Abstract

In any pulsed and repetitive laser process a part of the absorbed laser energy is thermalized and stays in the material as residual heat. This residual heat is accumulating from pulse to pulse, continuously increasing the temperature, if the time between two pulses does not allow the material to sufficiently cool down. Controlling this so-called heat accumulation is one of the major challenges for materials processing with high average power pulsed lasers and repetitive processing. Heat accumulation caused by subsequent pulses (HAP) on the same spot and heat accumulation caused by subsequent scans (HAS) over the same spot can significantly reduce process quality, e.g., when the temperature increase caused by heat accumulation exceeds the melting temperature. In both cases, HAS and HAP, it is of particular interest to know the limiting number of pulses or scans after which the heat accumulation temperature exceeds a critical temperature and a pause has to be introduced. Approximation formulas for the case, where the duration of the heat input is short compared to the time between two subsequent heat inputs are derived in this paper, providing analytical scaling laws for the heat accumulation as a function of the processing parameters. The validity of these approximations is confirmed for HAP with an example of surface ablation of CrNi-steel and for HAS with multi-scan cutting of carbon fiber reinforced plastics (CFRP), both with a picosecond laser at an average power of up to 1.1 kW. It is shown that for the important case of 1-dimensional heat flow the limiting number of heat inputs decreases with the inverse of the square of the average laser power.

© 2017 Optical Society of America

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References

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  1. D. Hellrung, A. Gillner, and R. Poprawe, “Laser beam removal of micro-structures with Nd: YAG lasers,” Proc. SPIE 3097, 267–273 (1997).
    [Crossref]
  2. 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 14(10), 2716–2722 (1997).
    [Crossref]
  3. T. Kononenko, V. Konov, S. Garnov, R. Danielius, A. Piskarskas, G. Tamoshauskas, and 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]
  4. L. Romoli, F. Fischer, and R. Kling, “A study on UV laser drilling of PEEK reinforced with carbon fibers,” Opt. Lasers Eng. 50(3), 449–457 (2012).
    [Crossref]
  5. R. Weber, M. Hafner, A. Michalowksi, and T. Graf, “Minimum damage in CFRP laser processing,” Phys. Procedia 12(2), 307–310 (2011).
    [Crossref]
  6. E. G. Gamaly and A. V. Rode, “Physics of ultra-short laser interaction with matter: From phonon excitation to ultimate transformations,” Prog. Quantum Electron. 37(5), 215–323 (2013).
    [Crossref]
  7. R. Weber, T. Graf, P. Berger, V. Onuseit, M. Wiedenmann, C. Freitag, and A. Feuer, “Heat accumulation during pulsed laser materials processing,” Opt. Express 22(9), 11312 (2014).
    [Crossref]
  8. F. Bauer, A. Michalowski, T. Kiedrowski, and S. Nolte, “Heat accumulation in ultra-short pulsed scanning laser ablation of metals,” Opt. Express 23(2), 1035–1043 (2015).
    [Crossref] [PubMed]
  9. T. V. Kononenko, C. Freitag, M. S. Komlenok, V. Onuseit, R. Weber, T. Graf, and V. I. Konov, “Heat accumulation effects in short-pulse multi-pass cutting of carbon fiber reinforced plastics,” J. Appl. Phys. 118(10), 103105 (2015).
    [Crossref]
  10. C. Freitag, M. Wiedenmann, J.-P. Negel, A. Loescher, V. Onuseit, R. Weber, M. Abdou Ahmed, and T. Graf, “High-quality processing of CFRP with a 1.1-kW picosecond laser,” Appl. Phys., A Mater. Sci. Process. 119(4), 1237–1243 (2015).
    [Crossref]
  11. P. Mucha, P. Berger, R. Weber, N. Speker, B. Sommer, and T. Graf, “Calibrated heat flow model for the determination of different heat-affected zones in single-pass laser-cut CFRP using a cw CO2-Laser,” Appl. Phys., A Mater. Sci. Process. 118(4), 1509–1516 (2015).
    [Crossref]
  12. N. N. Rykalin, Die Wärmegrundlagen des Schweißvorgangs (VEB Verlag Technik Berlin, 1957).
  13. D. Radaj, Heat Effects of Welding, Temperature Field, Residual Stress, Distortion (Springer Verlag, 1992).
  14. H. Hügel and T. Graf, Laser in der Fertigung 3rd Ed., (Vieweg + Teubner, 2014).
  15. T. Graf, P. Berger, R. Weber, H. Hügel, A. Heider, and P. Stritt, “Analytical expressions for the threshold of deep-penetration laser welding,” Laser Phys. Lett. 12(5), 056002 (2015).
    [Crossref]
  16. 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]

