 12mm, thereby limiting the power
and energy output capabilities of this laser. Doping concentrations for
Nd:YAG crystals are typically of the order of 0.725% by weight, which
corresponds to approximately 1.4*1026 atoms per cubic meter.
For Nd:glass laser gain media, very large-size laser materials have
been produced. Rods of up to 2 m long and 0.075 m in diameter and disks
of up to 0.9 m in diameter and 0.05 m thick have been successfully
demonstrated. The large-diameter disks have been used as amplifiers to
obtain laser pulse energies of many kilojoules. The drawback of Nd:glass
laser materials is their relatively poor thermal conductivity, which
restricts these lasers to relatively low pulse repetition rates[19].
11
Theory Background
2-3-3 High power diode laser.
These equipment are available at maximum 6kW power level. High
power diode laser equipment represent the newest generation of high
power lasers for materials processing. The lower wavelength (typically
0.8 and 0.94 µm) improves further the absorption characteristics of the
laser beam. Due to the very electrical/optical efficiency (30-50%), high
power diode laser equipment are remarkably smaller in size than other
lasers of the same kW level.[18]
2-4 Comparison between Co2 laser , Nd:YAG laser & high
power diode laser.
Tab.(2-2) provides a relative comparison of these three types of
lasers,.[23]
Laser type Wavelength
nm Absorption
efficiency
Initial
cost
Operating
cost
Expected
life
Co2 10,600 Low Low Moderate High
Nd:YAG 1,060 Moderate/high High High High
diode 800 High Moderate Low Low
Tab.(2-2) Relative comparison of different lasers used for heat
treatment.[23]
2-5 Laser processing
In laser processing, such as using laser energy to heat metals,
laser light is directed to the workpiece resulting in absorption
and reflection of light. Absorption by metals is highly dependent
12
Theory Background
on the wavelength of light, material type, angle of incidence and
surface condition. See Fig.(2-1), in general, the shorter the
wavelength, the better light is absorbed. Fig.(2-2) illustrates the
interaction of laser light with steel to produce a hardened layer.
Absorption begins at the leading edge of the spot and terminates
at the trialing edge. The time period, or exposure period,
generally is less than one second. The shape of the hardened
zone varies with the shape of the spot and the energy
distribution across the spot produced by the beam[23].
Fig.(2-1) The relationship between energy absorption and wavelength at
room temperature for iron, aluminum and copper[23].
13
Theory Background
Fig.(2-2) Laser hardening.[23]
2-6 Comparison between laser hardening and other
technologies
Advantages / Disadvantages Laser is charaacterized, in comparison with other sources , which
are used in transformation hardening, by the following[1]:
1- There is no need for air evacuation of the zone where laser beam
passes through, as it is the case when using electron beam.
2- Laser may be used in hardening mini areas, and the area , which is
affected by heat, is very limited, so the mechanical properties of the other
parts aren’t affected .
14
Theory Background
3- Laser beam can travel long distances without attenuation.
4- Getting higher power densities in comparison with other methods.
5- Materials, which are in closed mediums , can be treated through
certain windows, also area which is hard to reach by conventional
methods can be treated.
6- Chemical cleanllness by laser treatment because there is no contact
between the sample and any other material.
7- Very high speed in performing the hardening process.
In spite of these advantages, there are several disadvantages:
1- Limitation of penetration depth and the areas treated are small.
2- Laser parameters must be controlled to get the desired effect.
3- High accuracy is required in using the optical instruments to guide and
concentrate laser radiation .
4- The training, to an efficient technical team to deal with laser system,
is necessary .
5- High cost of treatment because of the high cost of laser system.
2-7 laser – material interaction
Laser beam interacts with target substances according to the
individual wavelengths. The different wavelength have several degrees of
relative absorption into the various components of hard . These
interactions include:
15
Theory Background
1- Reflection: a portion of the incident beam may be reflected off the
surface without penetration or interaction of light energy with the tissue.
2- Absorption: some of the light may be absorbed into a component of
the material, in this case there will be transference of the energy to the
tissue, and it is the most material interaction. When a material absorbs
laser energy, the light energy is converted into thermal energy .
Absorption of laser radiation is also determined by the chemical
composition of the component being irradiated, as well as the wavelength
(λ) of the incident laser beam[2]. The absorbed energy is determined by
following equation[24] :
where :
E : the energy ( J )
R : reflectivity ( % )
A : absorption coefficient ( cm-1 )
Z : depth of penetration ( cm )
EZ : absorption energy (J)
Most of the incident laser radiation on the sample is absorbed at the
surface and this in turn raises the surface temperature more than
depth[24] .
16
Theory Background
3- Scattering: This occurs when the target tissue can cause the laser
beam to spread out into a large area and this is useful in photo
polymerization of composite resin, but as the beam is scattered, its power
density eventually decreased to the point where it has no significant
effect.
4- Transmission: The energy travels directly through the material
causing no effect. Depending on the material, some lasers penetrate
deeper than others, e.g. the wavelength of argon laser is transmitted by
clear structure of the eyes, while it is absorbed by the blood vessels of the
retina.
(2-3) Laser-material itraction[20].
2-8 Residual stresses
Residual stresses are important in many of metalworking . They can
cause distortion, either directly or after subsequent heat treatment.
17
Theory Background
Residual stresses arise wherever there has been inhomogeneous
plastic deformation, but it is important to recognize that they are elastic
stresses due directly to differences in elastic strain and cannot exceed the
yield stress of the material [25].
Residual stresses should not be overlooked as sources of fatigue
failure. The rupture associated with fatigue failure is a brittle one, caused
by stresses acting in tension at right angles to the cleavage plane.
Therefore, residual tensile surface stresses are undesirable, because they
effectively decrease the stresses which produce failure. Residual tensile
surface stresses many exist in castings as a result of restraint of
dimensional change during cooling. They are similarly found in some
pieces rapidly cooled from hot working temperatures . Residual tensile
surface stresses are also found in welded structures when thermal
contraction is prevented by the rigidity of the structure. They are
encountered in electrodeposited metals, perhaps as a result of evolution
of hydrogen during formation of the deposit. Residual stresses are too
complicated to permit a simplified statement as to their origins[26].
The effect of temperature gradient alone. It was shown earlier, under
the effect of size and mass, that during quenching the surface is cooled
more rapidly than the inside. This results in a temperature gradient across
section of the piece or a temperature difference between the surface and
the center. Almost all solids expand as they are heated and contract as
they are cooled. This means that the surface, since it is at a much lower
temperature, should have contracted much more than the inside.
However, since the outside and inside are attached to each other, the
inside, being longer, will prevent the outside from contracting as much as
it should . it will therefore elongate the outside layers, putting them in
tension while the inside in turn will be in compression. The approximate
18
Theory Background
magnitude of this thermal stresses may be calculated from the following
formula[27]:
(2‐5)
where:
S : residual stresses (Mpa)
α : coefficient of linear expansion (cm/cm. Co)
e : modulus of elasticity (Mpa)
ΔT : change of temperature on the surface (Co )
Since cracks are propagated only by tensile stress, surface residual
compressive stress would be most desirable because they are opposite to
the applied load[27].
2-9 The Transformation phases
2-9-1 Ferrite
A solid solution of one or more elements in body-centered-cubic
iron. Unless otherwise designated, the solute is generally assumed to be
carbon. The lower area is alpha ferrite, the upper, delta ferrite. If there is
no designation, alpha ferrite is assumed[27] .
Regions which have attained a temperature above Ac1 and below
Ac3 still contain ferrite. The effect is more pronounced in lower carbon
steels, since the thicker ferrite network requires a longer time above Ac3
to pass completely into solution[29] Fig.(2-5)[1] .
19
Theory Background
Fig. (2‐4). The iron‐iron carbide equilibrium diagram[1].
2-9-2 Cementite
Cementite is a carbide of iron of the formula Fe3C .It may occur in
steel as free cementite or as a constituent of the eutectoid, pearlite. It
always exists in annealed steels with over 0.9 per cent of carbon and
occurs in the form of a continuous network in normalized steels with
more than 1 per cent of carbon[29].
2-9-3 Pearlite
Pearlite was so called on account of the iridescent colours it shows
and its resemblance to mother-of-pearl when viewed by oblique
illumination. It consists of alternate lamellae of ferrite and cementite , and
20
Theory Background
contains a little under 0.9 per cent of carbon. Annealed steels containing
less than 0.9 per cent of carbon (hypo-eutectoid steels) consist of pearlite
and ferrite those with more than 0.9 per cent carbon contain pearlite and
cementite. Since the whole of the carbon of a hypo-eutectoid steel
(except less than 0.01 per cent, dissolved in the ferrite) is in the
pearlite[29] .
2-9-4 Austenite
A solid solution of one or more elements in face-centered-cubic
iron. The solute is generally assumed to be carbon. An alloy steel whose
structure is normally austenitic at room temperature [27].
2-9-5 Martensite The name martensite honours one of the pioneers of metallurgy,
Professor A. Martens. Martensitic phase transformation is found in
numerous alloys without it necessarily being accompanied by hardening.
