## Heat accumulation during pulsed laser materials processing |

Optics Express, Vol. 22, Issue 9, pp. 11312-11324 (2014)

http://dx.doi.org/10.1364/OE.22.011312

Acrobat PDF (1410 KB)

### Abstract

Laser materials processing with ultra-short pulses allows very precise and high quality results with a minimum extent of the thermally affected zone. However, with increasing average laser power and repetition rates the so-called heat accumulation effect becomes a considerable issue. The following discussion presents a comprehensive analytical treatment of multi-pulse processing and reveals the basic mechanisms of heat accumulation and its consequence for the resulting processing quality. The theoretical findings can explain the experimental results achieved when drilling microholes in CrNi-steel and for cutting of CFRP. As a consequence of the presented considerations, an estimate for the maximum applicable average power for ultra-shorts pulsed laser materials processing for a given pulse repetition rate is derived.

© 2014 Optical Society of America

## 1. Introduction

1. J.-P. Negel, A. Voss, M. Abdou Ahmed, D. Bauer, D. Sutter, A. Killi, and T. Graf, “1.1 kW average output power from a thin-disk multipass amplifier for ultrashort laser pulses,” Opt. Lett. **38**(24), 5442–5445 (2013). [CrossRef] [PubMed]

2. H. Hügel, H. Schittenhelm, K. Jasper, G. Callies, and P. Berger, “Structuring with excimer lasers - experimental and theoretical investigations on quality and efficiency,” J. Laser Appl. **10**(6), 255–264 (1998). [CrossRef]

8. R. Weber, M. Hafner, A. Michalowksi, and T. Graf, “Minimum damage in CFRP laser processing,” Phys. Procedia **12**(2), 302–307 (2011). [CrossRef]

*η*, where

_{Abs}·E_{Pulse}*E*is the energy of the incident laser pulse and

_{Pulse}*η*the absorptance at the interaction zone, will always exceed the energy required for the mere material ablation process. For the case of material removal by sole evaporation (i.e. with neglectable melt expulsion) the ablation energy is given by the evaporated volume

_{Abs}*V*times the total volume specific enthalpy

_{Evap}*h*which is required for evaporation. The enthalpy

_{Evap}*h*includes the heating of the material and its phase transitions. The difference

_{Evap}*η*-

_{Abs}·E_{Pulse}*V*partly overheats the expanding vapor beyond the required evaporation temperature (by an amount of energy

_{Evap}·h_{Evap}*Q*) and partly is left as thermal energy

_{Vapor}*Q*in the surrounding material that is not ablated. In the following

_{heat}*Q*is referred to as residual heat. With this the energy balance readsDefining the thermal efficiency by

_{heat}*η*,

_{Th}*η*, and hence

_{Abs}*η*are usually complicated, time-dependent functions of processing parameters such as material properties, actual geometry of the interaction zone and the workpiece and in particular also of the incident fluence and the ablation threshold [9

_{Heat}9. B. Neuenschwander, B. Jaeggi, M. Schmid, U. Hunziker, B. Luescher, and C. Nocera, “Processing of industrially relevant non-metals with laser pulses in the range between 10ps and 50ps,” in *Proceedings of the International Congress on Applications of Lasers & Electro-Optics (ICALEO)*, Paper M (**Vol. 103**) (2011).

*η*is assumed to be constant for the following. Typically the residual heat generated during the ablation processes by a single ultra-short laser pulse is comparably small and avoids detrimental effects on the workpiece. With increasing repetition rate, however, the residual heat may not be removed fast enough by heat conduction into the workpiece which leads to a significant impact on the achievable process quality. Figure 1 shows helically drilled holes in CrNi-steel giving a typical example of the thermal influence on materials processing with a repetitively pulsed laser [10]. The upper row shows the drilling inlet (i.e. the side from which the laser processing takes place), the lower row the outlet. The respective laser parameters are noted below each pair of pictures.