2015 (5)

F. Bauer, A. Michalowski, T. Kiedrowski, and S. Nolte, “Heat accumulation in ultra-short pulsed scanning laser ablation of metals,” Opt. Express 23(2), 1035–1043 (2015).
[Crossref] [PubMed]

T. V. Kononenko, C. Freitag, M. S. Komlenok, V. Onuseit, R. Weber, T. Graf, and V. I. Konov, “Heat accumulation effects in short-pulse multi-pass cutting of carbon fiber reinforced plastics,” J. Appl. Phys. 118(10), 103105 (2015).
[Crossref]

C. Freitag, M. Wiedenmann, J.-P. Negel, A. Loescher, V. Onuseit, R. Weber, M. Abdou Ahmed, and T. Graf, “High-quality processing of CFRP with a 1.1-kW picosecond laser,” Appl. Phys., A Mater. Sci. Process. 119(4), 1237–1243 (2015).
[Crossref]

P. Mucha, P. Berger, R. Weber, N. Speker, B. Sommer, and T. Graf, “Calibrated heat flow model for the determination of different heat-affected zones in single-pass laser-cut CFRP using a cw CO2-Laser,” Appl. Phys., A Mater. Sci. Process. 118(4), 1509–1516 (2015).
[Crossref]

T. Graf, P. Berger, R. Weber, H. Hügel, A. Heider, and P. Stritt, “Analytical expressions for the threshold of deep-penetration laser welding,” Laser Phys. Lett. 12(5), 056002 (2015).
[Crossref]

2013 (2)

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]

E. G. Gamaly and A. V. Rode, “Physics of ultra-short laser interaction with matter: From phonon excitation to ultimate transformations,” Prog. Quantum Electron. 37(5), 215–323 (2013).
[Crossref]

2012 (1)

L. Romoli, F. Fischer, and R. Kling, “A study on UV laser drilling of PEEK reinforced with carbon fibers,” Opt. Lasers Eng. 50(3), 449–457 (2012).
[Crossref]

2011 (1)

R. Weber, M. Hafner, A. Michalowksi, and T. Graf, “Minimum damage in CFRP laser processing,” Phys. Procedia 12(2), 307–310 (2011).
[Crossref]

1999 (1)

T. Kononenko, V. Konov, S. Garnov, R. Danielius, A. Piskarskas, G. Tamoshauskas, and 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]

1997 (2)

Abdou Ahmed, M.

C. Freitag, M. Wiedenmann, J.-P. Negel, A. Loescher, V. Onuseit, R. Weber, M. Abdou Ahmed, and T. Graf, “High-quality processing of CFRP with a 1.1-kW picosecond laser,” Appl. Phys., A Mater. Sci. Process. 119(4), 1237–1243 (2015).
[Crossref]

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]

Bauer, D.

Bauer, F.

Berger, P.

P. Mucha, P. Berger, R. Weber, N. Speker, B. Sommer, and T. Graf, “Calibrated heat flow model for the determination of different heat-affected zones in single-pass laser-cut CFRP using a cw CO2-Laser,” Appl. Phys., A Mater. Sci. Process. 118(4), 1509–1516 (2015).
[Crossref]

T. Graf, P. Berger, R. Weber, H. Hügel, A. Heider, and P. Stritt, “Analytical expressions for the threshold of deep-penetration laser welding,” Laser Phys. Lett. 12(5), 056002 (2015).
[Crossref]

Chichkov, B. N.

Danielius, R.