Cooled under equilibrium conditions (slow cooling), steel carbon atoms
diffuse out of the austenite matrix to form a pearlite structure, iron atoms
orientate themselves into a Body Centred Cubic (BCC) crystallographic
structure, and with forced cooling rates carbon atoms are trapped in the
iron matrix which results in a highly distorted Body Centered Tetragonal
crystallographic structure [2]. The volumetric difference between martensite and austenite is about
4% resulting in compressive stresses on the surface. For the formation of
martensite, the steel component first needs to heated to the Ac3
(austenite
formation) temperature. This Ac3
temperature is dependent on the
chemical composition of the steel[2] .
21
Theory Background
The crystallographic structure of austenite above the Ac
3 temperature
is Face Centred Cubic (FCC).The component treated then needs to be
cooled rapidly to ensure that carbon atoms are trapped in the matrix of the
iron to form martensite. The Ms
and Mf
(“Martensite start” and
“Martensite finish”) temperatures are determined by the chemical
composition of the steel [27].
2-10 Heat treating of metals
The material in aerospace applications is often chosen because of
their heat and corrosion resistance, fatigue properties or low weight.
Depending on the base material of the component is the heat treating
done at different temperature and holding time. In order to describe a
number of common heat treating processes and their purpose, are steels
used an an example. Steel is define as an alloy of iron and carbon with the
carbon content up to about 2 wt%. Other alloy elements can be up to
5wt% in a low-alloy steel and more in a high-alloy steel.Heat treatment is
general name of a large number of thermal processes where the goal is
often to obtain a satisfactory hardeness. Fig.(2-9) shows typical heating
ranges in an Iron-Carbon diagram for different heat treating processes.A1
is the eutectoid line, or the lower critical temperature for austenite
transformation and A3 is the upper critical temperature. Acm represent the
upper critical temperature for hypereutectoid steels. The most common
heat treating processes for steels are described below.
22
Theory Background
Fig.(2-5) Iron-Iron Carbide phase diagram showing typical temperature
ranges for different heat treatment operations[30].
Annealing is a heat treatment process, refers to a material exposed to
an elevated temperature for an extended period of time , and thereafter
cooled down. This is primarily done in order to soften the material.
Ferrite and pearlite are the dominating phases in the material after the
annealing process. If the cooling rate is increased, then martensite will be
created, this process is called quenching. The hardness of the material is
controlled by the amount of the martensite created because of the rapid
cooling from the austenitizing (A3) or solution treating temperature, The
amount of martensite can be controlled by the selection of quench
medium. Common quench media are water, saltwater, oil, polymer
solution or some inert gas (helium, argon or nitrogen).
Tempering of steel is a process in which previously hardened or
normalized steel is heated to a temperature below the critical temperature
in order to increase ductility and toughness. The difference between
tempering and stress relife heat treating is that the aim of the tempering
operation is to create a certain microstructure. In the other case is the
primary aim to relieve stresses, but both procedures are performed in the
23
Theory Background
24
same temperature interval .
The part must be heated up above the A3/Acm temperature so a
homogenous austenite phase is created, in order to be classed as a
normalizing treatment. The chosen cooling rate from the austenizing
temperature is depends of the required strength and hardeness of the
material. At higher cooling rates, more pearlite is formed and the lamellae
are finer and more closely spaced. Larger amount of pearlite and fine
lamellae gives higher strength and hardness. Observe that the cooling rate
should not be as high as for the quenching process where martesite is
created [30].
Description of The Model
Chapter Three
Description of The Model 3-1 Introduction
In this chapter the steps of performing the mathematical model will be
described .
32 CK45 Steel
Material: CK 45
Standard: DIN
Country: Germany
Steel Group: Structural and constructional steels
Subgroup: DIN 1652-4 Bright steels for quenching and
Tempering
Comment: Technical delivery conditions DIN 1652-4 was
Superseded by EN 10277-5
Application: Automobile-and motor construction , mech,
engineering , Bolts and nuts, resistant to
elevated temperature up to 400 oC[31]
35
Description of The Model
33Properties (CK45 steel)
t<=5mm;KCold drawn[31]
(Yield stress,Rpo2 MPa) 640
Tensile stress,Rm(MPa) 770
Elongation,As(%) 4.00
5<t<= 10mm;K old drawn C
Yield stress,Rpo2(MPa) 560
Tensile stress,Rm(MPa) 730
Elongation As(%) 5.00
34Chemical Composition(%)
Table(31) The chemical composition Ck45steel.[31]
Max. Min. Criteria 0.5000 0.4200 C 0.4000 Si 0.8000 0.5000 Mn 0.0350 P 0.0350 S 0.4000 Cr 0.1000 Mo 0.4000 Ni 0.6300 Cr + Mo
36
Description of The Model
3-5 Calculating the power density (I)
Laser effect on perform the surface hardening process relies on
certain parameters and these parameters are power density and pulse
duration.
Eq. (2-1) is used to evaluate the proper power density to raise the
sample surface temperature to get the value proper to the surface
hardening by phase transformation .
A constant value of divergence , a certain energy band between (3-7
J) a lenses focal length between (5-25 cm) and a pulse duration between
(1*10-4 to 5*10-4 s ) were used to perform this search . The procedure was
done as follows fixing energy and focal length values and using variable
values of pulse duration and within the previously mentioned range.
The calculations within all energy , pulse duration and focal length
ranges were made by taking a constant value of the divergence , a wide
range of power density was obtained under different conditions (i.e.
energy , pulse duration and focal length values) at constant divergence
value .
3-6 Computing surface temperature (TS)
The results were obtained from Eq. (2-1). By using Eq.(2-2) different
temperature values were obtained of the sample surface and the proper
value was chosen which was 1500Co (1773k) because it is the nearest to
the sample melting point which is (1538Co) because the phase
transformation degree is very high and near the melting point. The other
values of temperature which were obtained are neglected because they
either higher than the melting point , which is unapplicable to the phase
transformation temperature to austenite phase , or lower than the melting
37
Description of The Model
point (very large difference ). This is not valid with the condition that the
phase transformation temperature is very high and near the alloy melting
point .
3-7 Thermal distribution calculation
Thermal distribution calculations in the mathematical model are
divided into two parts :
hermal distribution inside the sampleCalculations of tPart one :
Calculations of thermal distribution calculations inside the sample can be
done by using the thermal penetration depth which was calculated by
Matlab program (Appendix A) and by dividing this depth into five zones
between the surface and the thermal penetration depth, the temperature in
each zone can be calculated after that by appling the Matlab program. A
three-dimensional figure can be obtained and this figures describes the
thermal distribution inside the sample .
ermal distribution at the sample surfaceof thcalculation Part two:
calculations of thermal distribution at sample surface are done by
using Matlab program(Appendix B). By this program the distance , at
which heat is distributed, can be calculated from the limits of the
hardened spot (thermally treated spot) which equals laser beam spot area
incident on the sample surface. After that divide this distance into five
zones and the temperature for each zone at the sample surface is
calculated. By appling Matlab program two-dimensional figures are
obtained which describe thermal distribution at sample surface .
3-8 Residual stresses calculations
38
Description of The Model
39
The value of the residual thermal stresses at the sample surface is
computed by using Eq.(2-5) , at the beginning the residual thermal stress,
which is generated between the hardened spot (exposed to laser radiation
and its temperature is 1500Co) and the neighbour zone which is heated by
conductivity of heat, after that between the former zone and the
neighbour zone and soon the distribution of the compressive thermal
stresses at sample surface are computed. By using Matlab is program a
two dimensional graph obtained which clarifies the distribution of the
residual thermal stresses at the sample surface.
Results and Discussion
Chapter Four
Results and Discussion
4-1 Calculating the power density(I)
In table(4-1) the energy value is (3J), the focal length is (5cm) , and
pulse duration between (1*10-4 to 5*10-4 s) . Values of power density
were obtained . After that a focal length value of (10 cm) was used and
the same pulse duration between (1*10-4 to 5*10-4 s) . The focal length
variation continued (15,20,25cm ) with the same data mentioned above.
The value of laser energy was changed to (4J) table(4-2) the
previous procedure continued until the calculations within all ranges of
energy , pulse duration and focal length were made by taking a constant
value of divergence also table(4-3) ,table(4-40 &table(4-5) .
1) :-The results from using Eq.(2
Table.(4-1) The results from using energy 3J.
I(w/m2) at F=0.25m
I(w/m2) at F=0.20m
I(w/m2) at F=0.15m
I(w/m2) at F=0.10m
I(w/m2) at F=0. 005m
t (s)
3.8197*1065.9683*1061.0610*1072.3873*1079.5493*1071*10-4
1.9099*1062.9842*1065.3052*1061.1937*1074.7746*1072*10-4
1.2732*1061.9894*1063.5386*1067.9577*1063.1831*1073*10-4
9.5493*1061.4921*1062.6526*1065.9683*1062.3873*1074*10-4
7.6394*1051.1937*1062.1221*1064.7746*1061.9099*1075*10-4
50
Results and Discussion
Table.(4-2) The results from using energy 4J.
I(w/cm2) at F=25cm
I(w/cm2) at F=20cm
I(w/cm2) at F=15cm
I(w/cm2) at F=10cm
I(w/cm2) at F=5cm
t (s)
5.0930*1067.9577*1061.4147*1073.1831*1071.2732*1081*10-4
2.5465*1063.9789*1067.0736*1061.5915*1076.3662*1072*10-4
1.6977*1062.6526*1064.7157*1061.0610*1074.2441*1073*10-4
1.2732*1061.9894*1063.5368*1067.9577*1063.1831*1074*10-4
1.0186*1061.5915*1062.8294*1066.3662*1062.5465*1075*10-4
Table.(4-3) The results from using energy 5J.
