J. DOMAGA£A-DUBIEL et al.: ANALYSIS OF TEMPERATURE DISTRIBUTION IN LASER ALLOYING OF PURE COPPER
629–635
ANALYSIS OF TEMPERATURE DISTRIBUTION IN LASER
ALLOYING OF PURE COPPER
ANALIZA PORAZDELITVE TEMPERATURE MED LASERSKIM
LEGIRANJEM ^ISTEGA BAKRA
Justyna Domaga³a-Dubiel
1*
, Damian Janicki
2
, Grzegorz Muzia
1
, Jakub Lisicki
3
,
Jacek Ptaszny
4
, Joanna Kulasa
1
1
£ukasiewicz Research Network – Institute of Non-Ferrous Metals, Sowiñskiego street 5, 44-100 Gliwice, Poland
2
Welding Department, Faculty of Mechanical Engineering, Silesian University of Technology, Konarskiego Street 18A, 44-100 Gliwice, Poland
3
Silesian University of Technology (Graduate Student), Konarskiego Street 18A, 44-100 Gliwice, Poland
4
Department of Computational Mechanics and Engineering, Silesian University of Technology, Konarskiego Street 18A, 44-100 Gliwice, Po-
land
Prejem rokopisa – received: 2022-07-15; sprejem za objavo – accepted for publication: 2022-09-30
doi:10.17222/mit.2022.551
In many cases, the use of copper is limited by the unsatisfactory properties of its surface layer, i.e., low hardness and wear resis-
tance. Laser surface-layer treatment may be a better alternative to other techniques used in surface engineering intended for the
elements, whose high conductivity, combined with high functional properties, is required. In the present work, laser alloying of
pure copper with Ni powder is performed. Thermographic measurements during the process and measurements of the melt-pool
dimensions after the alloying are performed. A 3-D model of a cylindrical specimen is developed. The enthalpy-based material
model involving the phase change is applied. The nickel powder is taken into account with an appropriate value of the
workpiece absorptance in the heat flux boundary condition imposed in the moving laser spot area. This study utilized the
ANSYS-based Simulation software. Results of the temperature simulation show acceptable agreement with the experiment. The
developed model can be used to predict the temperature distribution and identify the workpiece absorptance.
Keywords: laser surface alloying, copper, temperature distribution, finite-element simulation
V mnogih primerih je uporaba ~istega bakra omejena zaradi njegovih relativno slabih mehanskih lastnosti oziroma njegove
nizke trdote in trdnosti ter slabe odpornosti proti obrabi. Povr{inska laserska obdelava bakra bi bila lahko bolj{a alternativa
nekaterim drugim postopkom oziroma tehnikam povr{inskega in`eniringa v primerih, ko se hkrati zahteva kombinacija njegove
odli~ne prevodnosti z drugimi funkcionalnimi lastnostmi. V ~lanku je opisana izvedba postopka laserskega legiranja ~istega
bakra z nikljevim prahom. Med postopkom so izvedli termo grafi~ne meritve dimenzij nastalega bazen~ka taline po legiranju.
Izdelali so tri dimenzionalni model cilindri~nega vzorca. Uporabili so entalpijski materialni model z upo{tevanjem faznih
sprememb. Upo{tevali so dovajanje primerne koli~ine nikljevega prahu s primerno vrednostjo absorbcije toplotnega toka pri
njegovih robnih pogojih, ustvarjenih z gibanjem povr{ine to~ke laserskega snopa. [tudijo so izvedli s pomo~jo simulacijskega
programskega orodja ANSYS. Rezultati temperaturne simulacije so pokazali sprejemljivo ujemanje s prakti~nimi preizkusi.
Ugotovili so, da se lahko razviti model uporablja za napoved porazdelitve temperature in identifikacijo vpojnosti preizku{anca.
