Finite Element Analysis of Stresses in a Welded pipe


Al-Khwarizmi 

Engineering   

Journal 

Al-Khwarizmi Engineering Journal,  Vol. 5, No. 1, PP 33-41  (2009) 

 

 

Investigation of Thermal Stress Distribution in Laser Spot Welding 

Process 
 

Osamah F. Abdulateef 
Department of Manufacture Operation Engineering / AL-Khwarizmi College of Eng. / University of Baghdad 

 

(Received  14 December 2008; accepted 19 March 2009) 

 

 

Abstract  
 

 The objective of this paper was to study the laser spot welding process of low carbon steel sheet. The investigations 
were based on analytical and finite element analyses. The analytical analysis was focused on a consistent set of 

equations representing interaction of the laser beam with materials. The numerical analysis based on 3-D finite element 

analysis of heat flow during laser spot welding taken into account the temperature dependence of the physical properties 
and latent heat of transformations using ANSYS code V.10.0 to simulate the laser welding process. The effect of laser 

operating parameters on the results of the temperature profile were studied in addition to the effect on thermal stresses  

and dimensions of the laser welded workpiece which showed good correlations between analytical and numerical 

results. It was found that the temperature gradients during laser welding are usually very large and it was viewed that 

very high temperature at the center of the workpiece, and is decreased very significantly as propagating along the radial 

direction. Also it found that the thermal residual stresses around the laser spot due to plastic strains were very small and 

localized within 1.0 mm range. It is concluded that the laser welding process is effective to reduce the welding residual 

stress. The stresses along the lateral direction of the workpiece changed from compression at the spot under the laser 

beam and tension away from the spot at the end of welding to tension at the spot under the laser beam and compression 

away from the spot when it cooled, which are in a good agreement with the published results.  

     
Keywords: Laser-spot welding, Residual stress, Non-linear thermal stress.    
 

  

1. Introduction:
       
 Laser welding represents a delicate balance 

between heating and cooling within a spatially 

localized volume to produce the liquid melt pool 

by absorption of incident radiation, allow it to 
grow to the desired size, and then to propagate 

this melt pool through the solid interface 

eliminating the original seam between the 
components to be joined. Laser beam welding has 

a number of desirable attributes. The heat affected 

zones are characteristically smaller and narrower 
than those produced using conventional welding 

techniques and distortion of the workpiece is 

reduced.  

 During laser spot welding, an intense beam is 
focused onto a small area. The material under the 

beam rapidly melts and may partly vaporise, 

leaving behind a small vapour filled crater, which 
enhances the absorptivity of the incident beam. 

The molten front extends more in the thickness 

than in the width direction if the laser power is 
sufficiently high. This can lead to a parallel sided 

molten pool and heat transfer occurs 

predominantly via radiative and convective modes 

through the vapour and molten material. 
 Numerical simulations of a laser welding 

process have been a major topic in welding 

research for several years. The results of 
simulations can be used to explain physical 

essence of some complex phenomena in the laser 

welding process explicitly and can be also used as 
the basis for optimization of the process. 

Simulations of the laser welding process enable 

estimation of transient stresses, residual stresses, 

and distortions. These can be used to evaluate 
structural misalignments and unexpected failures 

due to overstressing caused by the superposition 

of in-service loads and welding induced residual 
stresses. However, the simulation of the welding 

process is not an easy task since it involves 



Osama F. Abdulateef                                              Al-Khwarizmi Engineering Journal, Vol. 5, No. 1, PP 33-41 (2009) 

  

34 

interaction of thermal, mechanical, and 

metallurgical phenomena. For the study of stress 
distributions in laser welding process, early 

researches include the consideration of the 

thermoelasticity problem due to a moving heat 
source [1], development for the transient surface 

stress and displacement due to line heat sources in 

terms of Bessel functions [2], and the calculation 

of thermal stresses on an infinite slab caused by a 
moving square heat source on the surface [3]. 

More recently, an analytical solution for a semi-

infinite plane subjected to a moving Gaussian heat 
source was obtained in terms of Bessel functions 

and exponential integrals [4]. An explicit formula 

for the shape of the deformed target surface under 
laser irradiation was obtained as a function of the 

deposited Gaussian energy distribution [5]. 