I(w/cm2) at F=25cm
I(w/cm2) at F=20cm
I(w/cm2) at F=15cm
I(w/cm2) at F=10cm
I(w/cm2) at F=5cm
t (s)
6.3662*1069.9472*1061.7684*1073.9789*1071.5915*1081*10-4
3.1831*1064.9736*1068.8419*1061.9894*1077.9577*1072*10-4
2.1221*1063.3157*1065.8946*1061.3263*1075.3052*1073*10-4
1.5915*1062.4868*1064.4210*1069.9472*1063.9789*1074*10-4
1.2732*1061.9894*1063.5368*1067.9572*1063.1831*1075*10-4
Table.(4-4) The results from using energy 6J.
I(w/cm2) at F=25cm
I(w/cm2) at F=20cm
I(w/cm2) at F=15cm
I(w/cm2) at F=10cm
I(w/cm2) at F=5cm
t (s)
2.2282*1081.1937*1072.1221*1074.7746*1071.9099*1081*10-4
1.1141*1085.9683*1061.0610*1072.3873*1079.5493*1072*10-4
7.4272*1073.9789*1067.0736*1061.5915*1076.3662*1073*10-4
5.5704*1072.9842*1065.3052*1061.1937*1074.7740*1074*10-4
4.4563*1072.3873*1064.2441*1069.5493*1063.8197*1075*10-4
51
Results and Discussion
Table.(4-5) The results from using energy 7J.
I(w/cm2) at F=25cm
I(w/cm2) at F=20cm
I(w/cm2) at F=15cm
I(w/cm2) at F=10cm
I(w/cm2) at F=5cm
t (s)
8.9127*1061.3926*1072.4740*1075.5704*107 2.228*108 1*10-4
4.4563*1066.9630*1061.2379*1072.7852*1071.1141*1082*10-4
2.9709*1064.6420*1068.2525*1061.8568*1077.4272*1073*10-4
2.2282*1063.4815*1066.1894*1061.3926*1075.5704*1074*10-4
1.7825*1062.7852*1064.9515*1061.1141*1074.4563*1075*10-4
4-2Calculate thermal conductivity and diffusuivity
Thermal conductivity is a propperty of materials that expressed the
power density that will flow through the material if a certain temperature
gradient exists over the material.
The thermal conductivity is usually expressed in W/m.k .the usual
formala is;
Thermal conductivity=power density/temperature
It should be noted that thermal conductivity is a property that is
describes the semi static situation, temperature gradient is assumed to be
constant. As soon as the temperature starts changing,other prameters
enter the equation.
The immediately explains why it is so very difficult to measurment
thermal conductivity. Explains why it is so very difficult to measure
thermal conductivity. Idealy this would require a steady situation. This is
far from easy because it usaualy requires a carefully planned laboratory
experimentt a lot of time to get to an equilibrium.
52
Results and Discussion
In thermal parameters,also the heat capacity starts playing a role. The
heat capacity is again a material property. It expresses the fact that for
changing theb temperature of a certain volume of material energy must
flow in or out. The heat capacity is usally found in the textbooks a
specific heat capacity, which must be multiplied by the density to get the
full picture.
Heat capacity=density*specific heat capacity
When dynamic processes are involved,the change of temperature
versus time,at known boundary conditions is determined by both thermal
conductivity and heat capacity.
Thermal diffusuivity= thermal conductivity/heat capacity
4-3Computing surface temperature (TS)
The energy value was selected to be (3J) and the pulse duration is
(1*10-4 s) because they are the best conditions to make the power density
with suitable value to raise the temperature of the surface to the phase
transformation temperature degree table(4-6) .
When the focal length is decreased , the power density increases
according to Eq. (2-1). The relation between the surface temperature and
the power density is a direct relation this means that when the power
density is increased then the surface temperature rises according to Eq.
(2-2) . It can be realized from the previous figure that the rise in the
surface temperature is very little for the focal length values (20 to 25 cm)
that is because the resulting power density is not sufficient to raise the
53
Results and Discussion
surface sample temperature to a high value . For the focal length (15 cm)
the case is different, the change in temperature of the sample surface will
make the surface temperature get the required temperature value. After
the focal length value (10cm) the temperature rise will be so high because
at that point the power density will be so high that it is enough to melt
surface which will be at very high temperature. The energy value was
selected to be (3J) because it is the suitable value to get the proper power
density which raises the metal surface temperature to the phase
transformation temperature to the austenite phase also table(4-7)
,table(4-8),table(4-9),table(4-10)
.
2):-The results from using Eq.(2
Tab.(4-6) The results from using energy 3J.
Ts(k) I(w/cm2) t=5*10-4 s
I(w/cm2) t=4*10-4 s
I(w/cm2) t=3*10-4 s
I(w/cm2) t=2*10-4 s
I(w/cm2) t=1*10-4 s
F(cm)
13575 1.9099*1072.3873*1073.1831*104.7746*1079.5193*1075 3617 4.7746*1065.9683*1067.9577*1061.1937*10 2.3873*10710 1773 2.1221*1062.6526*1063.5368*1065.3052*1061.0610*10715 1127 1.1937*1061.4921*1061.9894*1062.9842*1065.9683*10620 829 7.6394*1059.5493*1051.2732*1061.9099*1063.8197*10625
Tab.(4-7) the results from using energy 4J.
Ts(k) I(w/cm2) t=5*10-4 s
I(w/cm2) t=4*10-4 s
I(w/cm2) t=3*10-4 s
I(w/cm2) t=2*10-4 s
I(w/cm2) t=1*10-4 s
F(cm)
18001 2.5165*1073.1831*1074.2241*1076.3662*1071.2732*1085 4723 6.3662*1067.9577*1061.0610*1071.5915*1073.1831*10710 2265 2.8294*1063.5368*1064.7157*1067.0736*1061.4147*10715 1404 1.5915*1061.9894*1062.6526*1063.9789*1067.9577*10620 1006 1.0186*1061.2732*1061.6977*1062.5465*1065.0930*10625
54
Results and Discussion
55
Tab.(4-8) The results from using energy 5J.
Ts(k) I(w/cm2) t=5*10-4 s
I(w/cm2) t=4*10-4 s
I(w/cm2) t=3*10-4 s
I(w/cm2) t=2*10-4 s
I(w/cm2) t=1*10-4 s
F(cm)
22427 3.1831*1073.9789*1075.3052*1077.9577*1071.5915*1085 5830 7.9572*1069.9472*1061.3263*1071.9894*1073.9789*10710 2756 3.5368*1064.4210*1065.8946*1068.8419*1061.7684*10715 1681 1.9894*1062.4868*1063.3157*1064.9736*1069.9472*10720 1183 1.2732*1061.5915*1062.1221*1063.1831*1066.3662*10625
Tab.(4-9) The results from using energy 6J.
Ts(k) I(w/cm2) t=5*10-4 s
I(w/cm2) t=4*10-4 s
I(w/cm2) t=3*10-4 s
I(w/cm2) t=2*10-4 s
I(w/cm2) t=1*10-4 s
F(cm)
26853 3.8197*1074.7740*1076.3662*1079.5493*1071.9099*1085 6936 9.5493*1061.1937*1071.5915*1072.3873*1074.7764*10710 3248 4.2441*1065.3052*1067.0736*1071.0610*1072.1221*10715 1957 2.3873*1062.9842*1063.9789*1065.9683*1061.1937*10720 1360 1.5279*1061.9099*1062.5465*1063.8197*1067.6394*10625
Tab.(4-10) The results from using energy 7J.
Ts(k) I(w/cm2) t=5*10-4 s
I(w/cm2) t=4*10-4 s
I(w/cm2) t=3*10-4 s
I(w/cm2) t=2*10-4 s
I(w/cm2) t=1*10-4 s
F(cm)
31278 4.4563*1075.5704*1077.4272*1071.1141*108 2.2282*108 5 8043 1.1141*1071.3926*1071.8568*1072.7852*107 5.5704*107 10 3740 4.9515*1066.1894*1068.2525*1061.2379*107 2.4740*107 15 2234 2.7852*1063.4815*1064.6420*1066.9630*106 1.3926*107 20 1537 1.7825*1062.2282*1062.9709*1064.4563*1068.9127*106 25
Results and Discussion
4-3 Energy distribution and depth of heat penetration
calculations
The energy distribution is calculated by using Eq.(2-4) . When the
sample thickness, which was obtained by Eq.(2-7), is used and laser pulse
duration is (1*10-4 s) and by substituting it in the equation , the absorbed
energy (Ez) at the thickness equals zero . When the thickness is made
half, the absorbed energy equals zero too. This means that there is no
absorbed energy at this depth and when the depth of 0.002795 cm was
reashed , there was an absorbed energy value and this is a proof that it is
the thermal penetration depth because when laser rays penetrate the
material , energy absorption happens. And by appling this equation to
various locations between the above mentioned depth and the surface , it
can be noticed that most energy is absorbed at the surface, as a result the
surface temperature will rise to average high value which is the phase
transformation temperature table(4-11) .