Klju~ne besede: lasersko povr{insko legiranje bakra, porazdelitev temperature, simulacija z metodo kon~nih elementov
1 INTRODUCTION
Copper and its alloys are widely used in everyday life
and in industrial practice, mainly due to their high elec-
trical and thermal conductivity. Semi-finished products
made from copper alloys with good mechanical proper-
ties and good electrical and thermal conductivity remain
stable and, at high temperatures, find an ever wider ap-
plication in technological solutions; they usually replace
grades of pure copper and other copper alloys of inferior
electrical conductivity. They are used, among others, in
the production of elastic elements for electrical and elec-
tronic devices, electrodes for the resistance welding of
car body sheets, tips of welding torches, trolley wires for
cranes and other lifting devices, elements of relays and
electric contactors, non-sparking tools used in mines and
ship engine rooms.
1,2
However, the main problems in
using copper components are its low hardness, poor
abrasion and oxidation resistance, tendency to electrical
erosion and atmospheric corrosion. Therefore, some at-
tractive techniques are used in surface engineering to in-
crease the performance of such components and to re-
duce their wear.
3
Significant improvement of the anticorrosive proper-
ties and increase in the resistance to abrasive wear can be
achieved with the application of the methods of surface
metal-layer shaping. One of them is laser alloying, also
known as the laser surface alloying – LSA, that is based
on the introduction of alloying elements into the alloyed
material.
4,5
Mutual intense mixing of the materials occurs
in the melt pool as a result of convection and gravita-
tional movements, and a laser beam. The liquid metal
rapidly cools down and solidifies as a result of a large
temperature gradient at the boundary of the melted sur-
Materiali in tehnologije / Materials and technology 56 (2022) 6, 629–635 629
UDK 669.15-194 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 56(6)629(2022)
*Corresponding author's e-mail:
justyna.domagala-dubiel@imn.lukasiewicz.gov.pl
(Justyna Domaga³a-Dubiel)

face layer and the substrate. The surface treatment can be
achieved with two techniques. The alloying material can
be fed to the melt pool in a continuous powder form, i.e.,
in a one-step process. On the other hand, the alloying
material can be pre-placed on the alloyed substrate in the
form of a powder or coating layer made by plasma
spraying, gas spraying or galvanizing, and then melted
with a laser beam – this is called two-stage alloying.
6
Copper and its alloys are characterized by high laser
radiation reflection coefficients, posing a serious prob-
lem in the processes of laser surface treatment of these
materials. Laser surface treatment is a method for im-
proving the wear resistance. Laser cladding of
Ni-based
7,8
, Co-based
9
, Mo-based
10
powder and laser al-
loyed layer of Cu–Fe–Al–Si
11
and Cr-WC powders
12
on a
copper substrate have been reported. A high-power diode
laser (HPDL) with direct beam transmission to the
treated surface is advantageous when laser alloying ma-
terials on a Cu matrix. This is due to, among others, the
multimode (even) power density distributions on the
beam focus surface (the "top hat" profile). The above-
mentioned advantage of HPDL lasers, in comparison to
the other types of lasers, provides an additional reduction
in the alloying linear energy as well as allowing a better
control of the thermal conditions in the melt pool.
13,14
To
reduce laboratory experiment costs, models are often de-
veloped. In the literature, analytical methods,
15
the fi-
nite-element method,
16–18
the finite-difference method
19
and the boundary-element method
20,21
are applied.
In the present work, laser surface alloying of a Cu
substrate is carried out by melting the preplaced Ni pow-
der. The Ni powder used increases of the absorption of
laser irradiation. The process is simulated to predict the
temperature distribution in the workpiece. The finite-ele-
ment method (FEM) simulations are performed, with
usual simplifications and assumptions concerning the
boundary conditions included in laser-treatment process
calculations.
22,23
The fluid flow, evaporation of the mate-
rial through the surface and interaction of the material
with the shielding gas are neglected. It is assumed that
the liquid in the melt pool is still, although the phase
change is involved with the enthalpy-based approach.
The powder volume is not discretized and the model ge-
ometry is not changed during the simulation. It is as-
sumed that the powder has an impact on the absorptance
coefficient of the workpiece. The coefficient is included
in the heat flux boundary condition imposed on the area
of the laser spot. The absorptance of the workpiece cov-
ered with the nickel powder is identified by changing the
parameter and a comparison of the simulated tempera-
ture field with the experimental data is made, including
the temperature at a point close to the melt pool and the
melt pool dimensions.