Furthermore, the numerical model of the thermal 

stresses generated by a moving elliptical weld 
pool in the welding of thin metal sheets were 

developed [6], and the stresses along the weld 

direction and the distortion of the workpiece from 
the laser welding process were evaluated using a 

Mellin-transform technique, where the 

considerations were restricted to the plane linear 

thermoelastic model in order to obtain the basic 
mathematical formula for the transient change in 

stresses, and the final results were expressed in 

terms of a convolution integral and illustrated by 
numerical calculations for the point heat source 

[7]. A number of analytical and numerical models 

of laser welding processes have been used to 
evaluate temperature and stress distribution during 

the welding process, as well as corresponding 

residual stresses and final distortions of structural 

components. These include analytical models [8], 
two-dimensional finite element models [9], and 

three-dimensional finite element models [10]. 

However, not all of parameters influencing the 
welding process, including microstructural 

changes due to phase transformation, heat flux 

simulation, and variation of thermal and 
mechanical material properties with temperature, 

were taken into account in the simulations listed 

above. [11], investigated the transient thermal and 

stress analyses of a laser spot-welded joint using 
nonlinear finite element method, and since the 

study was limited to the thermoelastic stresses, it 

was found that the stresses and deformations were 
overestimated.  

 Laser materials processing utilizes the high 

power density provided by the laser beam, which 

is focused on the workpiece. As a result, the 
workpiece material experiences heating, melting, 

and possible vaporization and re-solidification. 

Understanding the temporal evolution of the 

temperature field during laser material interaction 

is one of the most significant factors in achieving 
a desired quality of processing. The thermal 

history is required to determine dimensional 

changes in the machined part, the related stresses, 
phase transformations taking place, and the final 

metallurgical microstructures.  

 In order to achieve a satisfactory study of the 

laser welding process, it is first of all necessary to 
know the temperature distributions resulting from 

the irradiation of the laser beam. The next step 

that must be addressed is to use the fundamental 
equations of linear thermo-elasticity to arrive 

knowledge of the distribution of stress in the 

elastic material under certain boundary 
conditions. Once a combined understanding of the 

temperature and stress distribution is achieved it is 

possible to identify domains in which the stresses 

may have a value above the yield point of the 
material at a given temperature, as well as regions 

where possible phase changes can occur for the 

particular material.  
 

 

2. Theoretical Aspects: 
  

 The coupling of laser radiation into a metal to 

produce the localized heating required for spot 
welding involved a delicate balance among many 

parameters. Some of these parameters, such as 

laser intensity, pulse shape, and beam 

polarization, are under the control of the operator, 
whereas others, such as metal reflectivity, thermal 

conductivity, and heat capacity, are not. 

 
 

 

 
 

 

 

 
 

 

 
 

 

 
 

Fig. 1. Transverse Section of Thermal Model [13] 

 
 Under conduction limited conditions, the 

onset of surface melting can be estimated from the 

simple model (see figure 1). The temperature at 

the center of the beam focus(r =0) is: 
 



Osama F. Abdulateef                                              Al-Khwarizmi Engineering Journal, Vol. 5, No. 1, PP 33-41 (2009) 

  

35 

                                                                        ... (1) 

 
 

Where K is the thermal conductivity, k is thermal 

diffusivity, w is the Gaussian beam radius, T0 is 
the ambient temperature, and t is time. If T (0, t) 

=Tm, the melting temperature, then the laser beam 

intensity, Im(0), required to produce melting in 

time t can be obtained with equation 1. 
 An estimate of the depth of penetration, zm, of 

the weld pool under spot welding conditions in 

which melting is included can be obtained, when 
considered tm as the time at which T(z=0)=Tm, as 

[12]: 
 

                                                            

                                                                 … (2) 

 
Where ρ is the density of the melt and Lm is the 

latent heat of fusion. Equation 2 will be strictly 

valid only when tm<8k/w
2
. 

 In order to account for the thermomechanical 

effect during the heating process, the energy 

transport equation for a deformable solid body can 
be written for the specific enthalpy as 
 

                                            

                                                                  … (3) 

 
 

The equation describing the energy transport due 

to electron-photon interaction can be written as 
 

 

                    
                                                                  … (4) 

 

Combination of equations 3 and 4 yields 
 

 

 

                                                                  … (5) 
 

Equation 5 is the general energy transport 

equation, which includes the thermomechanical 
effect. 

