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Physics Procedia 56 (2014) 1208 - 1217

8th International Conference on Photonic Technologies LANE 2014

Calibrated Heat Flow Model for Determining the Heat Conduction

Losses in Laser Cutting of CFRP

P. Muchaa *, R. Weberb, N. Spekera, P. Bergerb, B. Sommerc, T. Graf5

aTRUMPF Laser- und Systemtechnik GmbH, Johann-Maus-Straße 2, 71254 Ditzingen, Germany bInstitut für Strahlwerkzeuge, University of Stuttgart, Pfaffenwaldring 43, D-70569 Stuttgart, Germany c GKN Aerospace Deutschland GmbH, Brunhamstr. 21, 81249 München, Germany

Abstract

Laser machining has great potential regarding automation in fabrication of CFRP (carbon-fiber-reinforced plastics) parts, due to the nearly force and tool-wear free processing at high process speeds. The high vaporization temperatures and the large heat conductivity of the carbon fibers lead to a large heat transport into the sample. This causes the formation of a heat-affected zone and a decrease of the process speed.

In the present paper, an analytical heat flow model was adapted in order to understand and investigate the heat conduction losses. Thermal sensors were embedded in samples at different distances from the kerf to fit the calculated to the measured temperatures. Heat conduction losses of up to 30% of the laser power were determined. Furthermore, the energy not absorbed by the sample, the energy for sublimating the composite material in the kerf, the energy for the formation of the HAZ, and the residual heat in the sample are compared in an energy balance.

© 2014TheAuthors.Publishedby ElsevierB.V.This is an open access article under the CC BY-NC-ND license

(http://creativecommons.Org/licenses/by-nc-nd/3.0/).

Peer-review under responsibility of the Bayerisches Laserzentrum GmbH

Keywords: Laser cutting; CFRP; heat conduction losses; HAZ; heat-affected zone; energy balance; carbon-fiber-reinforced plastic

* Corresponding author. Tel.: +49-7156-303-32203 ; fax: +49-7156-303-32057 . E-mail address: patrick.mucha@de.trumpf.com

1875-3892 © 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license

(http://creativecommons.Org/licenses/by-nc-nd/3.0/).

Peer-review under responsibility of the Bayerisches Laserzentrum GmbH

doi: 10.1016/j.phpro.2014.08.036

Nomenclature

CFRP carbon-fiber-reinforced plastics

Cp mass specific heat capacity

Cpf mass specific heat capacity of the fibers

cp,m mass specific heat capacity of the matrix

dk,mean measured mean width of the kerf

dMSZmean measured mean width of the matrix-sublimation zone

Eabs absorbed laser energy

Econd energy conducted into the sample

EL laser energy

Enot abs laser energy not absorbed by the sample

E -^res residual energy in the sample

Es,k energy for sublimating the composite material in the kerf

Es.m, MSZ energy for sublimating the matrix material in the MSZ

HAZ heat-affected zone

hs thickness of the material

k heat conductivity

k* fitted heat conductivity of the composite material describing the global heat transport

lc length of the cut

Ls latent heat of sublimation

Ls,f latent heat of sublimation of the fibers

Ls,m latent heat of sublimation of the matrix

MDZ matrix damage zone

MSZ matrix sublimation zone

P laser power

t time

^HeatLoad total effective heat load time

THeat,1 temperature in the sample for 0 < t < tHeatLoad

THeat,2 temperature in the sample for t > tHeatLoad

thom time of homogenisation

Tsub sublimation temperature

Tsub,f sublimation temperature of the fibers

Tsub,m sublimation temperature of the matrix

T0 room temperature

Td structure damage temperature

TD,m structure damage temperature of the matrix material

v cutting speed

Vf fiber volume fraction

w integration variable of the error function

x distance from the kerf wall

x' distance from the kerf wall in the temperature distribution just after heating has stopped

y distance in cutting direction

z distance in direction of the laser beam propagation

p density

pf density of the fibers

Pm density of the matrix

argument in the error function

1. Introduction

Carbon-fiber-reinforced plastics have great potential for light weight construction due to their high strength at low density. Especially in the aerospace and automotive industry the demand for high mileage capabilities has led to a mass reduction of many parts. Therefore, respective companies try to pursue this objective by extending the range of applications for CFRP.