2 EXPERIMENTAL PART
2.1 Characterization of the materials and experimental
methods
The substrate material for the laser surface treatment
was copper in the form of a rod with a 50-mm diameter
and 5-mm hight. Copper laser alloying was performed
using a HPDL, Rofin DL 020 (Table 1). During the pro-
cess, the laser spot length was set close to the minimum
possible length.
Table 1: Specifications of the Rofin DL 020
Parameter Value
Wavelength (nm) 808–940
Power range (W) 100–2000
Focal length (mm) 82
Power density range (kW/cm
2
) 0.8–36.5
Laser beam spot dimensions (mm) 1.5 × 6.6
Commercially pure Ni powder of particles with a size
of below 10 μm was used as the alloying material. Be-
fore the laser surface treatment, the samples were sand-
blasted and then rinsed in an ultrasonic bath. The Ni
powder mixed with ethyl alcohol in the form of a paste
with a thickness of 120–150 μm was applied to the sand-
blasted copper surface and then melted by means of the
laser beam. Argon was used as the shielding gas. Laser
copper treatment was performed at a 2.0 kW laser power
and 0.15 m/min feed speed. After the laser surface alloy-
ing, the samples were sectioned, polished and etched for
optical microscopy to measure the width and depth of the
melt pool.
Thermovision measurements of the Cu samples dur-
ing the laser alloying were done using a ThermaCam
SC640 infrared camera from FlirSystems. The initial test
parameter was the oxidized copper coefficient, ranging
from 0.6–0.7 (based on the emissivity table provided by
the FLIR camera manufacturer). The emissivity coeffi-
cient of the tested material was selected on the basis of a
test carried out with the use of a temperature meter and a
heating device (a furnace equipped with a temperature
controller) in which the reference samples were heated to
(300, 700 and 1000) °C, respectively. Then the
emissivity coefficient was calibrated to the obtained tem-
perature measurement results. On this basis, a factor of
0.7 was selected for a temperature in the 700–1000 °C
range. Temperature distributions during the laser surface
alloying of the Cu samples were developed along with
the recording of the cooling temperature of these sam-
ples. The sample temperature during the laser treatment
was determined based on the tests. The measurement
was made at a point near the melt pool and on the sur-
face of the sample during the laser treatment process.
J. DOMAGA£A-DUBIEL et al.: ANALYSIS OF TEMPERATURE DISTRIBUTION IN LASER ALLOYING OF PURE COPPER
630 Materiali in tehnologije / Materials and technology 56 (2022) 6, 629–635

2.2 Mathematical model for the non-stationary heat-
conduction problem
For the 3-D body made of a material that experiences
solid-liquid-solid transformations, the non-stationary
heat-conduction process can be described with Equation
(1):
17
∂
∂
∂
∂
H
t
T
Q
t
=∇ +  2 v
(1)
where t denotes the time, T is the temperature,  is the
thermal conductivity coefficient and Q
v
denotes the heat
density. H denotes the volumetric enthalpy in Equa-
tion (2):
HT cTd T
T
T
() () =
∫
 ref
(2)
that depends on material density  and heat capacity c.
T
ref
denotes the reference temperature.
The initial condition for Equation (1) is
Tx Tx x
t
(,) () 0
0
0
=∈
=
 (3)
where T
0
is the ambient temperature.
The following boundary conditions can be applied:
• The known heat flux q
2
on the boundary
2
∈∂ ,in
the direction of the outward normal vector n (the
Neumann boundary condition):
qxt
T
n
qxtx (,) (,) =− = ∈ 
∂
∂
22
(4)
• The convection boundary condition on
3
∈∂ , that
corresponds to the heat exchange with the surround-
ing medium with temperature T
0
and convection coef-
ficient h
c
:
qxt h T T x (,) ( ) =−∈
c 03
 (5)
• The radiation boundary condition on
4
∈∂ , that
involves the thermal radiation coefficient  and the
Stefan-Boltzmann constant b
:
qxt T T x (,) ( ) =−∈  
b
4
0
4
4
(6)
The problem involves phase changes and the enthalpy
(Equation (2)) must be defined. One can distinguish be-
tween two cases: the mushy and isothermal phase
change.