I.C's:       t=0, T=0 and U=0, 

Since the laser pulse length and heating duration 

are short, there is no convection or radiation 
losses are considered from the surface, therefore 

B.C's       at t>0 and at the surface, 0) 



surface

x

T
, 

                at t>0 and x = y = z = α, T= 0 and U= 0. 

  

 During laser materials processing, the heating 
is localized and therefore, a very large 

temperature variation occurs over a small region. 

Owing to this temperature gradient, large thermal 
stresses are generated in the substrate, which can 

lead to the defects in the material such as the 

formation of cracks and fractures in the material. 
The stress is related to strains by [14]: 
 

{σ}= [D] {ε
e
},                                             ... (6) 

 

Where {σ} is the stress vector, and [D] is the 
elasticity matrix. 
 

{ε
e
}= {ε}-{ε

th
},                                           …(7) 

 

Where {ε} is the total strain vector and {ε
th
} is the 

thermal strain vector. 

     Equation 7 may also be written as  
 

{ε}=[D]
-1
{σ}+{ε

th
}                                   … (8) 

 

But {ε
th
} =α e ΔT= α e (T-Tref)                     ... (9) 

 

Where Tref is the reference temperature at t=0. 
 The principle stresses (σ1, σ2, σ3) are 

calculated from the stress components by the 

cubic equation. The Von Mises or equivalent 

stress, σ
'
, is computed as 

 

 
 

 

                                                                 … (10) 
 

 The equivalent stress is stress is related to the 
equivalent strain through 
 

 σ
'
=E ε

'
                                                   …. (11) 

 

Where ε
'
 is the equivalent strain. 

 The boundary conditions for stresses are: 

since there is no surface tractions are involved in 

the problem under consideration the 
corresponding boundary and initial conditions are 

introduced: 

    at  t=0, σ=0, 
    at  t>0 and at surface, σsurface=0, 

    at  t>0 and x=y=z=α, σ=0. 

 

 

3. Finite Element Modeling Procedures: 
  
 The form of the representation used for the 

laser beam has a significant effect on the results of 

numerical models of the laser beam welding 

process. A Gaussian representation of the laser 
beam, assuming heat input only on the top surface 

of the material, may not lead to correct results, 

especially for high power lasers that penetrate 
rapidly some distance into the material thickness, 

2/1

2

1

2/1
)

8
(tan

)2(

)0(
),0(

w

kt

K

wAI
TtT






)(
16.0

)(
m

m

m
tt

L

AI
tz 



).()(. U
t

C

t

T
Cq

e

P
P
















)exp().
2

(

2

).
2

(. x
surf

IT
tf

P
C

TKq 








      )exp(.)(.2
2

.
2

x
surf

IU
te

T
tf

T
t

T





 















])()()[(
2

1 2
13

2

32

2

21

'
 



Osama F. Abdulateef                                              Al-Khwarizmi Engineering Journal, Vol. 5, No. 1, PP 33-41 (2009) 

  

36 

resulting in welds of high depth to width ratio. 

The present work is thus aimed at a heat transfer 
analysis following the double ellipsoidal 

representation of the laser beam, as this typically 

incorporates volumetric heat input from a heat 
source. The temperature dependence of the 

material properties, phase change phenomena, and 

convective and radiative heat losses from all the 

surfaces of a sheet are considered. The heat 
transfer analysis is therefore axisymmetric, with 

the y axis defined as the axis of symmetry. The 

volumetric heat input due to the laser is 
represented by adapting equation (12) for a 

stationary heat source [13],  

 
 

                                                                .... (12) 

 

 

Where Q is taken to be the incident laser power 

multiplied by the energy transfer efficiency 
(absorptive), a is the focal radius of the laser 

beam, b is the sheet thickness. 

 The FE analysis was carried out in two steps: 
1- Non- linear (material properties depend on 

temperature) transient thermal analysis using three 

modes of heat transfer: conduction, convection, 

and radiation; was conducted first to obtain the 
global temperature history generated during and 

after welding process. 