As tool-wear free process (Ehrenstein (2006), Caprino et al. (1996)) and non-contact operation at high cutting speeds, laser machining has been of major interest in recent investigations for example by Stock et al. (2012), Weber et al. (2013) or Crane and Brown (1981).

However, the high sublimation temperature of the fibers leads to high temperatures in and around the kerf. Together with the high heat conductivity, this leads to a large heat transport into the sample. Table 1 shows the different thermo-physical properties of the matrix material and the C-fibers, given from Haynes, CRC Handbook (2013), Sheng and Chryssolouris (1995), and Goeke and Emmelmann (2010).

Table 1. Thermo-physical properties of the CFRP components.

Matrix C-fiber parallel / perpendicular to fiber axis

Density p in kg/m3 1250 1850

Heat conductivity k in W/m K 0.2 50/5

Heat capacity cp in J/kg K 1200 710

Latent heat of sublimation Ls in kJ/kg 1000 43000

Sublimation temperature Tsub in K 800 4098

Structure damage temperature TD in K 450 3000

A specific part of the incident laser energy always flows into the material during thermal processes. This part is referred to as heat conduction losses in the following. To cut the material efficiently and fast, a process with low losses is necessary. For cutting or welding metals the heat conduction losses have already been calculated by Schultz et al. (1993), Mazumder and Steen (1980), Prusa et al. (1999) or measured by Fuerschbach (1996) in the past.

In laser machining of CFRP, the large heat transport into the sample leads to a decrease of quality in terms of a large heat-affected zone (HAZ). The formation of the HAZ was investigated for example by Abedin (2010), Weber (2011) or Jaeschke (2012). The low sublimation temperature of the matrix leads to a removal of the plastic structure within the matrix sublimation zone (MSZ). Fig. 1a) shows a cross section of a zone close to the kerf wall. The laser is depicted on the left side of the picture. It propagates in z direction and was moved in y direction for cutting the sample. The heat flows in x direction from the kerf wall into the sample. The MSZ is indicated by the dotted line. The measured mean width of the MSZ dMSZ, mean is given by the white double arrow and the dashed line.

A detail of Fig. 1a) in enlarged scale is shown in Fig. 1b). Inside the MSZ, on the left side of the picture, one can see only bare fibers and no matrix material. This proves that the matrix material was sublimated inside the MSZ. Outside the MSZ fibers and matrix material can be seen.

In a previous publication by Mucha et al. (2014) a heat flow model was used for determining the size of the visible MSZ and the matrix damage zone (MDZ, not visible in the picture). The same experimental setup and the same process parameters were used as in the present paper. A CO2 laser "TruFlow 5000" with a maximum average power of 5 kW was used. At the used spot diameter of 150 ^m the Rayleigh length was about 1 mm. The experiments were performed in ambient air without the use of additional process gases. For the experiments cuts were performed with a single-pass strategy at laser powers of 1 kW, 2 kW, and 5 kW. For each laser power the cutting speed was chosen about 5 to 10% lower than the maximum possible cutting speed to separate the material entirely. The material thickness was 2 mm. A unidirectional prepreg material with a quasi isotropic buildup sequence embedded in an epoxy matrix was used. Several thermal sensors were embedded in the material at different distances from the kerf for measuring the temperature.

b) 0.1 mm

a E in L_

Ú— > C O ™ "S E

WfíP QMPvi• ;

Fig. 1. SEM pictures of a cross section of a zone close to the kerf wall. a) The heat conduction from the kerf wall into the sample is symbolized by the red arrows. b) Detail of a) in enlarged scale. Within the visible MSZ nearly the total matrix material was ablated.

As mentioned above, the heat conduction losses have a large influence on the process speed and the formation of the HAZ. Therefore, in the present paper, the heat flow model and the measured temperatures were used to determine the heat conduction losses during laser cutting of CFRP. Furthermore, the energy for heating and sublimating the composite material in the kerf, the energy for heating and sublimating the matrix material in the MSZ and the energy that is not absorbed in the sample were determined using an energy balance.

2. Energy balance

The energy of the laser beam EL applied during cutting of the samples in the experiments is given by

where P is the laser power measured at the sample, v is the cutting speed and lc is the length of the cut. In laser cutting of CFRP the available laser energy

EL = Eabs + Enotabs = Es,k + Econd + Enotabs = Es,k + Es,m,MSZ + Eres + Enotabs (2)

can be divided into a fraction that is absorbed in the material, Eabs, and a fraction that is not absorbed in the material, Enot abs. Furthermore, the absorbed energy can be split into a fraction that is needed for the sublimation of the composite material in the kerf, Esk, and a fraction that is conducted into the sample, Econd. The heat that flows into the sample can be further divided into a fraction that sublimates the matrix material in the MSZ, Esm,MSZ, and the residual heat in the sample, Eres. In the following, the fractions of this energy balance will be determined.