)4‐2q.(E ingus The results
Ez(J) Z(cm) 00.0111000 00.0055500 00.0027960
1.5692*10‐990.0027950 9.8896*10‐800.0018236 6.2325*10‐600.0013677 3.9278*10‐400.0009118 2.4753*10‐200.0004559
1.560
Tab.(4-11)
56
Results and Discussion
4-4 Thermal distribution calculation
Thermal distribution calculations in the mathematical model are
divided into two parts :
ermal distribution inside the sampleth calculations of Part one :
The fig.(4-1) shows the thermal distribution in the selected areas of
the depth . It can be noticed at the surface exposed to radiation area is a
small are compared to the others because it represents the laser radiation
incidence area at the sample surface, the temperature of this area rises to
about 1500Co and the size of this area depends on the laser spot size and
this area is the hardened area . Also it can be noticed that when moving
inside the sample deeper temperature decreases and this is because that
(most thermal energy is absorbed at the surface and the rest is distributed
on the depth ) and the zone area increases because of the thermal
diffusivity which diffuses the thermal energy. The cause behind energy
penetration from the surface to the depth is the thermal conductivity it can
be noticed also the big difference in temperature between the surface and
the area near to it and this decreases with the increase in depth . This is
because of the short time of heating (laser pulse duration ) this prevents
radiation from penetrating to big depth and because of the surface
reflectivity which reflects part of the radiation table(4-12) .
57
Results and Discussion
The results
Tab.(4-12)
Temperature(k) Depth(cm) 177305380.0004559 3440.0009118 3090.0013677 3010.0018236 2980.0027950
Fig.(4‐1) The temperature distribution in the depth.
surface ermal distribution at the sampleth of calculationPart two:
The fig.(4-2) explains thermal distribution in the selected areas of the
sample surface . It can be noticed at the middle of the figure a small red
58
Results and Discussion
zone which represents laser radiation falling area on the sample surface
whose temperature reaches (1500Co) which is the hardening area (zone)
which is a small zone because the laser spot is small. A big difference in
temperature between the hardening zone and the adjacent one is because
surface sample exposure time to laser radiation is short and not enough
for large heat transfer to the adjacent zones table(4-13) .
The results
Tab.(4-13)
Temperature(K) Distance on the surface(cm) 177305930.00160366 3710.00320732 3220.00481098 3090.00641464 2980.00801830
59
Results and Discussion
Fig.(4‐2)The temperature distribution in the sample surface.
4-5 Residual stresses calculations
The fig.(4-3) clarifies the generated thermal stresses after the
hardening process. The small spot in the middle of the figure represents
the hardening zone which is the zone of the sample surface where the
laser radiation falls, because of the rapid rise in its temperature which
reaches about (1500Co). This zone expands, for the rest of the sample
surface which is not influenced by the temperature rise because the
thermal exposure is short (short laser pulse duration), this leads to oppose
the expansion and this in turn causes compressive stresses directed
towards the hardening zone. These stresses are useful because they act in
the opposite direction to the load which is applied on the sample increases
as shown in Eq.(2-5) & table (4-14) .
60
Results and Discussion
61
)5‐2q.(E ingsu The results
Tab.(4-14)
S (psi) ∆T (K)F (cm) Ts (K) 2589015 132775 13575 647205 331910 3617 287205 147515 1773 161655 82920 1127 103545 53125 829
Fig.(4‐3)The thermal stresses distribution in the sample surface.
Conclusion and Suggestion for Future work
Chapter Five
Conclusion and Suggestions for Future Work
5-1 Conclusions
The main conclusions from the present project are :
1- Not every laser system can be used in hardening, but a certain
condition must be available so as to use the laser system and alloy in
hardening.
A certain condition in the laser system:
I- A suitable pulse duration was found is equal (1*10-4s).
II-A suitable focal length of lenses was found is equal (15cm).
III- A suitable energy was found is equal (3J).
IV- A suitable power density to get the phase transformation temperature
(1500Co) of the surface alloy (1.061*107W/cm2).
The best conditions in the alloy transformation hardening on the surface:
I- A suitable reflectivity of the surface alloy for this laser wavelength
(1.064µm) is (48%) .
II- A suitable thickness of alloy was found to be equal (0.111mm)
because the remaining parts of the sample from a heat sink sufficient to
cool the heat surface at a cooling rate to form the martensite at the alloy
surface and there is no need for an exterior cooling medium and this
know self –quenching .
2- In the thermal distribution inside the sample noticed the big difference
in temperature between the surface and the area near to it and this
72
Conclusion and Suggestion for Future work
73
decreases with the increase in depth. This is because of the short time
heating (laser pulse duration) this prevents radiation from pentrating to
big depth and because of the surface reflectivity which reflects part of the
radiation.
3- In the thermal distribution at the sample surface a big difference in
temperature between the hardening zone and adjacent one is because
surface sample exposure time to laser radiation is short and not enough
for large heat transfer to the adjacent zones.
4- The residual stresses are compressive stresses directed towards the
hardening zone. These stresses are useful because they act in the opposite
direction to the load which is applied on the sample.
5-2 Suggestions for future work
1- Performing the practical application and comparing the results with the
mathematical model.
2- Set up a mathematical model to study the suitable parameters to make
the reflectivity match the laser wavelength and this is done by coating the
surface with a suitable paint and studying the conditions that lead to the
occurance of the thermal coupling between the paint and the surface.
3- Set up a mathematical model to study the effects of the residual
thermal stresses on the surface by using a pulse laser and a continuous
laser and comparing between them .
4- Set up a mathematical model to study the hardening process by
surface melting by laser .
5- Set up a mathematical model to study the hardening process by
surface alloying by laser .
Contents
No.p Subject I II
IIIVI I
VIIX 1 3 5 6 7 8
10 10 10 12 12 12 14 15 17 18 20 22 23 25 26 26 27 27
Dedication Acknowledgements Abstract Contents List of Figures List of Symbols
ctioion
Chapter one ‐ Introdu
t
n1‐1General Introduc1‐2Literature survey1‐3 Aim of the work1‐4 Outline of thesisChapter two – Theortical Background2‐1 Introduction2‐2 The parameters effect on the surface hardening process2‐3 Types of laser used in hardening process2‐3‐1 Carbon dioxide (Co2) laser2‐3‐2 Nd:YAG laser2‐3‐3 High power laser 2‐4 Comparison between Co2laser,Nd:YAG laser & high power diode laser 2‐5 Laser processing2‐6 Comparison between laser hardening with other Technologies2‐7 Laser‐ material interaction2‐8 Residual Stresses2‐9 The Transformation phases2‐9‐1 Ferrite2‐9‐2 Cementite2‐9‐3 Pearlite2‐9‐4 Austenite2‐9‐5 Martensite 2‐10 Heat treating of metals Chapter Three – Description of The Model
VI
3‐1 Introduction
VI
27 28 35 35 36 36 38 50 52 53 57 60 for Future Work 72 73
3‐2 CK45 Steel
3‐3Properties (CK45 steel)
3‐4Chemical Composition(%)
3‐5 Calculating the power density(I)3‐6 Computing surface temperature(Ts)3‐7 Thermal Distribution Calculation3‐8 Residual stresses Calculations
Chapter Four‐Discussion and Results4‐1 Introduction4‐2 Computing surface temperature(Ts)4‐3 Energy distribution and depth of heat penetration calculation4‐4 Thermal Distribution Calculation4‐5 Residual stresses Calculation
Chapter Five‐Conclusions and Suggestions
5‐1 Conclusion5‐2 Suggestions for Future Work
AppendixesReferences
References
74
References
1- Walaa .W.J.,"Methods of Low Carbon Steel and stainless Hardening
with Laser " , thesis of Ph. D in applied physics , University of
Technology,pp.1,2,10,11,13,16,22-26.(1999) .
2- Kenneth . L . ,"Investigative Study of Martensite Formation in Laser
Transformation Hardened Steels " ,thesis of M.S.c in technologiae
Engineering Metallurgy, Tshwane University of Technology , pp.
2,3,44,46.(2006).
3- H . J . M . Gejselasers , J . Huetink . ," Finite Element Analysis of
Transformation Hardening", University of Twente , Department of
Mechanical Engineering, the Netherlands,(1990).
4- K . G . Watkins , M .A . McMahon , W .M .Steen,"Microstructure and
Corrosion Properties of Laser Surface Processed Aluminum Alloys",
University of Liverpool , Department of Mechanical Engineering,
Italy(1996).
5- Mitton.S.F,Flavia.A.G,Rudirnar.R,Ana.M.d,"Laser Surface Remelting
and Hardening of an Automotive Shaft Sing a High-power Fiber
Laser ".University of Vale do Paraiba, Brazil (2007).
6- K.G.Watkins,S.P.Edwardson,J.Magee,G.Dearden,P.French,R.L.Cooke,
J.Sidhu,N.J.Calder,"Laser Forming of Aerospace Alloys ", society of
Automotive Engineers,Uk (2001).
7- Geijselaers , H.J.M, "Numerical Simulation of Stresses due to Solid
State Transformations", thesis University of Twente, the Netherlands.
(2003).
References
75
8- P.T.Mannion, J.Magee,E.Coyne, G.M.Oconnor, T.J.Glynn, "The effect
of Damage Accumulation Behavior on Ablation Thresholds and
Damage Morphology in Ultrafast Laser Micro-Machining of Common
Metals in Air " , National University of Ireland , Department of
Physics, Galway. Ireland . ( 2004).
9- Haitham El Kadiri , Yves. B,Kiran .s, Mark.F.H, Paul T.W, "Creep and
Tensile Behaviors of Fe - Cr-Al Foils and Laser Microwelds at High
Temperature " , Missippi state University , Center for advanced
Vehicular Systems .USA (2005).