2- Stress analysis was then developed with the 
temperatures obtained from the thermal analysis 

used as loading to the stress model.   

 The general purpose FE package ANSYS 
V10.0 was used for both thermal and stress 

analysis performed sequentially. The mesh used in 

the stress analysis was compatible to that in the 

thermal analysis. Figure 2 shows model geometry 
and the representative mesh.  

 

  
 

 

 

 
 

 

 
 

 

 
 

 

 

  
 

 

 
 

 

 
Fig.2. Model Geometry and Meshes 

 

 

 

4. Results and Discussions 
  
 The present study is based on calculated 

geometric and material data for laser spot welds in 

a single sheet. The heat source was a laser with a 

beam spot diameter of 1.0 mm focused normally 
onto the top surface of a 2.0 mm thickness low 

carbon steel sheet. Three levels of beam power, 

namely 1.0, 1.5, and 2.5 kW, and on-times 
varying in the range 0.15 – 2.65 s were 

considered. To model the results, a rectangular 
region of 15 mm (width) by 2 mm (thickness) is 

finely discretised (meshed) into divisions of 0.1 

mm along the thickness direction. Along the 

width direction, a division of 0.1 mm is used up to 
a distance of 5 mm, beyond which a division of 

0.2 mm is used for the remainder of the length. 3-

D 20-node elements are used. The time span of 
the transient analysis includes the on-time of a 

)
2

2

3exp()
2

2

3exp(
2/32

36
),(

b

y

a

x

ba

Q
yxq 





Osama F. Abdulateef                                              Al-Khwarizmi Engineering Journal, Vol. 5, No. 1, PP 33-41 (2009) 

  

37 

single laser pulse and the subsequent cooling 

stage. The analysis is carried out through a 
number of small time steps, each time step being 

0.001 s. Within each time step, a number of 

iterations are performed to achieve a convergence 
criterion of 1% (the difference in nodal 

temperature between two successive iterations). 

Figures 3(a,b) show the temperature dependent 

thermal and mechanical material properties used 

in the calculation. During the analysis, whenever 
the temperature of a node exceeds the boiling 

point of the steel (2800°C), it is allowed to remain 

in the mesh at the boiling temperature and is not 
considered further in the analysis until cooling 

starts after removal of the laser beam. 

 

 
 

 

 
 

 

 
 

 

 

 
 

 

 
 

 

 

 
 

 

 
 

 

 
 

-a-                                                                                         -b- 

Fig.3. [15] Material Properties with Temperature a- Variation of Thermal Material Properties with 

Temperature. b- Variation of Mechanical Material Properties with Temperature 
   
 

 

 
  

 
 

 

  

 
 

 

 
 

 

 

 
-a-  Along Radial Distance                                                           -b- Along Weld Depth 

 

Fig.4. Temperature Distribution 

    

0 

500 

1000 

1500 

2000 

2500 

3000 

0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014 0.0016 0.0018 0.002 
Weld Depth, m 

1 kw 
1.5 kw 
2.5 kw 

T
e
m

p
e
ra

tu
re

, 
o
K

 

o
K

 

0 

500 

1000 

1500 

2000 

2500 

3000 

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01 
Radial Distance, m 

1 kw 
1.5 kw 
2.5 kw 

T
e
m

p
e
ra

tu
re

, 
o
K

 

o
K

 



Osama F. Abdulateef                                              Al-Khwarizmi Engineering Journal, Vol. 5, No. 1, PP 33-41 (2009) 

  

38 

In figures 4(a,b) the maximum temperature 

for laser powers of 1.0, 1.5, 2.5 KW and an on-
times of 0.15 sec are compared. The weld width 

and penetration are estimated along the horizontal 

and vertical direction respectively. It can be 
shows that the weld dimensions do not changes 

significantly as the laser power is increased from 

1.0 to 1.5 KW for an on-time 0.15 sec. In contrast, 

an increase in laser power to 2.5 KW shows a 
marked increase in penetration from approximated 

0.5 mm (both at 1.0 and at 1.5 KW) to 1.0 mm at 

(2.5 KW). This is further evident as the on-time is 
increased from o.15 to 0.225 sec at 2.5KW laser 

power (see figure 5). 

