O. [UBA et al.: MODELLING OF A TRANSIENT-TEMPERATURE FIELD IN PLASTICS DURING LASER CUTTING
19–21
MODELLING OF A TRANSIENT-TEMPERATURE FIELD IN
PLASTICS DURING LASER CUTTING
MODELIRANJE PREHODNEGA TEMPERATURNEGA POLJA V
PLASTIKI MED LASERSKIM REZANJEM
Oldøich [uba, Libu{e Sýkorová, Vladimír Pata, Oldøich [uba jr., Milena Kubi{ová
Tomas Bata University in Zlín, Faculty of Technology, Vavre~kova 275, 760 01 Zlín, Czech Republic
osuba@ft.utb.cz
Prejem rokopisa – received: 2017-06-30; sprejem za objavo – accepted for publication: 2017-10-11
doi:10.17222/mit.2017.091
This article deals with the area of non-conventional technologies. It reports, in detail, on a research of a laser beam and its use
on different types of polymeric materials. The topic discussed in this article is mainly the thermal transmittance after the
transition of the laser beam, cutting the polymeric materials. At a small distance from the cutting edge, various structural and
chemical changes can occur due to the heat transfer to the material. An influence zone arises, which can play a significant role
affecting the product capabilities. To establish the affected-zone width, models of the transient-temperature field were prepared,
representing the distribution of the temperature in the vicinity of the cutting edge. Temperature functions of the material
properties were considered with respect to extensive dependencies of the mechanical behaviour of polymers.
Keywords: laser cutting, polymer materials, transient-temperature field
V ~lanku avtorji opisujejo nekonvencionalne tehnologije. Detajlno so raziskovali laserski snop in njegovo uporabo na razli~nih
vrstah polimernih materialov. Avtorji so v ~lanku osredoto~eni na razpravo o prenosu toplote pri laserskem rezanju polimernih
materialov. @e na majhnih razdaljah od roba rezanja se lahko zgodijo razli~ne strukturne in kemi~ne spremembe zaradi prenosa
toplote na material. Nekateri vplivi so lahko znatni in so pomembni s stali{~a kakovosti izdelka. Z namenom, da bi dolo~ili
{irino vplivane cone so avtorji modelirali prehodno temperaturno polje, ki predstavlja porazdelitev temperature v bli`ini roba
rezanja. Pri tem so upo{tevali odvisnost materialnih lastnosti od temperature zaradi velikega vpliva temperature na mehansko
obna{anje polimerov.
Klju~ne besede: lasersko rezanje, polimerni materiali, prehodno temperaturno polje
1 INTRODUCTION
The principle of this cutting method is the concen-
tration of power – electromagnetic radiation of visible
light – on a small surface of a product. The place of
impact heats up considerably, exceeding the melting
temperature of the machined material due to the trans-
formation of the power of this visible radiation light into
thermal power. The material melts and vaporises at the
place of impact. The beam reflects the part absorbed; the
part passes through the material after the impact of the
beam on the material (Figure 1). Absorbed beams share
the heating of the material. The amount of the reflected
beam depends on the material reflectance. Absorption
A(%) of luminous radiation implies the heating of the
surface layer. Reflectance and absorption are complex
events; the following relation shows their correlation in
Equation (1):
R + A = 100 % (1)
The absorption of luminous radiation and the follow-
ing heat depend on the thermal conductivity of the
material. The heat convection from the laser to the mate-
rial is a complicated effect. Today, no true theory of the
formulation of the thermal conductivity and temperature
calculation exists because the heat transfer is rapid. The
process propounded by Carslaw-Jaeger is used for
formulating the heat transfer for a mobile source with a
speed in m s–1. The process presents a solution in the form
of a partial differential equation for the heat convection
from a source with the dimensions of a focused beam to
the surface layer and in the material under specific
marginal conditions. It follows from the simplified hypo-
Materiali in tehnologije / Materials and technology 52 (2018) 1, 19–21 19
UDK 620.1/.2:621.96:67.017 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 52(1)19(2018)
Figure 1: Laser-beam effect on the material
thesis that the material of a product is isotropic and the
heat transfer can be described with the equation of diffu-
sion under definite marginal conditions in Equation (2):
∂
∂
T
t
T= 
Δ L (2)
where T is the absolute temperature (K), t is the time (s),
L is the specific elongation and 
 is the thermo-
diffusion given by the relation (Equation (3)):



=
⋅
k
c
(3)
where k is the thermal-conductivity coefficient
(W m–1 K–1),  is the density of the material (kg m–3)
and c is the specific heat (J kg–1 K–1) of solid mate-
rial.1–3
2 EXPERIMENTAL PART
For the laser cutting and subsequent simulation of the
temperature field during the passage of the laser beam
through the material, the following polymeric materials
were chosen: polymethyl methacrylate (PMMA) as the
representative of the amorphous polymer and poly-
ethylene PE 1000 as the representative of the crystalline
polymer. Commercial CO2 laser ILS 3 NM was used for
cutting of the chosen materials. For the experimental
machining, the maximum value of power (P = 100 W)
and the minimum cutting speed (fmax = 1524 mm s–1)
were chosen so that the interaction time between the
laser and materials was as large as possible. The speci-
mens were prepared, having dimensions of 30 mm × 30
mm and a thickness of 15 mm. One laser cut was per-
formed in the middle of each material and the depth of
cut was evaluated. The measured cutting depth for
PMMA was 15 mm and the measured cutting depth for
PE 1000 was 8 mm (Figure 2).