_{Heat}*f*, (from left to right) has a dramatic influence on the achieved processing quality although the laser fluence was about 40 times above ablation threshold. The reason for this behavior is usually referred to as “heat accumulation” which is often observed in pulsed laser processing [11

_{L}11. A. Ancona, S. Döring, C. Jauregui, F. Röser, J. Limpert, S. Nolte, and A. Tünnermann, “Femtosecond and picosecond laser drilling of metals at high repetition rates and average powers,” Opt. Lett. **34**(21), 3304–3306 (2009). [CrossRef] [PubMed]

12. S. Eaton, H. Zhang, P. Herman, F. Yoshino, L. Shah, J. Bovatsek, and A. Arai, “Heat accumulation effects in femtosecond laser-written waveguides with variable repetition rate,” Opt. Express **13**(12), 4708–4716 (2005). [CrossRef] [PubMed]

13. R. R. Gattass, L. R. Cerami, and E. Mazur, “Micromachining of bulk glass with bursts of femtosecond laser pulses at variable repetition rates,” Opt. Express **14**(12), 5279–5284 (2006). [CrossRef] [PubMed]

15. T. Tamaki, W. Watanabe, and K. Itoh, “Laser micro-welding of transparent materials by a localized heat accumulation effect using a femtosecond fiber laser at 1558 nm,” Opt. Express **14**(22), 10460–10468 (2006). [CrossRef] [PubMed]

16. A. A. Cenna and P. Mathew, “Evaluation of cut quality of fibre-reinforced plastic – a review,” Int. J. Mach. Tools Manuf. **37**(6), 723–736 (1997). [CrossRef]

21. R. Weber, C. Freitag, T. Kononenko, M. Hafner, V. Onuseit, P. Berger, and T. Graf, “Short-pulse laser processing of CFRP,” Phys. Procedia **39**, 137–146 (2012). [CrossRef]

22. H. Deutsche Edelstahlwerke Gmb, Werkstoffdatenblatt 1.4301_de.pdf, http://www.dew-stahl.com/fileadmin/files/dew-stahl.com/documents/Publikationen/Werkstoffdatenblaetter/RSH/1.4301_de.pdf.

28. R. Rolfes and U. Hammerschmidt, “Transverse thermal conductivity of CFRP laminates; a numerical and experimental validation of approximation formulae,” Compos. Sci. Technol. **54**(1), 45–54 (1995). [CrossRef]

29. F. R. Barnet and M. K. Norr, “A three-dimensional structural model for a high modulus pan-based carbon fibres,” Composites **7**(2), 93–99 (1976). [CrossRef]

## 2. Temperature fields induced by a single pulse

*T*is the temperature increase with respect to the initial temperature

_{nD}*T*,

_{0}*ρ*is the mass density of the solid or liquid material,

*c*its specific heat capacity,

_{p}*κ*=

*λ*(

_{th}/*ρ c*) the temperature conductivity,

_{p}*λ*the heat conductivity,

_{th}*t*is time, and

*x*,

*y*,

*z*are the spatial coordinates. As a simplification, the material properties

*ρ*,

*c*, and

_{p}*λ*are assumed to be constant with respect to temperature. Typically

_{th}*Q*left in the workpiece and the corresponding temperature distributions reached therein. In this context the heat inputs

_{heat}*Q*, are determined by the residual energy as defined in Eq. (2). The heat sources

_{nD}*Q*and

_{1D}[energy per unit area], Q_{2D}[energy per unit length],*Q*define the heat which is released in an infinitely short time at

_{3D}[energy]*t*= 0. Actually

*Q*is a plane source,

_{1D}*Q*a line source and

_{2D}*Q*a point source, but to ease the notation in the following, these sources are labeled with the dimensionality of the corresponding heat flow. Explicitly, the heat sources read where

_{3D}*A*and

*t*= 0), i.e. the heating phase is not considered with this formalism: At this instance of time Eqs. (3a)–(3c) always yield an unphysical infinite temperature [30].

*Q*

_{1}

*and*

_{D}*Q*

_{2}

*and to consider the analytical solutions only in the domains which are consistent with the underlying assumptions of 1D or 2D heat flow as discussed above.*

_{D}*r*, is extended by one coordinate axis. Hence Eqs. (3a)–(3c) can be written in the convenient, generalized formAs an example Fig. 3 shows the calculated temperature evolution

*Q*

_{3}

*= 0.1 µJ and*

_{D}*Q*

_{3}

*= 1 µJ of residual heat deposited on the surface at*

_{D}*x*=

*y*=

*z*= 0 (b).