 
 

 

 

 
 

 

 
 

 

 

 
 

 
-a- Along Radial Distance 

 
 

 

 
 

 

 
 

 

 

 
 

 
 

-b- Along Weld Depth 

 

Fig.5. Temperature Distribution 

 

 The temperature gradients during laser 

welding are usually very large, due to the high 
power density, and small local area provided by 

the laser. Figures 6 and 7 show the large 

temperature gradient at the workpiece radial 

distance at a laser power of 2.5KW, and it can be 
viewed that very high temperature occur at the 

center of the workpiece, and is decreased very 

significantly as propagating along the radial 

direction, and for nodes that more1.5 m.m away 

from the center, the temperature drop down to 
very close to room temperature indicating that 

most of the heat affected zone are localized within 

the 1.5 m.m range. 
 

 

 

 
 

 

 
 

 

 
 

 

 

 
Fig.6. Temperature Distribution Along Radial 

Distance 

 

 

 

 
 

 

 
 

 

 

 
 

 

 
 

 

 
Fig.7. Temperature Distribution During Laser Spot 

Welding 
 

 For stress calculation, the temperature fields 

at the various time steps are then used as an input 
to the mechanical analysis, Von Mises stress was 

calculated. The maximum Von Mises stress was 

about 380 MPa, while the yield strength of low 

carbon steel is about 290 MPa, indicating that the 
workpiece would undergo plastic deformation. 

The thermal residual stresses around the laser spot 

due to plastic strain can be calculated from figure 
8 at yield strength value. It was found that the 

residual stresses were very small and localized 

within 1.0 mm range in radial distance and 0.5mm 
range in depth; these values are very small 

compared with 4 mm range in radial distance for 

resistance spot welding process[16]. 

0 

500 

1000 

1500 

2000 

2500 

3000 

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01 
Radial Distance, m 

t=0.15 sec 
t=0.65 sec 
t=1.15 sec 
t=1.65 sec 
t=2.15 sec 
t=2.65 sec 

T
e
m

p
e
ra

tu
re

, 
o
K

 

o
K

 

0 

500 

1000 

1500 

2000 

2500 

3000 

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01 
Radial Distance, m 

t=0.15 sec 
t=0.165 sec 
t=0.18 sec 
t=0.225 sec 

T
e
m

p
e
ra

tu
re

, 
o
K

 

o
K

 

0 

500 

1000 

1500 

2000 

2500 

0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014 0.0016 0.0018 0.002 
Weld Depth, m 

t=0.15 sec 
t=0.165 sec 
t=0.18 sec 
t=0.225 sec 

T
e
m

p
e
ra

tu
re

, 
o

K
 

o
K

 



Osama F. Abdulateef                                              Al-Khwarizmi Engineering Journal, Vol. 5, No. 1, PP 33-41 (2009) 

  

39 

 

 
 

 

 
 

 

 

 
 

 

 
 

 

 

-a- Along Radial Distance                                                         -b- Along Weld Depth 
 

Fig.8. Von Mises Thermal Stress Distribution After Laser Spot Welding 

 

 
 

In laser spot welding, a weldment is  locally 

heated by intense beam which focused on small 

area. Due to non-uniform temperature distribution 
during the thermal cycle, incompatible strains lead 

to thermal stresses. These incompatible strains 

due to dimensional changes associated with 
solidification of the weld metal, metallurgical 

transformations, and plastic deformations, are the 

sources of residual stresses. The stresses along the 

lateral direction of the workpiece changed from 

compression at the spot under the laser beam and 
tension away from the spot at the end of welding 

(t=2.65 sec) to tension at the spot under the laser 

beam and compression away from the spot when 
it cooled (t=400 sec), which are a good agreement 

with the published results[11,15],  see figure 9. 