10- Alexander .G.P,"Feasibility Investigation of laser Welding Aluminum
Alloy 7075-T6 Through The use of A 300w , Single-mode, Ytterbium
Fiber Optic Laser " , thesis M.S.c of Science in Mechanical and
Aerospace Engineering , North Carolina State University,(2005).
11- L. Costa, R.Vilar, T.Reti, A.M.Dens,"Rapid Tooling by Laser Powder
Deposition " , Szechenyi Istvan University , Department of
Engineering and Materials , Hungary.(2005).
12- V.Ocelik,D.Matthews,J.Th.M.De Hosson," Sliding wear Resistance
of Metal Matrix Composite Layers Prepared by High Power Laser",
University of Groningen, Department of Physics, the Netherlands
(2004).
13- Peng.C,Yajun.F,Jie.Z,Y.Lawrence.Y,David.P.M,Wenwu.z, Michael.
G,Jud.M,Marshall.J,"Laser Forming of Varying Thickness Plate-part
References
76
I", Columbia University, Department of Mechanical Engineering,
New York .(2006).
14- Dennis. K ,Helmut. P, Gert. G, Heinz G.W," Correlation Between
Hardening Depth and Thermal Parameters Based on Photo thermal
Measurements ", Bremen Institute for Metrology, Automation and
Quality Science, Germany (2007).
15- David . H . P . M , " Surface Hardening and Wear Performance of
Ausferritic Silicon Steels ", thesis M.S.c of Advanced material
Science and Engineering , Lulea University of Technology ,
Department of Applied Physics and Mechanical Engineering.(2007)
16- M.Marticorena, G.Corti,D.Olmedo,M.B.Guglielmotti and S.Duhalde,
" Laser Surface Modification of Ti implants to Improve
Osseointegration", University Buenos Aires, Argentina.(2007).
17- G . Labeas , S . Tsirkas , Al .Kermanidis and Sp.Pantelakis,"Fatique
Behavior Predication of Laser Surface Treated Aluminum Plates
Through Simulation of the Laser Stripping Process" , University of
Patras, Department of Mechanical Engineering and Aeronautics,
Greece.
18- A.Sinan, "Laser Hardening of metals ".
19- William T. Silvast , " Laser Fundamentals " , Cambridge University
References
77
Press. First South Asian Paperback Edition , Foundation Books ,
New delhi.pp453-454.(1998).
20- W.Koechner,R.Beck ,W . Englisch and k . Curs , " Solid-state Laser
Engineering ",Verlag New York.pp. 57.(1976).
21- Jose .P.S.S & Jorge. V .C, "Laser and Hybrid Laser-Mig welding for
Born 02- Docol 420 and Usibor 1500P-Dogal 420 lap joint" thesis
M.S.c of science program Mechanical Engineering (2007).
22- J.Hannweber,S.Bonss,B.Brenner,E.Beyer, "Integrated Laser System
For Heat Treatment with High Power Diode Laser " , Fraunhofer
Institute for Materials and Beam Technology, Dresden , Germany.
(2004).
23- Joel De Kock , " Laser Heat Treating ",Industrial Heating (2001).
24- Bassam.K.R," Drilling of the material by laser", , thesis of M.S.c in
applied physics , University of Technology,pp.3,8(1992).
25- Geoferey.W.Rowe,"Principles of Industrial Metalworking Processes"
University of Birmingham, Edward Arnold, Maryland USA ,pp 322.
(1959).
26- Carl .A . Keyser , "Basic Engineering Metallurgy" Prentice-Hall.Inc
Uk pp.153 (1959).
27- Sidney.H.Avner, "Introduction to Physical Metallurgy" McGraw-Hill
New Delhi pp228,230,259,654,668,675(1997).
References
78
28- Sommersemester,"Surface Engineering" Werkstoffwissenschaft
V ,(2004).
29- Richard.H.G and Harold.W, "Practical Microscopical Metallography"
Chapman and Hall ltd ,London pp89,90,106(1971).
30- Daniel.B, "Simulation of Welding and Stress Relief Heat Treating in
The Development of aerospace Components " , Lulea Tekniska
University pp.5-6 (2001).
31-Key to metal steel.
O=2*10^‐3;
E=3;
t=1*10^‐4;
F=5;
I=E/(pi*F^2*O^2*t(
I=9.5493*10^7
t=2*10^‐4;
I=E/(pi*F^2*O^2*t(
I=4.7746*10^7
t=3*10^‐4;
I=E/(pi*F^2*O^2*t(
I=3.1831*10^7
t=4*10^‐4;
I=E/(pi*F^2*O^2*t(
I=2.3873*10^7;
t=5*10^‐4;
I=E/(pi*F^2*O^2*t(
I=1.9099*10^7
F=10;
t=1*10^‐4;
I=E/(pi*F^2*O^2*t(
I=2.3873*10^7
t=2*10^‐4;
I=E/(pi*F^2*O^2*t(
I=1.1937*10^7
t=3*10^‐4;
I=E/(pi*F^2*O^2*t(
I=7.9577*10^6
t=4*10^‐4;
I=E/(pi*F^2*O^2*t(
I=5.9683*10^6
t=5*10^‐4;
I=E/(pi*F^2*O^2*t(
I=4.7746*10^6
F=15 ;%
t=1*10^‐4;
I=E/(pi*F^2*O^2*t (
I=1.0610*10^7
t=2*10^‐4 ;
I=E/(pi*F^2*O^2*t (
I=5.3052*10^6
t=3*10^‐4 ;
I=E/(pi*F^2*O^2*t(
I=3.5368*10^6
t=4*10^‐4;
I=E/(pi*F^2*O^2*t(
I=2.6526*10^6
t=5*10^‐4;
I=E/(pi*F^2*O^2*t(
I=2.1221*10^6 %
F=20;
t=1*10^‐4;
I=E/(pi*F^2*O^2*t(
I=5.9683*10^6
t=2*10^‐4;
I=E/(pi*F^2*O^2*t(
I=2.9842*10^6
t=3*10^‐4;
I=E/(pi*F^2*O^2*t(
I=1.9894*10^6
t=4*10^‐4;
I=E/(pi*F^2*O^2*t(
I=1.4921*10^6
t=5*10^‐4;
I=E/(pi*F^2*O^2*t(
I=1.1937*10^6
F=25;
t=1*10^‐4;
I=E/(pi*F^2*O^2*t(
I=3.8197*10^6
t=2*10^‐4;
I=E/(pi*F^2*O^2*t(
I=1.9099*10^6
t=3*10^‐4;
I=E/(pi*F^2*O^2*t(
I=1.2732*10^6
t=4*10^‐4;
I=E/(pi*F^2*O^2*t(
I=9.5493*10^5
t=5*10^‐4;
I=E/(pi*F^2*O^2*t(
I=7.6394*10^5
E=4;
F=5;
t=1*10^‐4;
I=E/(pi*F^2*O^2*t(
I=1.2732*10^8
t=2*10^‐4;
I=E/(pi*F^2*O^2*t(
I=6.3662*10^7
t=3*10^‐4;
I=E/(pi*F^2*O^2*t(
I=4.2441*1067
t=4*10^‐4;
I=E/(pi*F^2*O^2*t(
I=3.1831*1067
t=5*10^‐4;
I=E/(pi*F^2*O^2*t(
I=2.5465*10^7
F=10;
t=1*10^‐4;
I=E/(pi*F^2*O^2*t(
I=3.1831*10^7
t=2*10^‐4;
I=E/(pi*F^2*O^2*t(
I=1.5915*10^7
t=3*10^‐4;
I=E/(pi*F^2*O^2*t(
I=1.0610*10^7
t=4*10^‐4;
I=E/(pi*F^2*O^2*t(
I=7.9577*10^6
t=5*10^‐4;
I=E/(pi*F^2*O^2*t(
I=6.3662*10^6
F=15;
t=1*10^‐4;
I=E/(pi*F^2*O^2*t(
I=1.4147*10^7;
t=2*10^‐4;
I=E/(pi*F^2*O^2*t(
I=7.0736*10^6;
t=3*10^‐4;
I=E/(pi*F^2*O^2*t(
I=4.7157*10^6
t=4*10^‐4;
I=E/(pi*F^2*O^2*t(
I=3.5368*10^6
t=5*10^‐4;
I=E/(pi*F^2*O^2*t(
I=2.8294*10^6
F=20;
t=1*10^‐4;
I=E/(pi*F^2*O^2*t(
I=7.9577*10^6
t=2*10^‐4;
I=E/(pi*F^2*O^2*t(
I=3.9789*10^6
t=3*10^‐4;
I=E/(pi*F^2*O^2*t(
I=2.6526*10^6
t=4*10^‐4;
I=E/(pi*F^2*O^2*t(
I=1.9894*10^6
t=5*10^‐4;
I=E/(pi*F^2*O^2*t(
I=1.5915*10^6
F=25
t=1*10^‐4;
I=E/(pi*F^2*O^2*t(
I=5.0930*10^6
t=2*10^‐4;
I=E/(pi*F^2*O^2*t(
I=2.5465*10^6
t=3*10^‐4;
I=E/(pi*F^2*O^2*t(
I=1.6977*10^6
t=4*10^‐4;
I=E/(pi*F^2*O^2*t(
I=1.2732*10^6
t=5*10^‐4;
I=E/(pi*F^2*O^2*t(
I=1.0186*10^6
E=5;
F=5;
t=1*10^‐4;
I=E/(pi*F^2*O^2*t(
I=1.5915*10^8
t=2*10^‐4;
I=E/(pi*F^2*O^2*t(
I=7.9577*10^7
t=3*10^‐4;
I=E/(pi*F^2*O^2*t(
I=5.3052*10^7
t=4*10^‐4;
I=E/(pi*F^2*O^2*t(
I=3.9789*10^7
t=5*10^‐4;
I=E/(pi*F^2*O^2*t(
I=3.1831*10^7
F=10;
t=1*10^‐4;
I=E/(pi*F^2*O^2*t(
I=3.9789*10^7
t=2*10^‐4;
I=E/(pi*F^2*O^2*t(
I=1.9894*10^7
t=3*10^‐4;
I=E/(pi*F^2*O^2*t(
I=1.3263*10^7
t=4*10^‐4;
I=E/(pi*F^2*O^2*t(
I=9.9472*10^6
t=5*10^‐4;
I=E/(pi*F^2*O^2*t(
I=7.9577*10^6
F=15;
t=1*10^‐4;
I=E/(pi*F^2*O^2*t(
I=1.7684*10^7
t=2*10^‐4;
I=E/(pi*F^2*O^2*t(
I=8.8419*10^6
t=3*10^‐4;
I=E/(pi*F^2*O^2*t(
I=5.8946*10^6
t=4*10^‐4;
I=E/(pi*F^2*O^2*t(
I=4.4210*10^6
t=5*10^‐4;
I=E/(pi*F^2*O^2*t(
I=3.5368*10^6
F=20;
t=1*10^‐4;
I=E/(pi*F^2*O^2*t(
I=9.9472*10^6
t=2*10^‐4;
I=E/(pi*F^2*O^2*t(
I=4.9736*10^6
t=3*10^‐4;