## 3. Multi-pulse temperature fields

*f*, Eq. (5) can be extended in the formto denote the contribution to the temperature increase by the

_{L}*N-th*pulse which is incident at a time delay of (

*N-1)*/

*f*after the first pulse at

_{L}*t*= 0. The Heaviside function Θ is equal to zero for arguments <0 and equal to one for arguments ≥0.

*N*pulses is given by the sum over the contribution given in Eq. (6) of the individual pulseswhere

_{P}*N*=

_{P}*floor(t*+ 1 is the number of pulses which are incident at the interaction zone with the repetition rate

_{IntAct}·f_{L})*f*during the interaction time,

_{L}*t*. The function

_{IntActroc}*floor(x)*yields the largest integer which is smaller or equal to the real argument

*x*.

*N*pules, delivered at a repetition rate

_{p}*f*.

_{L}*T*

_{Sum,}_{3}

*, on the surface at the location (i.e.*

_{D}*x*=

*y*= z = 0 mm) of the released heat energy is shown for different examples in Fig. 4. To demonstrate the effect of repetitive pulses with

*Q*

_{3}

*= 5 µJ Fig. 4(a) shows the temperature evolution for the two different repetition rates*

_{D}*f*= 50 kHz and

_{L}*f*= 250 kHz, again calculated for CrNi-steel.

_{L}*f*= 50 kHz in Fig. 4(a), the surface temperature after the first pulse cools down to a residual increase of about 100 K after 20 µs before the second pulse hits the same spot (solid green arrow). With every subsequent pulse the surface is heated again in the same manner as after the first pulse but starting at a different, slightly increased offset temperature (dashed black arrows). In the following we refer to this increased offset temperature as the effect of heat accumulation.

_{L}8. R. Weber, M. Hafner, A. Michalowksi, and T. Graf, “Minimum damage in CFRP laser processing,” Phys. Procedia **12**(2), 302–307 (2011). [CrossRef]

## 4. Maximum reach of a given temperature

*T*(e.g. to the melting temperature in the case of steel or to the matrix damage temperature in the case of CFRP) this damaging extent results from Eq. (7) by solving for the respective coordinate. The maximum reach of a given critical temperature is then found by differentiating with respect to time and setting the result to zero. As the coordinate giving the extent of the critical temperature is part of the function in the exponent inside the sum this can only be solved numerically and is beyond the scope of this paper. An example for such a solution was given in [8

8. R. Weber, M. Hafner, A. Michalowksi, and T. Graf, “Minimum damage in CFRP laser processing,” Phys. Procedia **12**(2), 302–307 (2011). [CrossRef]

21. R. Weber, C. Freitag, T. Kononenko, M. Hafner, V. Onuseit, P. Berger, and T. Graf, “Short-pulse laser processing of CFRP,” Phys. Procedia **39**, 137–146 (2012). [CrossRef]

## 5. Discussion of the thermal efficiency and the portion of the residual heat

*η*defines the fraction of the incident pulse energy being converted to the thermal energy required for the process. As discussed in the introduction the remaining heat is left in the workpiece and its amount

_{Th}*η*depends on the material properties, the pulse energy, the pulse duration, the beam intensity distribution and the fluence above threshold, as partly discussed in [9

_{Heat}9. B. Neuenschwander, B. Jaeggi, M. Schmid, U. Hunziker, B. Luescher, and C. Nocera, “Processing of industrially relevant non-metals with laser pulses in the range between 10ps and 50ps,” in *Proceedings of the International Congress on Applications of Lasers & Electro-Optics (ICALEO)*, Paper M (**Vol. 103**) (2011).

*η*is usually even changing with time during processing of the material. One reason is that depth and shape of the structure which is created during the process changes with the number of pulses – and hence with time – modifying the absorbed fluence due to scattering on the structure walls, the changing angle of incidence, and the changing total area of the interacting surface. As

_{Heat}*η*is additionally affected by the material-dependent absorptivity (see Eq. (2)) this leads to temporal variations of

_{Heat}*Q*during the process in anisotropic materials.