 
 

 

 

 
 

 

 
 

 

 

 

 

 

 

 

 

 

 

 

 

 
 

Fig.9.  Thermal Stress Distribution During and After Laser Spot Welding 

 

 

 

0 

50 

100 

150 

200 

250 

300 

350 

400 

0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014 0.0016 0.0018 0.002 
Weld Depth, m 

Numerical 
Theoretical 

T
h
e
rm

a
ll

 S
tr

e
ss

, 
M

P
a

 

M
P

a
 

0 

50 

100 

150 

200 

250 

300 

350 

400 

0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014 0.0016 0.0018 
Radial Distance, m 

Numerical 
Theoretical 

T
h
e
rm

a
l 

S
tr

e
ss

, 
M

P
a

 

M
P

a
 

-400 

-300 

-200 

-100 

0 

100 

200 

300 

400 

0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014 0.0016 0.0018 

Radial Distance, m 

t=2.65 sec 
t=400 sec 

T
h
e
rm

a
l 

S
tr

e
ss

, 

M
P

a
 



Osama F. Abdulateef                                              Al-Khwarizmi Engineering Journal, Vol. 5, No. 1, PP 33-41 (2009) 

  

40 

5. Conclusions: 
  

 An analytical and finite element analyses have 

been investigated to simulate the laser spot 

welding process on a low carbon steel sheet. The 
analytical analysis was focused on a set of 

equations representing interaction of the laser 

beam with materials. The numerical analysis 
based on 3-D finite element analysis of heat flow 

during laser spot welding taken into account the 

temperature dependence of the physical properties 
and latent heat of transformations using ANSYS 

code V.10.0. The effect of laser operating 

parameters on the results of the temperature 

profile, thermal stresses, and dimensions of the 
laser welded workpiece were studied which 

showed good correlations between analytical and 

numerical results. We conclude that: 
1- The temperature gradients during laser 
welding are usually very large and it was viewed 

that very high temperature at the center of the 
workpiece, and is decreased very significantly as 

propagating along the radial direction.  

2- The thermal residual stresses around the laser 
spot due to plastic strains were very small and 
localized within 1.0 mm range. 

3- Laser welding process is effective to reduce 
the welding residual stress. 
4- Stresses along the lateral direction of the 
workpiece changed from compression at the spot 

under the laser beam and tension away from the 

spot at the end of welding to tension at the spot 
under the laser beam and compression away from 

the spot when it cooled.  

 
 

6. References: 
 
[1] W.Nowacki, 1962, Thermoelasticity, 

Addison-Wesely, Reading, MA. 

[2] J.R.Barber, 1984, "Thermoelastic 
displacements and stresses due to heat source 

moving over the surface of half plane," J. 

Appl. Mech., 51:636-340. 
[3] N.Sumi, R.B.Hetnazske, and N.Noda, 1987, 

"Transient thermal stresses due to a local 

source of heat moving over the surface of an 

infinite slab," J. Therm. Stresses, 10:83-96. 
[4] I.C.Sheng and Y.Chen, 1991, "Thermoelastic 

analysis for a semi-infinite plane subjected to 

a moving Gaussian heat source," J. Therm. 
Stresses, 14:129-141. 

[5] M.Vicanek, A.Rosch, F.Piron, and G.Simon, 
1994, "Thermal deformation of a solid surface 

under laser irradiation," Appl. Phys., 59:407-

412. 
[6] N.Postacioglu, P.Kapadia, and J.M.Dowdeu, 

1997, "The thermal stress generated by a 

moving elliptical weld pool in the welding of 
thin metal sheets," Journal of Physics, 

D:Applied Physics, 30:2304-2312.  

[7] Y.Dain, P.D, Kapadia, and J.M.Dowden, 
1999, "The distortion gap width and stresses 

in laser welding of thin elastic plates," J. 

Phys. D:Appl. Phys., 32:168-175. 

[8] L.J.Yang and Z.M.Xiao, 1995, "Elastic-
Plastic modeling of the residual stress caused 

by welding," J. Materials Processings 

Technology, 84:589-601. 
[9] S.Fujii, N.Takahashi, S.Sakai, T.Nakabayashi, 

and M.Muro, 2000, "Development of 2D 

simulation model for laser welding," Proc. 
SPIE, 3888:115-214. 

[10] M.R.Frewin and D.A.Scott, 1999, "Finite 
element model of pulsed laser welding," 

welding J., 78:15-22. 
[11] M.K.Apalak, K.Aldas, and F.Sen, 2003, 

"Thermal non-linear stresses in an 

adhesively bonded and laser spot welded 
single-lap joint during laser-metal 

interaction," J. Materials Processing 

Technology, 142:1-19.  

[12] W.W.Duley, 1999, Laser Welding, Wiley, 
New York, NY. 