2.1. Energy for heating and sublimating the material in the kerf and the MSZ

The energy for sublimating the composite material in the kerf, Evk, (assuming complete sublimation) is given by

• Tsubf - To)) + (1 -Vf)-Pm ■ (Ls,

E , = l • h ■ d, • (V ■ pr ■ (L , + c „

s,k c s k, mean V f rï V s, f p, f

-s,m ^Cp,m ' (^subjn T0))),

where hs is the thickness of the sample, dkmean is the mean width of the kerf measured at different z and y positions, Vf is the fiber volume fraction, pf is the density of the fibers, pm is the density of the matrix material, Ls f is the latent heat of the fibers, Ls m is the latent heat of the matrix material, cp f is the heat capacity of the fibers, cpmm is the heat capacity of the matrix material, Tsub,m is the sublimation temperature of the matrix material, and Tsub,f is the sublimation temperature of the fibers.

The energy for sublimating the matrix material in the MSZ EsmMSZ

E = 2 • l

s, m, MSZ ^ 1■

■ h ■ d

c s MSZ,mean

■Pm ■ (1 - Vf) • (Ls,m + cp,m

(Tsub, m T0 )) ,

can be derived from the measured mean width of the MSZ dMSZmean (see Fig. 1a). The existence of a MSZ on both sides of the kerf is considered by the factor 2.

2.2. Residual heat in the sample

It was shown by Mucha et al (2014) that the temperatures in the different fiber layers become identical after a certain time of homogenization thom = 3 s (using the same setup). From this time of homogenization thom onwards, the temperature gradient in z direction was found to be approximately zero (dT/dz ~ 0 at t > thom). The temperature gradient in y direction can be taken as dT/dy ~ 0 for t > thom. Thus, a one-dimensional heat flow model (Carslaw and Jaeger (1959)) is used for determining the residual heat in the sample. At t < thom the heat conduction is not one-dimensional. The temperatures in the different fiber layers are not identical, yet. However, as the extent of the heat wave at the end of the total effective heat load time is much shorter than the extent of the heat wave of interest, i.e. after thom, one-dimensional heat flow was assumed during heating for the sake of simplicity. The process was split in two distinct phases: During the first phase, the total effective heat load time, tHeatLoad, the material in the kerf is heated and sublimated. In the second phase (t > tHeatLoad), the material on both lateral surfaces inside the kerf cools down and the heat decays in the sample.

As seen from the material parameters in Table 1, about sixteen times more energy is needed for the sublimation of the fibers than for heating them to sublimation temperature. Therefore, the time for heating the material is much shorter than the time for sublimating the material and is neglected. In the first phase, the surface of the kerf is supposed to be at the sublimation temperature of the fibers. The one-dimensional evolution of the temperature in the sample for a constant kerf surface temperature during the effective heat load time tHeatLoad is given by

THeat,1(x t) = (Tsub,f " T0) " efc

1 * k t

Pmean c

mean p,mean

where rsub,f is the sublimation temperature of the fibers, T0 is the room temperature. The mean heat conductivity k of the composite was assumed to describe the global heat transport into the composite material. The complementary error function erfc(^) is given by

erfc(£) -1 - erf(^) -1 - -= i e"

The mean density pmean

Anean =Pf Vf +Pm ' (1 " Vf )

of the composite material is approximated with the fiber volume fraction Vf, the density of the matrix pm and the fibers pf. According to this, the mean heat capacity of the composite material cp, mean is approximated with

= CPf 'Pi 'Vf + CPm 'Pm ' (1 - f

Cp,mean Tr Tr \ , (8)

Pi • V +Pm ■ 0 - Vf)

where cp f and cpm are the mass specific heat capacities of the fibers and the matrix material. After the effective heat load time, the temperature has the distribution THeat1(x,tHeatLoad). This is the initial temperature distribution for the decay of the heat wave, when heating has stopped. The undisturbed decay of the heat wave that starts at the instant of time t = tHeatLoad is described by Carslaw and Jaeger (1959)

(x'-x )2

~^HeatLoad )

1 * v "HeatLoad /

Tfcatf (X, t) = , * J ?Heat1 (X', ^tLoad) ' « ^dX (9)

2 n k ( _ )

2 J (t tHeatLoad)

V Pmean Cp,mean

for t > tHeatLoad. The coordinate in the initial temperature distribution THeat1(x',tHeatLoad) was changed to x' to distinguish it from the coordinate x in the temperature distribution THeat,2(x,t).