_{Heat}*η*of the incident energy converted to the residual heat

_{Heat}*Q*is even a function of the heat accumulation itself, as material properties and surface structures also depend on the temperature. The determination of the correct amount of the residual energy

_{Heat}*Q*is therefore a complex topic and is subject of further investigations.

_{Heat}*η*. Despite this quite constricting assumption the experimental results are explained with very good agreement confirming that the basic understanding of heat accumulation is not significantly compromised by this simplification.

_{Heat}## 6. Solution for the temperature increase caused by heat accumulation

*N*pulses at the origin of the heat source at the time just before the subsequent pulse is regarded as suitable indicator to assess the processing quality.

_{P}*x*=

*y*=

*z*= 0, where the exponential function in Eq. (8) equals 1, this temperature offset immediately before each individual pulse is given by evaluating Eq. (8) at the times

*t*= (

*N*-δ)/

_{t}*f*, which yieldswhere

_{L}*N*is an integer and δ/

_{t}*f*is an infinitesimally small time. This expression (with

_{L}*N*pulses is then found at the time given by

_{p}*N*=

_{t}*N*which (for

_{p}## 7. Comparison with experimental results

### 7.1 Heat accumulation for 3D heat flow in CrNi-steel

*d*= 20 µm. With the helical drilling radius of 40 µm and the used helical revolution speed of 2000 rpm this yields a feed rate of

_{Beam}*v*= 8.4 mm/s. The local interaction time

### 7.2 Heat accumulation for 1D heat flow in CFRP

*d*= 15 µm onto the CFRP surface containing fibers with a (typical) diameters of

_{Beam}*d*= 5 µm with 50% of fill factor.

_{Fiber}33. C. Freitag, R. Weber, and T. Graf, “Polarization dependence of laser interaction with carbon fibers and CFRP,” Opt. Express **22**(2), 1474–1479 (2014). [CrossRef] [PubMed]

*A*=

_{Fiber}*π·*(

*d*/ 2)

_{Fiber}^{2}. The 1D heat source as defined in Eq. (4a) is therefore given by

*Q*≅ 3·10

_{1D}^{4}J/m

^{2}. The feed rate of

*v*= 6 m/min together with the laser spot diameter of

*d*= 15 µm resulted in a local interaction time of

_{Beam}*t*=

_{IntAct}(6 m/min)*d*/

_{Beam}*v*= 0.15 ms. For the lower feed rate of 0.12 m/min the interaction time was

*t*= 7.5 ms. The resulting heat accumulation temperature increase Δ

_{IntAct}(0.12 m/min)*T*

_{HA,}_{1}

*of the calculation with the above numbers is shown in Fig. 7(a).*

_{D}## 8. Maximum tolerable average power

*T*, caused by heat accumulation should be limited to below a defined critical maximum temperature increase ∆

_{HA,nD}*T*to ensure given quality criteria. For metals this is usually the melting temperature. In view of the productivity of laser processing it is therefore of great interest to determine at what average power this critical temperature increase is reached. The sum in the heat accumulation Eq. (10) is of the form

_{Max}*f*is the average laser power. Combining all material and geometrical constants into a figure of merithaving the units

_{L}·E_{Pulse}= P_{L}*P*one findsThis simple equation defines the maximum average power which is tolerable for a given repetition rate

_{L}*f*at one single position to avoid that the heat accumulation increases the temperature by more than the critical temperature increase Δ

_{L}*T*. It is noted that in the 3D case discussed here the maximum tolerable average power is proportional to

_{Max}_{}and therefore decreases with increasing pulse repetition rate!

## 9. Implication on laser processing system design

*T*= 1500°C to be the melting temperature and using

_{Max}*η*= 12.5%, from the above drilling example the power limit for steel is given by

_{Heat}*η*strongly depends on the experimental conditions and might vary from close to 0% up to 100% if the intensity is below ablation threshold. In addition, the material parameters are usually not exactly known. Therefore

_{Heat}*η*can be used as only free parameter in order to correctly describe the experimental results. For explaining the above CrNi-steel and CFRP experiments

_{Heat}*η*had to be set to 12.5% ± 1%.