[13] A.De, S.K.Maiti, C.A.Walash and 
H.K.D.H.Bhadeshia, 2003, "Finite element 
simulation of laser spot welding," Science 

and Technology of Welding and joining, 

Vol.8, No.5:377-384. 
[14] B.S.Yilbas, S.A.Gbadebo, and M.Sami, 

2000, "Laser heating: an electro-kinetic 

theory approach and induced thermal 

stresses," Optics and Laser Engineering, 
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[15] S.A.Tsirkas, P.Papanikos, Th.Kermanidis, 
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welding process in butt-joint specimens," 

Journal of Materials Processing 

Technology, 134:59-69. 
[16] Nabeel K. Alsahib, Somer M. Nacy, Faiz F. 

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College of    Eng., University of Baghdad, 

Vol.14, No.1:2202-2215. 

 



200 )41-33، صفحة 1، العذد 5مجلة الخوارزمي الهنذسية المجلذ اسامة فاضل عبذ اللطيف                                                                      9) 
  

41 

 

توزيع األجهادات الحرارية في عملية اللحام النقطي بالليسر  أستقصاء 
 

أسامة فاضل عبذ اللطيف 
خايؼت بغذاد  \ كهٍت انهُذست انخىاسصيً \ قسى هُذست ػًهٍاث انخصٍُغ

 

 

 

  الخالصة

انداَب انخحهٍهً أػخًذ . ٌهذف هزا انبحث انى دساست ػًهٍت انهحاو انُقطً بانهٍضس نصفائح انكاسبىٌ انًُخفط انفىالرٌت ححهٍهٍا و ػذدٌا 

أيا انداَب انؼذدي فقذ أسخُذ ػهى ححهٍم ػُصش ثالثً األبؼاد . ػهى يدًىػت ثابخت يٍ انًؼادالث انخً حًثم انخفاػم بٍٍ شؼاع انهٍضس وانًؼذٌ

نخًثٍم انحشاسة انًخىنذة أثُاء ػًهٍت انهحاو انُقطً أخزٌٍ بُظش األػخباس أػخًاد انخصائص انفٍضٌائٍت وانحشاسة انكايُت ػهى دسخاث انحشاسة 

, حى فً هزا انبحث دساست حأثٍش يخغٍشاث شؼاع انهٍضس ػهى حىصٌغ دسخاث انحشاسة.  يخؼذد األغشاضANSYS 10.0بأسخخذاو بشَايح 

وقذ حى يالحظت حصىل . نقذ الحظُا يٍ خالل انُخائح وخىد أسحباغ خٍذ بٍٍ انداَبٍٍ انخحهٍهً وانؼذدي. وأبؼاد يُطقت انهٍضس, األخهاد انحشاسي

كزنك . أسحفاع كبٍش خذا فً دسخاث انحشاسة أثُاء انهحاو بانهٍضس فً يشكض انبقؼت ثى ٌبذأ بانخُاقص بصىسة كبٍشة كهًا أبخؼذَا باألحداِ انشؼاػً

 يههًٍخش وهزا ٌذل 1.0حًج يالحظت حىنذ أخهاد حشاسي يخبقً حىل بقؼت انهٍضس بسبب األَفؼال انهذٌ يىصػا فً يُطقت ظٍقت خذا الحخداوص 

اٌعا حى األسخُخاج بأٌ اإلخهاد ػهى غىل اإلحّداِ . ػهى أٌ ػًهٍت انهحاو بانهٍضس فؼانت نخخفٍط األخهاداث انحشاسٌت انًخبقٍت َخٍدت ػًهٍت انهحاو

انداَبً نهقطؼت انًهحىيت قذ حغٍّش يٍ األخهاد األَعغاغً فً انبقؼت ححج شؼاع انهٍضس وأخهاد شذ بؼٍذا ػٍ انبقؼت فً نحظت َهاٌت انهحاو إنى 

أخهاد شذ فً انبقؼت ححج شؼاع انهٍضس وأخهاد أَعغاغ  بؼٍذا ػٍ انبقؼت ػُذيا بّشدث, وهزا ٌخىافق يغ األدبٍاث انًُشىسةانخً نها ػالقت 

 .  بانًىظىع