The residual energy in the sample Eres is given by the integral of the increase of the temperature T(x)-T0 according

E = 2-p ■ c ■ l ■ h •f(r(x)-T0)dx, (10)

res rmean p,mean c^^^V^O/'

where lc is the length of the cut (150 mm), hs is the thickness of the sample (2 mm), T(x) is the temperature distribution in x direction and T0 is the room temperature. The factor 2 represents the assumption that the heat conduction in the material on both sides of the kerf is the same.

3. Results and discussion

Determination of the temperature distribution

The temperatures in the model were fitted to temperatures measured in a sample during and just after cutting it (in the cooling phase at t > thom ). The mean heat conductivity k of the composite, which was assumed to describe the global heat transport into the composite material, and tHeatLoad were used as fit parameters. The points in Fig. 2 indicate the measured increase of the temperatures AT in the sample at 3 s (triangles), 5 s (circles), and 10 s (crosses) after cutting a sample. The cutting speed was 7 m/min and the laser power of 2 kW. The quantities of k and tHeatLoad in equation (9) were used to fit the experimental data in the cooling phase, i.e. at t > thom. With this fit the calculations correlate very well with the measurement as seen in Fig. 2: The root mean square deviations for all curves were less than 4 K. The values of the fit parameters tHeatLoad and k were within ±5% for all three curves. This confirms the suitability of the one dimensional approximation.

100 90 80 70 60 50 -FitI = 3s

---FitI = 5 s

.......Fit!'10b

\ - N \ A * Measurement (= 3s

• Measurement l= 5s

h-< 40 30 x Measurement <= 10s

__>S, __

20 10 Vi-.,

.........

0 S 10 1S JO

Fig. 2. Increase of temperature as a function of the distance from the kerf 3 s (triangles), 5 s (circles), 10 s (crosses) alter cutting a sample. The curves represent the corresponding calculated temperature increase using the fit described in the text.

In addition, the temperature measurements and the fits were performed at laser powers of 1 kW and 5 kW and cutting speeds of 3 m/min and 20 m/min. For all these process parameters k was found to be 4 W/mK ±0.1 W/m K. This can be explained by the fact that k depends on the material which was identical for all experiments.

The value of the total heat load time /HeatLoad varied between 1.6 ms at a cutting speed of 20 m/min (P = 5 kW) and 11 ms at a cutting speed of 3 m/min (P = 1 kW). The dependence between the process parameters and /HeatLoad is discussed by Mucha et al. (2014).

At the cutting speed of 3 m/min and a laser power of 1 kW the residual energy in the sample is 670 J. The cutting speed of 20 m/min at a laser power of 5 kW leads to a residual energy in the sample of 280 J. During the much shorter heat load time of 1.7 ms at the cutting speed of 20 m/min less heat is conducted into the material than during the heat load time of 11 ms at a cutting speed of 3 m/min.

With the constant mean heat conductivity k = 4 W/mK, the temperature distribution in equation (5) is only dependent on /HeatLoad. Using the temperature distribution T(x) = THeat1(x,/HeatLoad) in equation (10) Eres can be determined as a function of /HeatLoad. The residual heat increases at increasing heat load time /HeatLoad, as shown in Fig. 4.

Fig. 4. Residual heat in the sample for the used sample geometry (length of the cut lc

of ¿HeatLoad.

150 mm; thickness of the sample hs = 2 mm) as a function

Energy balance

As shown in Fig. 2, three seconds after cutting the sample the maximum temperature in the sample is about 380 K (AT~ 85 K). This is lower than the sublimation temperature of the matrix material. Therefore, the sublimation of the matrix material within the MSZ was already completed at the moment when temperatures in the sample were measured. The energy for sublimating the matrix material in the MSZ Es,m,MSZ is resulting from equation (4). It is given in Fig. 4a) for the used process parameters. For calculating Es,m,MSZ the mean width of the MSZ was measured. The error bars show the standard deviation of the determined values of Es,m,MSZ. The variation of the values is resulting from the measurement of the mean width of the MSZ.