_{Heat}## 10. Conclusion

## Acknowledgments

## References and links

1. | J.-P. Negel, A. Voss, M. Abdou Ahmed, D. Bauer, D. Sutter, A. Killi, and T. Graf, “1.1 kW average output power from a thin-disk multipass amplifier for ultrashort laser pulses,” Opt. Lett. |

2. | H. Hügel, H. Schittenhelm, K. Jasper, G. Callies, and P. Berger, “Structuring with excimer lasers - experimental and theoretical investigations on quality and efficiency,” J. Laser Appl. |

3. | W. Schulz, U. Eppelt, and R. Poprawe, “Review on laser drilling I. Fundamentals, modeling, and simulation,” J. Laser Appl. |

4. | S. Nolte, C. Momma, H. Jacobs, A. Tünnermann, B. N. Chichkov, B. Wellegehausen, and H. Welling, “Ablation of metals by ultrashort laser pulses,” J. Opt. Soc. Am. B |

5. | D. Hellrung, A. Gillner, and R. Poprawe, “Laser beam removal of micro-structures with Nd: YAG lasers,” Proc. Lasers Mater. Processing Laser |

6. | T. V. Kononenko, V. I. Konov, S. V. Garnov, R. Danielius, A. Piskarskas, G. Tamosauskas, and F. Dausinger, “Comparative study of the ablation of materials by femtosecond and pico- or nanosecond laser pulses,” Quantum Electron. |

7. | R. Weber, A. Michalowski, M. Abdou-Ahmed, V. Onuseit, V. Rominger, M. Kraus, and T. Graf, “Effects of radial and tangential polarization in laser material processing,” Phys. Procedia |

8. | R. Weber, M. Hafner, A. Michalowksi, and T. Graf, “Minimum damage in CFRP laser processing,” Phys. Procedia |

9. | B. Neuenschwander, B. Jaeggi, M. Schmid, U. Hunziker, B. Luescher, and C. Nocera, “Processing of industrially relevant non-metals with laser pulses in the range between 10ps and 50ps,” in |

10. | M. Kraus, C. Markmann, A. Michalowski, R. Weber, and T. Graf, “Gas-assisted microdrilling in steel with ultrashort pulsed laser radiation,” in |

11. | A. Ancona, S. Döring, C. Jauregui, F. Röser, J. Limpert, S. Nolte, and A. Tünnermann, “Femtosecond and picosecond laser drilling of metals at high repetition rates and average powers,” Opt. Lett. |

12. | S. Eaton, H. Zhang, P. Herman, F. Yoshino, L. Shah, J. Bovatsek, and A. Arai, “Heat accumulation effects in femtosecond laser-written waveguides with variable repetition rate,” Opt. Express |

13. | R. R. Gattass, L. R. Cerami, and E. Mazur, “Micromachining of bulk glass with bursts of femtosecond laser pulses at variable repetition rates,” Opt. Express |

14. | R. Weber, V. Onuseit, S. Tscheulin, and T. Graf, “High-efficiency laser processing of CFRP,” in |

15. | T. Tamaki, W. Watanabe, and K. Itoh, “Laser micro-welding of transparent materials by a localized heat accumulation effect using a femtosecond fiber laser at 1558 nm,” Opt. Express |

16. | A. A. Cenna and P. Mathew, “Evaluation of cut quality of fibre-reinforced plastic – a review,” Int. J. Mach. Tools Manuf. |

17. | D. Herzog, P. Jaeschke, O. Meier, and H. Haferkamp, “Investigations on the thermal effect caused by laser cutting with respect to static strength of CFRP,” Int. J. Mach. Tools Manuf. |

18. | A. Goeke and C. Emmelmann, “Influence of laser cutting parameters on CFRP part quality,” Phys. Procedia |

19. | A. Klotzbach, M. Hauser, and E. Beyer, “Laser cutting of carbon fibre reinforced polymers using highly brilliant laser beam sources,” Phys. Procedia. |

20. | R. Weber, M. Hafner, A. Michalowski, P. Mucha, and T. Graf, “Analysis of thermal damage in laser processing of CFRP,” in Proc. ICALEO 2011 (2011). |