T. Kononenko, V. Konov, S. Garnov, R. Danielius, A. Piskarskas, G. Tamoshauskas, and 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]

Dausinger, F.

T. Kononenko, V. Konov, S. Garnov, R. Danielius, A. Piskarskas, G. Tamoshauskas, and 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]

Fischer, F.

L. Romoli, F. Fischer, and R. Kling, “A study on UV laser drilling of PEEK reinforced with carbon fibers,” Opt. Lasers Eng. 50(3), 449–457 (2012).
[Crossref]

Freitag, C.

T. V. Kononenko, C. Freitag, M. S. Komlenok, V. Onuseit, R. Weber, T. Graf, and V. I. Konov, “Heat accumulation effects in short-pulse multi-pass cutting of carbon fiber reinforced plastics,” J. Appl. Phys. 118(10), 103105 (2015).
[Crossref]

C. Freitag, M. Wiedenmann, J.-P. Negel, A. Loescher, V. Onuseit, R. Weber, M. Abdou Ahmed, and T. Graf, “High-quality processing of CFRP with a 1.1-kW picosecond laser,” Appl. Phys., A Mater. Sci. Process. 119(4), 1237–1243 (2015).
[Crossref]

Gamaly, E. G.

E. G. Gamaly and A. V. Rode, “Physics of ultra-short laser interaction with matter: From phonon excitation to ultimate transformations,” Prog. Quantum Electron. 37(5), 215–323 (2013).
[Crossref]

Garnov, S.

T. Kononenko, V. Konov, S. Garnov, R. Danielius, A. Piskarskas, G. Tamoshauskas, and 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]

Gillner, A.

D. Hellrung, A. Gillner, and R. Poprawe, “Laser beam removal of micro-structures with Nd: YAG lasers,” Proc. SPIE 3097, 267–273 (1997).
[Crossref]

Graf, T.

P. Mucha, P. Berger, R. Weber, N. Speker, B. Sommer, and T. Graf, “Calibrated heat flow model for the determination of different heat-affected zones in single-pass laser-cut CFRP using a cw CO2-Laser,” Appl. Phys., A Mater. Sci. Process. 118(4), 1509–1516 (2015).
[Crossref]

T. Graf, P. Berger, R. Weber, H. Hügel, A. Heider, and P. Stritt, “Analytical expressions for the threshold of deep-penetration laser welding,” Laser Phys. Lett. 12(5), 056002 (2015).
[Crossref]

T. V. Kononenko, C. Freitag, M. S. Komlenok, V. Onuseit, R. Weber, T. Graf, and V. I. Konov, “Heat accumulation effects in short-pulse multi-pass cutting of carbon fiber reinforced plastics,” J. Appl. Phys. 118(10), 103105 (2015).
[Crossref]

C. Freitag, M. Wiedenmann, J.-P. Negel, A. Loescher, V. Onuseit, R. Weber, M. Abdou Ahmed, and T. Graf, “High-quality processing of CFRP with a 1.1-kW picosecond laser,” Appl. Phys., A Mater. Sci. Process. 119(4), 1237–1243 (2015).
[Crossref]

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]

R. Weber, M. Hafner, A. Michalowksi, and T. Graf, “Minimum damage in CFRP laser processing,” Phys. Procedia 12(2), 307–310 (2011).
[Crossref]

Hafner, M.

R. Weber, M. Hafner, A. Michalowksi, and T. Graf, “Minimum damage in CFRP laser processing,” Phys. Procedia 12(2), 307–310 (2011).
[Crossref]

Heider, A.

T. Graf, P. Berger, R. Weber, H. Hügel, A. Heider, and P. Stritt, “Analytical expressions for the threshold of deep-penetration laser welding,” Laser Phys. Lett. 12(5), 056002 (2015).
[Crossref]

Hellrung, D.

D. Hellrung, A. Gillner, and R. Poprawe, “Laser beam removal of micro-structures with Nd: YAG lasers,” Proc. SPIE 3097, 267–273 (1997).
[Crossref]

Hügel, H.

T. Graf, P. Berger, R. Weber, H. Hügel, A. Heider, and P. Stritt, “Analytical expressions for the threshold of deep-penetration laser welding,” Laser Phys. Lett. 12(5), 056002 (2015).
[Crossref]

Jacobs, H.