3 RESULTS AND DISCUSSION
The polymer wall is cooled down gradually in a cer-
tain section after the beam passes and, at the same time,
the heat flux extends away from the point of cut to the
internal-wall volumes. The thermal process in the non-
stationary, transient mode is described by the Fourier-
Kirchhoff differential equation, as mentioned above. Due
to their specific values of the thermal-conductivity
coefficient, in the case of sudden local heating, the
thermoplastics keep their significant temperature
differences in the heating area for a relatively long time.
A particular problem is the fact that the thermoplastics
exhibit significant physical, temperature dependencies.
Consequently, the solution with constant material
parameters is not valid and the physical characteristics
have to be entered, as a function of temperature, in the
temperature curves. When solving the problem, we
considered the fact that a certain amount of energy of the
laser beam is realised as a certain value of the heat flux
O. [UBA et al.: MODELLING OF A TRANSIENT-TEMPERATURE FIELD IN PLASTICS DURING LASER CUTTING
20 Materiali in tehnologije / Materials and technology 52 (2018) 1, 19–21
Figure 2: Measured values of the depth of grooves
Figure 3: Temperature field in the crosscut of the wall (PE 1000)
Figure 6: Profile of the temperature on the surface of the wall
(PMMA)
Figure 4: Profile of the temperature on the surface of the wall (PE
1000)
Figure 5: Temperature field in the crosscut of the wall (PMMA)
entering the surface of the remaining, solid part of the
polymer at the cutting point. The rigid part is limited by
the cracking temperature. By repeatedly changing the
entered heat-flow value and following the analysis of the
temperature field, the maximum temperature in the
sectional area was adjusted to the above cracking tempe-
rature.4,5 The obtained results are shown in the following
figures. The temperature field in the crosscut of the wall
used for both polymeric materials can be seen in Fig-
ures 3 and 5. Figures 4 and 6 show profiles of the tem-
perature on the surface of the wall.
Table 1: Material properties (PE 1000)
Material Material properties Numericalvalues
PE
Cracking temperature Tp (°C) > 300
Density  (kg·m-3) 930
Specific heat cp (J·kg-1·K-1) 1750
Thermal conductivity  (W·m-1·K-1) 0.4
Depth of cut / thickness of mat. (mm) 6.3 / 15
Table 2: Material properties (PMMA)
Material Material properties Values
PMMA
Cracking temperature Tp (°C) > 300
Density  (kg m–3) 1180
Specific heat cp (J kg–1 K–1) 1465
Thermal conductivity  (W m–1 K–1) 0.2
Depth of cut / thickness of the mat.
(mm) 15 / 15
4 CONCLUSIONS
From the results of the experiment, it is evident that
the "laser machinability" of various polymeric materials
varies. It follows from the unlike physical properties of
the materials, especially the specific heat and thermal
conductivity, that it is also possible to consider the influ-
ence of different crystal-lattice layouts. Based on the
performed simulations of the temperature field, it can be
seen that the high-temperature region, which can cause
structural changes in the material, is narrow compared to
metals. The simulations show that the area, in which
depolymerisation and degradation of various materials
can occur, is very small and reaches the maximum depth
of 0.7 mm. High-temperature gradients induce a high
residual stress in the vicinity of the cut. Due to the com-
plex mechanical behaviour of the polymers, the tem-
perature and time dependence of this behaviour generally
remain in the product after the end of the technological
process involving the residual stress, which partially
relaxes within the time. The residual stress negatively
affects the utility properties of the respective plastic pro-
duct. Unlike the elastic strain, the residual stress cannot
be quantified due to the complex behaviour of the
polymers at higher temperatures. The resulting residual
stress is the result of various aspects. These include, in
addition to the technological causes (a non-uniform heat
dissipation, high-temperature gradients) material aspects,
especially the orientation of the macromolecular struc-
ture or the degree of crystallinity.
5 REFERENCES
1 W. Ozgowicz, Numerical simulation of an equilibrium segregation of
impurities on the grain boundaries of copper and its alloys, Mater.
Tehnol., 51 (2017) 3, 363–372
2 L. Sykorova, O. Suba, J. Knedlova, Laser micro-machining and
temperature field simulation, Key Engineering Materials, 581 (2014),
322–325, doi:10.4028/www.scientific.net/KEM.581.112
3 M. Kubi{ová, V. Pata, L. Sýkorová, Creating and Evaluating Replicas
of Surfaces Machined by Laser Beam, MATEC Web Conf., 121
(2017). 03013, doi:10.1051/matecconf/201712103013
4 L. Sýkorová, V. Pata, M. Kubi{ová, J. Knedlová, Effect of concen-
trated energy of laser beam on polymer material, MATEC Web
Conf., 121 (2017), 03021, doi:10.1051/matecconf/ 201712103021
5 V. Pata, L. Sýkorová, M. Kubi{ová, M. Malachova, Resolving
problems of finding surface boundaries during laser machining,
(2016), doi:10.4028/www.scientific.net/MSF.862.66
6 L. Sýkorová, V. Pata, M. Kubi{ová, M. Malachova, The "laser
machinability" of polymeric materials, (2016), doi:10.4028/
www.scientific.net/MSF.862.141
O. [UBA et al.: MODELLING OF A TRANSIENT-TEMPERATURE FIELD IN PLASTICS DURING LASER CUTTING
Materiali in tehnologije / Materials and technology 52 (2018) 1, 19–21 21