I=E/(pi*F^2*O^2*t(
I=3.3157*10^6
t=4*10^‐4;
I=E/(pi*F^2*O^2*t(
I=2.4868*10^6
t=5*10^‐4;
I=E/(pi*F^2*O^2*t(
I=1.9894*10^6;
F=25;
t=1*10^‐4;
I=E/(pi*F^2*O^2*t(
I=6.3662*10^6
t=2*10^‐4;
I=E/(pi*F^2*O^2*t(
I=3.1831*10^6
t=3*10^‐4;
I=E/(pi*F^2*O^2*t(
I=2.1221*10^6
t=4*10^‐4;
I=E/(pi*F^2*O^2*t(
I=1.5915*10^6
t=5*10^‐4;
I=E/(pi*F^2*O^2*t(
I=1.2732*10^6
E=6;
F=5;
t=1*10^‐4;
I=E/(pi*F^2*O^2*t(
I=1.9099*10^8
t=2*10^‐4;
I=E/(pi*F^2*O^2*t(
I=9.5493*10^7
t=3*10^‐4;
I=E/(pi*F^2*O^2*t(
I=6.3662*10^7
t=4*10^‐4;
I=E/(pi*F^2*O^2*t(
I=4.7746*10^7
t=5*10^‐4;
I=E/(pi*F^2*O^2*t(
I=3.8197*10^7
F=10;
t=1*10^‐4;
I=E/(pi*F^2*O^2*t(
I=4.7746*10^7
t=2*10^‐4;
I=E/(pi*F^2*O^2*t(
I=2.3873*10^7
t=3*10^‐4;
I=E/(pi*F^2*O^2*t(
I=1.5915*10^7
t=4*10^‐4;
I=E/(pi*F^2*O^2*t(
I=1.1937*10^7
t=5*10^‐4;
I=E/(pi*F^2*O^2*t(
I=9.5493*10^6;
F=15;
t=1*10^‐4;
I=E/(pi*F^2*O^2*t(
I=2.1221*10^7
t=2*10^‐4;
I=E/(pi*F^2*O^2*t(
I=1.0610*10^7
t=3*10^‐4;
I=E/(pi*F^2*O^2*t(
I=7.0736*10^6
t=4*10^‐4;
I=E/(pi*F^2*O^2*t(
I=5.3052*10^6
t=5*10^‐4;
I=E/(pi*F^2*O^2*t(
I=4.244*10^6
F=20;
t=1*10^‐4;
I=E/(pi*F^2*O^2*t(
I=1.1937*10^7
t=2*10^‐4;
I=E/(pi*F^2*O^2*t(
I=5.9683*10^6
t=3*10^‐4;
I=E/(pi*F^2*O^2*t(
I=3.9789*10^6
t=4*10^‐4;
I=E/(pi*F^2*O^2*t(
I=2.9842*10^6
t=5*10^‐4;
I=E/(pi*F^2*O^2*t(
I=2.3873*10^6
F=25;
t=1*10^‐4;
I=E/(pi*F^2*O^2*t(
I=1.1937*10^7
t=2*10^‐4;
I=E/(pi*F^2*O^2*t(
I=5.9683*10^6
t=3*10^‐4;
I=E/(pi*F^2*O^2*t(
I=3.9789*10^6
t=4*10^‐4;
I=E/(pi*F^2*O^2*t(
I=2.9842*10^6
t=5*10^‐4;
I=E/(pi*F^2*O^2*t(
I=2.3873*10^6
F=25;
t=1*10^‐4;
I=E/(pi*F^2*O^2*t(
I=7.6394*10^6
t=2*10^‐4;
I=E/(pi*F^2*O^2*t(
I=3.8197*10^6
t=3*10^‐4;
I=E/(pi*F^2*O^2*t(
I=2.5465*10^6
t=4*10^‐4;
I=E/(pi*F^2*O^2*t(
I=1.9099*10^6
t=5*10^‐4;
I=E/(pi*F^2*O^2*t(
I=1.5279*10^6
E=7;
F=5;
t=1*10^‐4;
I=E/(pi*F^2*O^2*t(
I=2.2282*10^8
t=2*10^‐4;
I=E/(pi*F^2*O^2*t(
I=1.1141*10^8
t=3*10^‐4;
I=E/(pi*F^2*O^2*t(
I=7.4272*10^7
t=4*10^‐4;
I=E/(pi*F^2*O^2*t(
I=5.5704*10^7
t=5*10^‐4;
I=E/(pi*F^2*O^2*t(
I=4.4563*10^7
F=10;
t=1*10^‐4;
I=E/(pi*F^2*O^2*t(
I=5.5704*10^7
t=2*10^‐4;
I=E/(pi*F^2*O^2*t(
I=2.7852*10^7
t=3*10^‐4;
I=E/(pi*F^2*O^2*t(
I=1.8568*10^7
t=4*10^‐4;
I=E/(pi*F^2*O^2*t(
I=1.3926*10^7
t=5*10^‐4;
I=E/(pi*F^2*O^2*t(
I=1.1141*10^7
F=15;
t=1*10^‐4;
I=E/(pi*F^2*O^2*t(
I=2.4757*10^7
t=2*10^‐4;
I=E/(pi*F^2*O^2*t(
I=1.2379*10^7
t=3*10^‐4;
I=E/(pi*F^2*O^2*t(
I=8.2525*10^6
t=4*10^‐4;
I=E/(pi*F^2*O^2*t(
I=6.1894*10^6
t=5*10^‐4;
I=E/(pi*F^2*O^2*t(
I=4.9515*10^6
F=20;
t=1*10^‐4;
I=E/(pi*F^2*O^2*t(
I=1.3926*10^7
t=2*10^‐4;
I=E/(pi*F^2*O^2*t(
I=6.9630*10^6
t=3*10^‐4;
I=E/(pi*F^2*O^2*t(
I=4.6420*10^6
t=4*10^‐4;
I=E/(pi*F^2*O^2*t(
I=3.4815*10^6
t=5*10^‐4;
I=E/(pi*F^2*O^2*t(
I=2.7852*10^6
F=25;
t=1*10^‐4;
I=E/(pi*F^2*O^2*t(
I=8.9127*10^6
t=2*10^‐4;
I=E/(pi*F^2*O^2*t(
I=4.4563*10^6
t=3*10^‐4;
I=E/(pi*F^2*O^2*t(
I=2.9709*10^6
t=4*10^‐4;
I=E/(pi*F^2*O^2*t(
I=2.2282*10^6
t=5*10^‐4;
I=E/(pi*F^2*O^2*t(
I=1.7825*10^6
IF E=3; F=5;
K=0.1800;
To=298;
N=0.3064;
R=0.4800;
t=1*10^‐4;
I=9.5493*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=13575
t=2*10^‐4;
I=4.7746*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=13575
t=3*10^‐4;
I=3.1831*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=13575
t=4*10^‐4;
I=2.3873*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=13575
t=5*10^‐4;
I=1.9099810^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=13575
IF E=3; F=10;
t=1*10^‐4;
I=2.3873*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=3617
t=2*10^‐4;
I=1.1937*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=3617
t=3*10^‐4;
I=7.9577*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=3617
t=4*10^‐4;
I=5.9683*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=3617
t=5*10^‐4;
I=4.7746*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=3617
IF E=3; F=15 ; %
t=1*10^‐4;
I=1.0610*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1773
t=2*10^‐4;
I=5.3052*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1773
t=3*10^‐4;
I=3.5368*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1773
t=4*10^‐4;
I=2.6526*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1773
t=5*10^‐4;
I=2.1221*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1773 %
IF E=3; F=20;
t=1*10^‐4;
I=5.9683*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1127
t=2*10^‐4;
I=2.9842*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1127
t=3*10^‐4;
I=1.9894*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1127
t=4*10^‐4;
I=1.4921*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1127
t=5*10^‐4;
I=1.1937*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1127
IF E=3; F=25;
t=1*10^‐4;
I=3.8197*10^6
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=829
t=2*10^‐4;
I=1.9099*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=829
t=3*10^‐4;
I=1.2732*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=829
t=4*10^‐4;
I=9.5493*10^5;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=829
t=5*10^‐4;
I=7.6394*10^5;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=829
IF E=4; F=5;
t=1*10^‐4;
I=1.2732*10^8;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=18001
t=2*10^‐4;
I=6.3662*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=18001
t=3*10^‐4;
I=4.2441*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=18001
t=4*10^‐4;
I=3.1831*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=18001
t=5*10^‐4;
I=2.5465*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=18001
IF E=4; F=10;
t=1*10^‐4;
I=3.1831*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=4723
t=2*10^‐4;
I=1.5915*1067;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=4723
t=3*10^‐4;
I=1.0610*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=4723
t=4*10^‐4;
I=7.9577*10^6
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=4723
t=5*10^‐4;
I=6.3662*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=4723
IF E=4; F=15;
t=1*10^‐4;
I=1.4147*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=2265
t=2*10^‐4;
I=7.0736*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=2265
t=3*10^‐4;
I=4.7157*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=2265
t=4*10^‐4;
I=3.5368*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=2265
t=5*10^‐4;
I=2.8294*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=2265
IF E=4; F=20;
t=1*10^‐4;
I=7.9577*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1404
t=2*10^‐4;
I=3.9789*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1404
t=3*10^‐4;
I=2.6526*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1404
t=4*10^‐4;
I=1.9894*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1404
t=5*10^‐4;