21. | R. Weber, C. Freitag, T. Kononenko, M. Hafner, V. Onuseit, P. Berger, and T. Graf, “Short-pulse laser processing of CFRP,” Phys. Procedia |

22. | H. Deutsche Edelstahlwerke Gmb, Werkstoffdatenblatt 1.4301_de.pdf, http://www.dew-stahl.com/fileadmin/files/dew-stahl.com/documents/Publikationen/Werkstoffdatenblaetter/RSH/1.4301_de.pdf. |

23. | D. E. Kline, “Thermal Conductivity Studies of Polymers,” J. Polym. Sci., Polym. Phys. Ed. |

24. | S. D. McIvor, M. I. Darby, G. H. Wostenholm, B. Yates, L. Banfield, R. King, and A. Webb, “Thermal conductivity measurements of some glass fibre- and carbon fibre-reinforced plastics,” J. Mater. Sci. |

25. | P. Morgan, |

26. | M. W. Pilling, B. Yates, M. A. Black, and P. Tattersall, “The thermal conductivity of carbon fibre-reinforced composites,” J. Mater. Sci. |

27. | C. Pradere, J. C. Batsale, J. M. Goyhénèche, R. Pailler, and S. Dilhaire, “Thermal properties of carbon fibers at very high temperature,” Carbon |

28. | R. Rolfes and U. Hammerschmidt, “Transverse thermal conductivity of CFRP laminates; a numerical and experimental validation of approximation formulae,” Compos. Sci. Technol. |

29. | F. R. Barnet and M. K. Norr, “A three-dimensional structural model for a high modulus pan-based carbon fibres,” Composites |

30. | N. N. Rykalin, |

31. | D. Radaj, |

32. | M. Hafner, R. Weber, and T. Graf, “Modeling of laser ablation of CFRP - influence of beam profile,” Stuttgarter Lasertage SLT 12, Neue Messe Stuttgart (2012). |

33. | C. Freitag, R. Weber, and T. Graf, “Polarization dependence of laser interaction with carbon fibers and CFRP,” Opt. Express |

34. | T. Graf, R. Weber, V. Onuseit, M. Hafner, C. Freitag, and A. Feuer, “Laser applications from production to machining of composite materials,” in |

**OCIS Codes**

(140.3390) Lasers and laser optics : Laser materials processing

(140.6810) Lasers and laser optics : Thermal effects

**ToC Category:**

Laser Microfabrication

**History**

Original Manuscript: February 24, 2014

Revised Manuscript: March 29, 2014

Manuscript Accepted: March 31, 2014

Published: May 2, 2014

**Citation**

Rudolf Weber, Thomas Graf, Peter Berger, Volkher Onuseit, Margit Wiedenmann, Christian Freitag, and Anne Feuer, "Heat accumulation during pulsed laser materials processing," Opt. Express **22**, 11312-11324 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-9-11312