24
In the former case, the enthalpy is defined by:
HT
cTT TT
cTT
L
T
T
T
T
()
()
() =
≤
∫
∫
 
ss
s
df o r
d+
ref
ref
s
∂
∂T
TTTT
cTT L cTT
T
T
T
T
T
d for <
dd
s
ref
s
l
s l
s l
∫
∫
≤
++  () ()
T
TT
∫
>
⎧ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ ⎪ ⎪ ⎪ ⎪ for
l
(7)
where c
s
and c
l
are the heat capacities in the solid and
liquid state, respectively, (T
s
– T
l
) is the phase change
temperature interval and L is the latent heat.
With the application of the Galerkin procedure (or
the method of weighted residuals) and the weak formula-
tion, the continuous initial boundary value problem de-
scribed in this section is transformed into a discrete
problem.
18
This leads to the formulation of the finite-ele-
ment method algebraic system of equations that are
solved in each step of the discretized time. Due to tem-
perature-dependent material properties, the system is
non-linear and can be solved, e.g., with the New-
ton-Raphson method.
16
2.3 Parameters of the finite element model
2.3.1 Geometry, boundary and initial conditions
The laser-alloying process using a nickel-copper
coating on the copper substrate is modelled. The top sur-
face of the model is covered with the nickel powder to
form the coating. The specimen is placed on a ceramic
base plate that is turning around its axis to provide the la-
ser scanning speed v of 0.15 m/min. The laser beam
scans the surface along a circular path with a radius of
15 mm, coaxial with the top surface. The width of the
path is 1.5 mm. A full cycle of the alloying corresponds
to the full turn of the base plate (angle  =2  rad). The
geometry of the model is shown in Figure 1.
On the bottom face, a perfect insulation boundary
condition is imposed. On the free faces (top and lateral),
convection and radiation are imposed (Equations (4) and
(5)). The laser beam is modelled as the heat flux
q
kP
S
L
= (8)
uniformly distributed over the laser spot area. The sym-
bols denote the following: k – the workpiece absorp-
tance, P – the laser power, and S – the area of the laser
spot. The flux q
L
is imposed on an area corresponding to
the spot that is moving relative to the specimen along
the scanning path, with the velocity v. The laser is active
for a period of t
h
= 37.7 s. It is assumed that there is no
internal heat source.
The workpiece absorptance k in Equation (8) depends
on the absorptivity of the material and the angle between
the surface and the laser beam. Its value can be changed
to fit the simulation results to the experimental data.
15
In
the present work, the laser power is mainly absorbed by
the nickel-powder layer. Accordingly, three values of ab-
sorptivity are considered based on the data reported in
the literature. In rference
22
theoretical values for the
nickel powder with different geometries (hexagonal,
Gaussian and bimodal) are in a range of 0.51–0.56. In
the same paper, formulas for the powder absorptivity, de-
pendent on the flat-surface absorptivity, is given. If one
takes into account the values for the nickel flat surface
measured by other authors,
22
and apply the formulas
given in reference,
25
the calculated powder absorptivity
can exceed 0.7. In the present work, the parameter de-
pending on the absorptivity of the top-surface material
takes three values (0.56, 0.60, 0.64). The values of all the
J. DOMAGA£A-DUBIEL et al.: ANALYSIS OF TEMPERATURE DISTRIBUTION IN LASER ALLOYING OF PURE COPPER
Materiali in tehnologije / Materials and technology 56 (2022) 6, 629–635 631

parameters that refer to the boundary conditions are
listed in Table 2.
Table 2: Boundary-condition parameters
Parameter Value
Convection film coefficient h
c
(W/(m
2
·K)) 10
Ambient (initial) temperature T
0
(K) 295
Radiation coefficient (emissivity)  0.70
Workpiece absorptance k 0.56, 0.60, 0.64
Laser power P (kW) 2
Scanning speed v (m/s) 2.5 × 10
–3
Heating time t
h
(s) 37.7
2.3.2 Material model parameters
The copper material basic parameters are included in
the applied FEM software. However, to model the mate-
rial behaviour in a broader range of temperature, the data
are complemented with temperature-dependent material
properties. The properties of copper up to the melting
point are available in reference.