I=1.5915*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1404
IF E=4; F=25;
t=1*10^‐4;
I=5.0930*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1006
t=2*10^‐4;
I=2.5465*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1006
t=3*10^‐4;
I=1.6977*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1006
t=4*10^‐4;
I=1.2732*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1006
t=5*10^‐4;
I=1.0186*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1006
IF E=5; F=5;
t=1*10^‐4;
I=1.5915*10^8;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=22427
t=2*10^‐4;
I=7.9577*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=22427
t=3*10^‐4;
I=5.3052*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=22427
t=4*10^‐4;
I=3.9789*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=22427
t=5*10^‐4;
I=3.1831*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=22427
IF E=5; F=10;
t=1*10^‐4;
I=3.9789*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=5830
t=2*10^‐4;
I=1.9894*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=5830
t=3*10^‐4;
I=1.3263*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=5830
t=4*10^‐4;
I=9.9472*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=5830
t=5*10^‐4;
I=7.9577*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=5830
IF E=5; F=15;
t=1*10^‐4;
I=1.7684*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=2756
t=2*10^‐4;
I=8.8419*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=2756
t=3*10^‐4;
I=5.8946*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=2756
t=4*10^‐4;
I=4.4210*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=2756
t=5*10^‐4;
I=3.5368*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=2756
IF E=5; F=20;
t=1*10^‐4;
I=9.9472*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1681
t=2*10^‐4;
I=4.9736*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1681
t=3*10^‐4;
I=3.3157*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1681
t=4*10^‐4;
I=2.4868*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1681
t=5*10^‐4;
I=1.9894*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1681
IF E=5; F=25;
t=1*10^‐4;
I=6.3662*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1183
t=2*10^‐4;
I=3.1831*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1183
t=3*10^‐4;
I=2.1221*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1183
t=4*10^‐4;
I=1.5915*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1183
t=5*10^‐4;
I=1.2732*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1183
IF E=6; F=5;
t=1*10^‐4;
I=1.9099*10^8;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=26853
t=2*10^‐4;
I=9.5493*1067;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=26853
t=3*10^‐4;
I=6.3662*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=26853
t=4*10^‐4;
I=4.7740*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=26853
t=5*10^‐4;
I=3.8197*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=26853
IF E=6; F=10;
t=1*10^‐4;
I=4.7746*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=6936
t=2*10^‐4;
I=2.3873*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=6936
t=3*10^‐4;
I=1.5915*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=6936
t=4*10^‐4;
I=1.1937*10^7
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=6936
t=5*10^‐4;
I=9.5493*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=6936
IF E=6; F=15;
t=1*10^‐4;
I=2.1221*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=3248
t=2*10^‐4;
I=1.0610*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=3248
t=3*10^‐4;
I=7.0736*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=3248
t=4*10^‐4;
I=5.3052*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=3248
t=5*10^‐4;
I=4.2441*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=3248
IF E=6; F=20;
t=1*10^‐4;
I=1.1937*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1957
t=2*10^‐4;
I=5.9683*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1957
t=3*10^‐4;
I=3.9789*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1957
t=4*10^‐4;
I=2.9842*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1957
t=5*10^‐4;
I=2.3873*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1957
IF E=6; F=25;
t=1*10^‐4;
I=7.6394*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1360
t=2*10^‐4;
I=3.8197*10^6
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1360
t=3*10^‐4;
I=2.5465*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1360
t=4*10^‐4;
I=1.9099*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1360
t=5*10^‐4;
I=1.5279*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1360
IF E=7; F=5;
t=1*10^‐4;
I=2.2282*10^8;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=31278
t=2*10^‐4;
I=1.1141*10^8;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=31278
t=3*10^‐4;
I=7.4272*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=31278
t=4*10^‐4;
I=5.5704*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=31278
t=5*10^‐4;
I=4.4563*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=31278
IF E=7; F=10;
t=1*10^‐4;
I=5.5704*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=8043
t=2*10^‐4;
I=2.7852*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=8043
t=3*10^‐4;
I=1.8568*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=8043
t=4*10^‐4;
I=1.3926*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=8043
t=5*10^‐4;
I=1.1141*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=8043
IF E=7; F=15;
t=1*10^‐4;
I=2.4740*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=3740
t=2*10^‐4;
I=1.2379*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=3740
t=3*10^‐4;
I=8.2525*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=3740
t=4*10^‐4;
I=6.1894*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=3740
t=5*10^‐4;
I=4.9515*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=3740
IF E=7; F=20;
t=1*10^‐4;
I=1.39226*10^7;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=2234
t=2*10^‐4;
I=6.9630*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=2234
t=3*10^‐4;
I=4.6420*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=2234
t=4*10^‐4;
I=3.4815*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=2234
t=5*10^‐4;
I=2.7852*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=2234
IF E 7; F=25;
t=1*10^‐4;
I=8.9127*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1537
t=2*10^‐4;
I=4.4563*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1537
t=3*10^‐4;
I=2.9709*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1537
t=4*10^‐4;
I=2.2282*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1537
t=5*10^‐4;