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### References

- J.-P. Negel, A. Voss, M. Abdou Ahmed, D. Bauer, D. Sutter, A. Killi, T. Graf, “1.1 kW average output power from a thin-disk multipass amplifier for ultrashort laser pulses,” Opt. Lett. 38(24), 5442–5445 (2013). [CrossRef] [PubMed]
- H. Hügel, H. Schittenhelm, K. Jasper, G. Callies, P. Berger, “Structuring with excimer lasers - experimental and theoretical investigations on quality and efficiency,” J. Laser Appl. 10(6), 255–264 (1998). [CrossRef]
- W. Schulz, U. Eppelt, R. Poprawe, “Review on laser drilling I. Fundamentals, modeling, and simulation,” J. Laser Appl. 25(1), 012006 (2013). [CrossRef]
- S. Nolte, C. Momma, H. Jacobs, A. Tünnermann, B. N. Chichkov, B. Wellegehausen, H. Welling, “Ablation of metals by ultrashort laser pulses,” J. Opt. Soc. Am. B 14(10), 2716–2722 (1997). [CrossRef]
- D. Hellrung, A. Gillner, R. Poprawe, “Laser beam removal of micro-structures with Nd: YAG lasers,” Proc. Lasers Mater. Processing Laser 97, 267–273 (1997).
- T. V. Kononenko, V. I. Konov, S. V. Garnov, R. Danielius, A. Piskarskas, G. Tamosauskas, F. Dausinger, “Comparative study of the ablation of materials by femtosecond and pico- or nanosecond laser pulses,” Quantum Electron. 29(8), 724–728 (1999). [CrossRef]
- R. Weber, A. Michalowski, M. Abdou-Ahmed, V. Onuseit, V. Rominger, M. Kraus, T. Graf, “Effects of radial and tangential polarization in laser material processing,” Phys. Procedia 12, 21–30 (2011). [CrossRef]
- R. Weber, M. Hafner, A. Michalowksi, T. Graf, “Minimum damage in CFRP laser processing,” Phys. Procedia 12(2), 302–307 (2011). [CrossRef]
- B. Neuenschwander, B. Jaeggi, M. Schmid, U. Hunziker, B. Luescher, and C. Nocera, “Processing of industrially relevant non-metals with laser pulses in the range between 10ps and 50ps,” in Proceedings of the International Congress on Applications of Lasers & Electro-Optics (ICALEO), Paper M (Vol. 103) (2011).
- M. Kraus, C. Markmann, A. Michalowski, R. Weber, and T. Graf, “Gas-assisted microdrilling in steel with ultrashort pulsed laser radiation,” in LPM2010, Stuttgart, June 7- June 10 (2010).
- A. Ancona, S. Döring, C. Jauregui, F. Röser, J. Limpert, S. Nolte, A. Tünnermann, “Femtosecond and picosecond laser drilling of metals at high repetition rates and average powers,” Opt. Lett. 34(21), 3304–3306 (2009). [CrossRef] [PubMed]
- S. Eaton, H. Zhang, P. Herman, F. Yoshino, L. Shah, J. Bovatsek, A. Arai, “Heat accumulation effects in femtosecond laser-written waveguides with variable repetition rate,” Opt. Express 13(12), 4708–4716 (2005). [CrossRef] [PubMed]
- R. R. Gattass, L. R. Cerami, E. Mazur, “Micromachining of bulk glass with bursts of femtosecond laser pulses at variable repetition rates,” Opt. Express 14(12), 5279–5284 (2006). [CrossRef] [PubMed]
- R. Weber, V. Onuseit, S. Tscheulin, and T. Graf, “High-efficiency laser processing of CFRP,” in Proc. ICALEO 2013 (2013), Paper LMP 1901.
- T. Tamaki, W. Watanabe, K. Itoh, “Laser micro-welding of transparent materials by a localized heat accumulation effect using a femtosecond fiber laser at 1558 nm,” Opt. Express 14(22), 10460–10468 (2006). [CrossRef] [PubMed]
- A. A. Cenna, P. Mathew, “Evaluation of cut quality of fibre-reinforced plastic – a review,” Int. J. Mach. Tools Manuf. 37(6), 723–736 (1997). [CrossRef]
- D. Herzog, P. Jaeschke, O. Meier, H. Haferkamp, “Investigations on the thermal effect caused by laser cutting with respect to static strength of CFRP,” Int. J. Mach. Tools Manuf. 48(12-13), 1464–1473 (2008). [CrossRef]
- A. Goeke, C. Emmelmann, “Influence of laser cutting parameters on CFRP part quality,” Phys. Procedia 5, 253–258 (2010). [CrossRef]
- A. Klotzbach, M. Hauser, E. Beyer, “Laser cutting of carbon fibre reinforced polymers using highly brilliant laser beam sources,” Phys. Procedia. 12, 572–577 (2011). [CrossRef]
- R. Weber, M. Hafner, A. Michalowski, P. Mucha, T. Graf, “Analysis of thermal damage in laser processing of CFRP,” in Proc. ICALEO 2011 (2011).
- R. Weber, C. Freitag, T. Kononenko, M. Hafner, V. Onuseit, P. Berger, T. Graf, “Short-pulse laser processing of CFRP,” Phys. Procedia 39, 137–146 (2012). [CrossRef]
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