26
In the present calcula-
tions, it is assumed that the material properties above the
melting point remain constant. The specifications of the
basic material parameters is given in Table 3.
Table 3: Material model parameters
Parameter Value
Density  (kg/m
3
) 8978
Latent heat of fusion L (J/kg) 205 × 10
3
Thermal conductivity  (T) (W/(m⋅K)) tabular
26
Specific heat c(T) (J/(kg⋅K)) tabular
26
Melting temperature T
l
(K) 1 356
For the enthalpy calculations, the mushy phase-
change model is applied, having a narrow range of the
phase-change temperature (T
s
= 1356 K, T
l
= 1361 K)
that allows one to avoid numerical instabilities during the
solving process.
24
The tabular data for the enthalpy are
listed in Table 4. The points are used to the linear inter-
polation of the data in three characteristic temperature
intervals defined by Equation (7).
Table 4: Enthalpy tabular data
Temperature T(K) Enthalpy H(T) (J/m
3
)
293 10
3
1356 5×10
9
1 361 6.84 × 10
9
2 500 12.10 × 10
9
2.3.3 Geometry and time discretization
To minimize the geometry discretization effect, a
high-quality mesh is applied, composed of 8-node hexa-
hedral elements as its major part. Linear shape functions
are applied to reduce the computation time. The mesh is
densified in the region of the high-temperature gradient.
The position of the specimen is fixed and the moving
heat flux q
L
is applied by an APDL (ANSYS Parametric
Design Language) script. The script selects the nodes
that are located in the laser spot area. The area moves
along the scanning path with the rotation of a local coor-
dinate system at an angle corresponding to a single time
step. The heating time t
h
corresponds to the move of the
laser spot along the full scanning path ( =2 ). The time
is divided into 800 equal time steps that correspond to
the angle increments of the laser spot movement or,
equivalently, the rotation of the specimen with a fixed la-
ser spot in the laboratory experiment.
3 RESULTS AND DISCUSSION
The temperature distribution in the workpiece is cal-
culated. The distribution for the selected time corre-
sponding to four values of (0.5, 1, 1.5 and 2 ) and the
highest value of the workpiece absorptance (k = 0.64) is
shown in Figure 2. The temperature distribution is char-
acteristic for laser treatment processes. The temperature
increases with the time in the whole volume of the speci-
men. High temperature values and high gradients occur
near the area of the laser spot. The volume with a tem-
perature greater than T
l
, corresponding to the melt pool,
is filled up with white colour. It moves along the scan-
ning path and its size increases in time. The maximum
size is observed at the end time (t = 37.7 s). The temper-
ature at point B is measured using the thermographic
camera and compared to the FEM results. Figure 3
shows the temperature plot versus time.
The FEM models initially underestimate the mea-
sured temperature (Figure 3). However, for the simula-
tions and experiment, the trends are similar. For the mea-
surements, high fluctuations can be observed that can be
caused by the non-uniform thickness of the Ni powder
layer and thus its variable absorptance. These fluctua-
tions are not observed in the simulation results. At the
end time, the measured temperature is placed between
the FEM with k = 0.60 and k = 0.64. The smallest rela-
J. DOMAGA£A-DUBIEL et al.: ANALYSIS OF TEMPERATURE DISTRIBUTION IN LASER ALLOYING OF PURE COPPER
632 Materiali in tehnologije / Materials and technology 56 (2022) 6, 629–635
Figure 1: Geometry of the model (mm) with boundary conditions

tive difference in the measurement is observed for FEM
with k = 0.60 and is about 1.2 %. For k = 0.64, the differ-
ence is about 4.3 %. At the simulation end time, the tem-
perature of point B is close to the melting temperature of
pure copper. From the temperature distribution near the
laser spot, one can deduce the melt pool shape and di-
mensions. The width and depth of the pool can be mea-
sured experimentally after the process, by taking micro-
scopic images of the selected sections of a specimen.