I=1.7825*10^6;
Ts=To+(2*I*(1‐R)*(N*t)^1/2)/K*pi^1/2
Ts=1537
IF E=3; F=15;
N=0.3064;
X=0.2775;
T=(x^2)/(4*N(
T=6*10^‐2
t=1*10^‐4;
r=t/T
r=1*10^‐3;
X=0.0555;
T=(x^2)/(4*N(
T=2*10^‐3;
t=1*10^‐4;
r=t/T
r=5*10^‐3
X=0.0111 ;%
T=(x^2)/(4*N(
T=1*10^‐4;
t=1*10^‐4;
r=t/T
r=1 %
X=0.0022
T=(x^2)/(4*N(
T=3*10^‐6;
t=1*10^‐4;
r=t/T
r=33.33
X=0.0004;
T=(x^2)/(4*N(
T=1*10^‐7;
t=1*10^‐4;
r=t/T
r=1000
X=0.3925;
T=(x^2)/(4*N(
T=1*10^‐3;
t=2*10^‐4;
r=t/T
r=2*10^‐3
X=0.0785;
T=(x^2)/(4*N(
T=5*10^‐3;
t=2*10^‐4;
r=t/T
r=4*10^‐1
X=0.0157 ;%
T=(x^2)/(4*N(
T=2*10^‐4;
t=2*10^‐4;
r=t/T
r=1 %
X=0.0031;
T=(x^2)/(4*N(
T=7*10^‐6;
t=2*10^‐4;
r=t/T
r=2.85
X=0.0006;
T=(x^2)/(4*N(
T=2*10^‐7;
t=2*10^‐4;
r=t/T
r=100
X=0.4800;
T=(x^2)/(4*N(
T=1*10^‐1;
t=3*10^‐4;
r=t/T
r=3*10^‐3
X=0.0960;
T=(x^2)/(4*N(
T=7*10^‐3;
t=3*10^‐4;
r=t/T
r=4*10^‐3
X=0.0192 ;%
T=(x^2)/(4*N(
T=3*10^‐4;
t=3*10^‐4;
r=t/T
r=1 %
X=0.0038;
T=(x^2)/(4*N(
T=1*10^‐5;
t=3*10^‐4;
r=t/T
r=3
X=0.0007;
T=(x^2)/(4*N(
T=3*10^‐7;
t=3*10^‐4;
r=t/T
r=100
X=0.5525;
T=(x^2)/(4*N(
T=2*10^‐1;
t=4*10^‐4;
r=t/T
r=2*10^‐3
X=0.1105;
T=(x^2)/(4*N(
T=9*10^‐3;
t=4*10^‐4;
r=t/T
r=4*10^‐4
X=0.0221 ;%
T=(x^2)/(4*N(
T=4*10^‐4;
t=4*10^‐4;
r=t/T
r=1 %
X=0.0044;
T=(x^2)/(4*N(
T=1*10^‐5;
t=4*10^‐4;
r=t/T
r=4
X=0.0008;
T=(x^2)/(4*N(
T=5*10^‐7;
t=4*10^‐4;
r=t/T
r=80
X=0.6200;
T=(x^2)/(4*N(
T=3*10^‐1;
t=5*10^‐4;
r=t/T
r=1*10^‐3
X=0.1240;
T=(x^2)/(4*N(
T=1*10^‐2;
t=5*10^‐4;
r=t/T
r=5*10^‐3
X=0.0248 ;%
T=(x^2)/(4*N(
T=5*10^‐4;
t=5*10^‐4;
r=t/T
r=1 %
X=0.0049;
T=(x^2)/(4*N(
T=1*10^‐5;
t=5*10^‐4;
r=t/T
r=5
X=0.0009;
T=(x^2)/(4*N(
T=6*10^‐7;
t=5*10^‐4;
r=t/T
r=83.33
IF E=3;
a=6.5*10^‐6;
e=30*10^6;
Ti=298;
Ts=13575;
IF F=5;
)Ts‐Ti)=13277
S=a*e*(Ts‐Ti(
S=2589015
Ts=3617;
IF F=10;
)Ts‐Ti)=3319
S=a*e*(Ts‐Ti(
S=647205
Ts=1773 ;%
IF F=15;
)Ts‐Ti)=1475
S=a*e*(Ts‐Ti(
S=287625 %
Ts=1127;
IF F=20;
)Ts‐Ti)=829
S=a*e*(Ts‐Ti(
S=161655
Ts=829;
IF F=25;
)Ts‐Ti)=531
S=a*e*(Ts‐Ti(
S=103545
IF
E=3;
R=0.48;
A=10^5;
Z=0.011100;
Ez=(E*(1‐R))*(exp(‐A*Z(
Ez=0
Z=0.005550;
Ez=(E*(1‐R))*(exp(‐A*Z(
Ez=0
Z=0.002796;
Ez=(E*(1‐R))*(exp(‐A*Z(
Ez=0
Z=0.002795;
Ez=(E*(1‐R))*(exp(‐A*Z(
Ez=1.5692*10^‐99
Z=0.0018236;
Ez=(E*(1‐R))*(exp(‐A*Z(
Ez=9.8896*10^‐80
Z=0.0013677;
Ez=(E*(1‐R))*(exp(‐A*Z(
Ez=6.2325*10^‐40
Z=0.0004559;
Ez=(E*(1‐R))*(exp(‐A*Z(
Ez=2.4753*10^‐20
Z=0;
Ez=(E*(1‐R))*(exp(‐A*Z(
Ez=1.56
IF d1=0; T1=1773;
IF d2=0.0004559; T2=;
IF d6=0.002795; T6=298;
0.0004559-0=0.0004559
0.002795-0=0.002795
1773-298=1475
)1475/0.002795*(0.0004559=240
T2=240+298
T2=538
IF d2=0.00045559; T2=538;
IF d3=0.0009118; T3=;
IF d6=0.002795; T6=298;
0.0009118-0.0004559=0.0004559
0.002795-0.0004559=0.0023391
538-298=240
)240/0.0023391*(0.0004559=46
T3=298+46
T3=344
IF d3=0.0009118; T3=344;
IF d4=0.0013677; T4=;
IF d6=0.002795; T6=298;
0.0013677-0.0009118=0.0004559
0.002795-0.0009118=0.0018832
344-298=46
)46/0.0018832*(0.0004559=11
T4=298+11
T4=309
IF d4=0.0013677; T4=309;
IF d5=0.0018236; T5=;
IF d6=0.002795; T6=298;
0.0018236-0.0013677=0.0004559
0.002795-0.0013677=0.0014273
309-298=11
)11/0.0014273*(0.0004559=3
T5=298+3=301
IF
I=2.1221*10^6;
t=5*10^‐4;
spot area=E/(I*t(
spot area=0.00282738
IF
density=0.87;
V=1/density
V=1.14
M=density*V
M=0.9918
C=0.064;
Ts=1773;
Ti=298;
Q=M*C(Ts‐Ti(
Q=94.19
area=0.0028273;
K=0.18;
depth=(k*area*(Ts‐Ti))/Q
depth=0.0080183
area=0.00282738;
)radius1)^2=area/pi
radius1=0.02999971
radius2=radius1+depth
radius2=0.03801801
diameter=2*radius2
diameter=0.07603602
IF D1=0; T01=1773;
IF D2=0.00160366; T02=;
IF D6=0.0080183; T06=298;
0.00160366-0=0.00160366
0.00801830-0=0.0080183
1773-298=1475
)1475/0.0080183*(0.00160366=295
T02=298+295
T02=593
IF D2=0.00160366; T02=593;
IF D3=0.00320732; T03=;
IF D6=0.00801830; T06=298;
0.00320732-0.00160366=0.00160366
0.00801830-0.00160366=0.00641464
593-298=295
)295/0.00641464*(0.00160366=73
T03=298+73
T03=371
IF D3=0.00320732; T03=371;
IF D4=0.00481098; T04=;
IF D6=0.00801830; T06=298;
0.00481098-0.00320732=0.00160366
0.00801830-0.00320732=0.00481098
371-298=73
)73/0.00481098*(0.00160366=24
T04=298+24
T04=322
IF D4=0.00481098; T04=322
IF D5=0.00641464; T05=;
IF D6=0.00801830; T06=298;
0.00641464-0.00481098=0.00160366
0.00801830-0.00481098=0.00320740
322-298=24
)24/0.00320740*(0.00160366=11
T05=298+11
T05=309
List of symbols
symbol The energy of the laser (J)E Focal length of lens (cm)f The divergence of laser (rad)θ Pulse duration (µs)t Power density (w/cm2)I Initial surface temperature (k)To
Reflectivity (%)R Thermal conductivity(cal/sec/cm/Co)K Thermal diffusivity (cm2/s)N Additional energy is provided by the oxygenPch
Process energy (laser energy available for heating , melting or viporisation
Pproc
Energy loss due to heat conduction into the work piecePc
Energy loss due to reflectionPR Energy loss due to convectionPcon
Absorption coefficient ( cm‐1 ) A Depth of penetration ( cm ) Z Residual stresses (psi) S Coefficient of linear expansion (cm/cm. Co) α Modulus of elasticity (psi) e Change of temperature on the surface (Co ) ΔT Time cycle (s) Interlamellar spacing (cm) ℓ Diffusion coefficient, about 10
‐9 cm
2.s
‐1at elevated
temperatures
D
Thermal time constant ( s/cm ) T Thickness of the alloy ( cm ) X
X
الخالصة
باستخدام برنامج الماتالب ( ألطوريفي ھذه الدراسة تم عمل موديل رياضي لعملية التصليد بالتحول الكربونالتي يصعب تصليدھا بالطرق االعتيادية وذلك لكون نسبة (لسبيكة الحديد المطاوع مع النيكل ) 6.5
.ياك النبضي - باستخدام ليزر الندميوم) فيھا منخفضة
, حساب درجة حرارة سطح المعدن باالعتماد على مواصفات السبيكة التي ھي التوصيلية الحرارية تم لليزر المستخدم ودرجة الحرارة االبتدائية للسطح التي ھي ألموجياالنعكاسية للطول , االنتشارية الحرارية
ابق وزمن النبضة المستخدمة قيم كثافة القدرة التي تم حسابھا في الس إلى باإلضافةدرجة حرارة الغرفة ألطوريدرجة انصھار السبيكة والتي بلغت الن درجة حرارة التحول إلى األقربواخترنا درجة الحرارة
طور االوستنايت بالكامل ھي قريبة جدا من درجة االنصھار وبذلك نختار مقدار كثافة القدرة التي ترفع إلى .ي والطاقة التي تؤدي للحصول على كثافة القدرة ھذهوالبعد البؤر إلىدرجة حرارة السطح
ألطوريالذاتي والذي ھو الظرف المناسب للتحول اإلخمادتم حساب سمك العينة المناسب لحصول البعد , الكامل من طور االوستنايت الى طور المارتنسايت الذي ھو طور التصليد فعند ما تكون الطاقة
.البؤري وزمن نبضة الليزر
ومعامل تم حساب توزيع االجھادات الحرارية المتخلفة على سطح العينة باستخدام معامل التمدد الطولي داخل السبيكة باستخدام انعكاسية سطح السبيكة والطاقة األشعةنتمكن من معرفة عمق نفاذ المرونةالمتخلفة بواسطة الى معامل االمتصاص ورسم مخطط توزيع االجھادات الحرارية السطحية باإلضافة
.برنامج الماتالب
على طول عمق النفاذ الحراري (تم حساب توزيع درجات الحرارة على سطح السبيكة وداخل العينة .ورسم مخطط للتوزيعين الحراريين بواسطة برنامج الماتالب ) الليزر داخل العينة ألشعة