Kiedrowski, T.

Killi, A.

Kling, R.

L. Romoli, F. Fischer, and R. Kling, “A study on UV laser drilling of PEEK reinforced with carbon fibers,” Opt. Lasers Eng. 50(3), 449–457 (2012).
[Crossref]

Komlenok, M. S.

T. V. Kononenko, C. Freitag, M. S. Komlenok, V. Onuseit, R. Weber, T. Graf, and V. I. Konov, “Heat accumulation effects in short-pulse multi-pass cutting of carbon fiber reinforced plastics,” J. Appl. Phys. 118(10), 103105 (2015).
[Crossref]

Kononenko, T.

T. Kononenko, V. Konov, S. Garnov, R. Danielius, A. Piskarskas, G. Tamoshauskas, and 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]

Kononenko, T. V.

T. V. Kononenko, C. Freitag, M. S. Komlenok, V. Onuseit, R. Weber, T. Graf, and V. I. Konov, “Heat accumulation effects in short-pulse multi-pass cutting of carbon fiber reinforced plastics,” J. Appl. Phys. 118(10), 103105 (2015).
[Crossref]

Konov, V.

T. Kononenko, V. Konov, S. Garnov, R. Danielius, A. Piskarskas, G. Tamoshauskas, and 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]

Konov, V. I.

T. V. Kononenko, C. Freitag, M. S. Komlenok, V. Onuseit, R. Weber, T. Graf, and V. I. Konov, “Heat accumulation effects in short-pulse multi-pass cutting of carbon fiber reinforced plastics,” J. Appl. Phys. 118(10), 103105 (2015).
[Crossref]

Loescher, A.

C. Freitag, M. Wiedenmann, J.-P. Negel, A. Loescher, V. Onuseit, R. Weber, M. Abdou Ahmed, and T. Graf, “High-quality processing of CFRP with a 1.1-kW picosecond laser,” Appl. Phys., A Mater. Sci. Process. 119(4), 1237–1243 (2015).
[Crossref]

Michalowksi, A.

R. Weber, M. Hafner, A. Michalowksi, and T. Graf, “Minimum damage in CFRP laser processing,” Phys. Procedia 12(2), 307–310 (2011).
[Crossref]

Michalowski, A.

Momma, C.

Mucha, P.

P. Mucha, P. Berger, R. Weber, N. Speker, B. Sommer, and T. Graf, “Calibrated heat flow model for the determination of different heat-affected zones in single-pass laser-cut CFRP using a cw CO2-Laser,” Appl. Phys., A Mater. Sci. Process. 118(4), 1509–1516 (2015).
[Crossref]

Negel, J.-P.

C. Freitag, M. Wiedenmann, J.-P. Negel, A. Loescher, V. Onuseit, R. Weber, M. Abdou Ahmed, and T. Graf, “High-quality processing of CFRP with a 1.1-kW picosecond laser,” Appl. Phys., A Mater. Sci. Process. 119(4), 1237–1243 (2015).
[Crossref]

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]

Nolte, S.

Onuseit, V.

C. Freitag, M. Wiedenmann, J.-P. Negel, A. Loescher, V. Onuseit, R. Weber, M. Abdou Ahmed, and T. Graf, “High-quality processing of CFRP with a 1.1-kW picosecond laser,” Appl. Phys., A Mater. Sci. Process. 119(4), 1237–1243 (2015).
[Crossref]

T. V. Kononenko, C. Freitag, M. S. Komlenok, V. Onuseit, R. Weber, T. Graf, and V. I. Konov, “Heat accumulation effects in short-pulse multi-pass cutting of carbon fiber reinforced plastics,” J. Appl. Phys. 118(10), 103105 (2015).
[Crossref]

Piskarskas, A.

T. Kononenko, V. Konov, S. Garnov, R. Danielius, A. Piskarskas, G. Tamoshauskas, and 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]

Poprawe, R.