Here, such images are taken in planes including points B
and C. The sections correspond to = 1.5 and 2 . The
simulated temperature distributions for k = 0.64 are
shown in Figures 4a and 4b. Selected numerical data
from the simulations and experiment are collected in Ta-
ble 5. The data include the maximum temperature at
point B and melt pool dimensions. The dimensions are
also compared in Figures 5a and 5b, for  = 1.5 and
2 , respectively. In the figures, the microscopic images
are shown.
Table 5: Simulation and experiment results – maximum temperature
at point B and melt pool dimensions
Method
Max
(T
B), K
Melt pool width
(mm)
Melt pool depth
(mm)
 = 1.5 =2 = 1.5 =2  FEM, k = 0.56 1 227 1.8 3.3 0.6 1.5
FEM, k = 0.60 1 289 2.2 4.5 0.9 2.3
FEM, k = 0.64 1 343 2.7 6.3 1.2 3.5
Experiment 1 304 2.7 7.7 0.9 3.2
The width and depth of the measured melt pool for
two different cross-sections are generally placed between
the FEM results for the workpiece absorptance of
k = 0.60 and 0.64. Only simulated depth for k = 0.64
J. DOMAGA£A-DUBIEL et al.: ANALYSIS OF TEMPERATURE DISTRIBUTION IN LASER ALLOYING OF PURE COPPER
Materiali in tehnologije / Materials and technology 56 (2022) 6, 629–635 633
Figure 4: Simulated melt-pool cross-section for k = 0.64 and:
a) 1
= 1.5 ,b) 2
=2 Figure 3: Temperature at point B versus time
Figure 2: Simulated temperature distribution for k = 0.64: a) = 0.5π,b) =1 ,c) = 1.5 ,d) =2

slightly exceeds the measured value. The maximum dif-
ference between dimensions of the actual and simulated
melt pool for k = 0.64 does not exceed 1.5 mm. Such a
value can be considered acceptable in simulations if one
takes into account the width of the laser beam (1.5 mm)
and the maximum width of the melt pool (7.7 mm), Fig-
ure 5b). Thus, the developed model can be used in the
identification of the workpiece absorptance. Here, the
identified absorptance is in the interval of 0.60–0.64.
Such values are close to the Ni powder absorption coeffi-
cients reported in the literature.
22
4 CONCLUSIONS
In this work, a computer model for the prediction of
the temperature distribution in the surface laser alloying
of pure copper with Ni powder is developed. To the sim-
ulation, the ANSYS finite element code is applied. The
phase transformation is taken into account by varying the
enthalpy. To simplify the model, typical assumptions are
introduced, e.g., a still melt pool with constant proper-
ties. The domain of the powder is not discretized. In-
stead, its absorptance is taken into account when moving
the heat-flux boundary condition in the area of the mov-
ing laser spot. Approximate absorptance of the
workpiece is identified by comparing the simulated tem-
perature and melt pool size with the experimental data.
Laboratory measurements show that the melt pool in-
creases through the process. The computational model
gives results that correlate with the experimental data.
Thus, the model can be used to control the melt pool size
along the scanning path. This can be achieved by chang-
ing the laser power through the laser surface alloying
process. To improve the model, more phenomena should
be considered, e.g., the liquid flow in the melt pool,
evaporation of the material, interaction with the shield
gas, and others. However, one can expect that such im-
provements will substantially increase the computation
time. Despite the rigorous assumptions, the present
model gives acceptable results.
Acknowledgment
This research was carried out as a part of the project
financed by the National Centre for Research and Devel-
opment of Poland, project number LIDER/33/0091/L-
7/NCBR/2016 and partially within the framework of the
statutory subsidy of the Department of Computational
Mechanics and Engineering, Silesian University of Tech-
nology, Poland.
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634 Materiali in tehnologije / Materials and technology 56 (2022) 6, 629–635
Figure 5: Comparison between the measured and simulated melt pool: a) 1
= 1.5 ,b) 2
=2

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