Ul 100

■ 1000

1 kW; 3 m/m in 2 kW; 7 m/min 5 kW: 20 m/m in a)

1 kW; 3 m/min 2 kW; 7 m/min 5 kW; 20 mfmin b)

Fig. 4. a) Energy for heating and sublimating the matrix material in the MSZ for different laser powers and cutting speeds. b) Energy for heating and sublimating the composite material in the kerf for different laser powers and cutting speeds.

The mean width of the MSZ varies from 0.22 mm at v = 20 m/min and P = 5 kW up to 0.71 mm at v = 3 m/min and P = 1 kW. Therefore, the energy for sublimating the matrix material in the MSZ varies between 105 J and 340 J.

The energy for sublimating the material in the kerf Es,k was calculated with equation (3) and is depicted in Fig. 4b) for the used process parameters. For calculating Es,k the mean width of the kerf was measured. The error bars show the standard deviation of the determined values of Es,k. The variation of the values is resulting from the measurement of the kerf width. The measured mean kerf width was found to be approximately constant for all process parameters. The volume of the sublimated material and, therefore, the energy for heating and sublimating the material in the kerf is constant at about 1700 J.

In Fig. 5 the above determined energy fractions are shown in relation to the total laser energy EL for cutting the sample. The remaining part is the energy not absorbed by the sample as resulting from equation (2). It includes excessive energy that is transmitted through the kerf, reflected energy at the cutting front, scattered and reflected

energy in the plume, and so on. About 10% of the energy was not absorbed in the sample (white parts of the bars) in any case.

Fig. 5. Energy fractions for cutting the material for three different process parameters related to the total energy of the laser beam for cutting the sample.

At a laser power of 1 kW and a cutting speed of 3 m/min about 11% of the laser energy dissipates with the sublimated matrix material in the MSZ (light grey parts of the bars) and 23% of the total laser energy remains in the sample (dark grey parts of the bars). In total, about one third of the total laser energy is lost by heat conduction into the sample (Econd = Esm,MSZ + Eres). About 55% of the total laser energy heats and sublimates the composite material in the kerf (black bars).

At increasing laser power and cutting speed the fractions of all losses decrease. The fraction for heating and sublimating the material in the kerf increases to 75% at a laser power of 5 kW. This implies that the process efficiency increases at increasing cutting speed and laser power. The reduced losses explain the disproportional increase of the maximum cutting speed at increasing laser power (v = 3 m/min at P = 1 kW compared to v = 20 m/min at P = 5 kW). At the same time the reduced fraction of the heat conduction losses at high laser powers and cutting speeds causes a smaller MSZ. However, for realizing short heat-load times in a single pass strategy, high average powers are needed.

4. Conclusion

Investigations on an energy balance in laser cutting CFRP were shown. The heat conduction losses were determined by fitting experimental data with temperatures calculated with a one-dimensional heat flow model. The heat conduction losses were found to be dominated by the effective heat-load time of the laser with a single point in the kerf. The heat conduction losses were found to decrease at increasing cutting speed and laser power. Furthermore, the energy for sublimating the matrix material in the matrix sublimation zone and the energy for sublimating the composite material in the kerf were determined. The experiments showed that about one third of the laser energy was lost by heat conduction into the material at the lowest laser power of 1 kW and a cutting speed of 3 m/min. About 11% of the laser energy dissipated with the sublimated matrix material in the MSZ and 23% of the total laser energy remained in the sample. At the highest laser power of 5 kW and a cutting speed of 20 m/min heat conduction losses of 18% were found. About 5% of the laser energy dissipated with the sublimated matrix material in the MSZ and 13% of the total laser energy remained in the sample. The reduced heat conduction losses into the sample lead to both, smaller matrix sublimation zones and a disproportional increase of the maximum possible cutting speed to separate the material entirely. Therefore, high average laser powers lead to an increase in productivity and a higher quality in terms of smaller matrix sublimation zones.

Acknowledgements

This research and development project is funded by the German Federal Ministry of Education and Research (BMBF) within the Framework Concept "Research for Tomorrow's Production" (FlexiCut, 02PJ2207) and managed by the Project Management Agency Karlsruhe (PTKA). The authors are responsible for the contents of this publication.

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