D. Hellrung, A. Gillner, and R. Poprawe, “Laser beam removal of micro-structures with Nd: YAG lasers,” Proc. SPIE 3097, 267–273 (1997).
[Crossref]

Rode, A. V.

E. G. Gamaly and A. V. Rode, “Physics of ultra-short laser interaction with matter: From phonon excitation to ultimate transformations,” Prog. Quantum Electron. 37(5), 215–323 (2013).
[Crossref]

Romoli, L.

L. Romoli, F. Fischer, and R. Kling, “A study on UV laser drilling of PEEK reinforced with carbon fibers,” Opt. Lasers Eng. 50(3), 449–457 (2012).
[Crossref]

Sommer, B.

P. Mucha, P. Berger, R. Weber, N. Speker, B. Sommer, and T. Graf, “Calibrated heat flow model for the determination of different heat-affected zones in single-pass laser-cut CFRP using a cw CO2-Laser,” Appl. Phys., A Mater. Sci. Process. 118(4), 1509–1516 (2015).
[Crossref]

Speker, N.

P. Mucha, P. Berger, R. Weber, N. Speker, B. Sommer, and T. Graf, “Calibrated heat flow model for the determination of different heat-affected zones in single-pass laser-cut CFRP using a cw CO2-Laser,” Appl. Phys., A Mater. Sci. Process. 118(4), 1509–1516 (2015).
[Crossref]

Stritt, P.

T. Graf, P. Berger, R. Weber, H. Hügel, A. Heider, and P. Stritt, “Analytical expressions for the threshold of deep-penetration laser welding,” Laser Phys. Lett. 12(5), 056002 (2015).
[Crossref]

Sutter, D.

Tamoshauskas, G.

T. Kononenko, V. Konov, S. Garnov, R. Danielius, A. Piskarskas, G. Tamoshauskas, and 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]

Tünnermann, A.

Voss, A.

Weber, R.

T. Graf, P. Berger, R. Weber, H. Hügel, A. Heider, and P. Stritt, “Analytical expressions for the threshold of deep-penetration laser welding,” Laser Phys. Lett. 12(5), 056002 (2015).
[Crossref]

T. V. Kononenko, C. Freitag, M. S. Komlenok, V. Onuseit, R. Weber, T. Graf, and V. I. Konov, “Heat accumulation effects in short-pulse multi-pass cutting of carbon fiber reinforced plastics,” J. Appl. Phys. 118(10), 103105 (2015).
[Crossref]

C. Freitag, M. Wiedenmann, J.-P. Negel, A. Loescher, V. Onuseit, R. Weber, M. Abdou Ahmed, and T. Graf, “High-quality processing of CFRP with a 1.1-kW picosecond laser,” Appl. Phys., A Mater. Sci. Process. 119(4), 1237–1243 (2015).
[Crossref]

P. Mucha, P. Berger, R. Weber, N. Speker, B. Sommer, and T. Graf, “Calibrated heat flow model for the determination of different heat-affected zones in single-pass laser-cut CFRP using a cw CO2-Laser,” Appl. Phys., A Mater. Sci. Process. 118(4), 1509–1516 (2015).
[Crossref]

R. Weber, M. Hafner, A. Michalowksi, and T. Graf, “Minimum damage in CFRP laser processing,” Phys. Procedia 12(2), 307–310 (2011).
[Crossref]

Wellegehausen, B.

Welling, H.

Wiedenmann, M.

C. Freitag, M. Wiedenmann, J.-P. Negel, A. Loescher, V. Onuseit, R. Weber, M. Abdou Ahmed, and T. Graf, “High-quality processing of CFRP with a 1.1-kW picosecond laser,” Appl. Phys., A Mater. Sci. Process. 119(4), 1237–1243 (2015).
[Crossref]

Appl. Phys., A Mater. Sci. Process. (2)

C. Freitag, M. Wiedenmann, J.-P. Negel, A. Loescher, V. Onuseit, R. Weber, M. Abdou Ahmed, and T. Graf, “High-quality processing of CFRP with a 1.1-kW picosecond laser,” Appl. Phys., A Mater. Sci. Process. 119(4), 1237–1243 (2015).
[Crossref]

P. Mucha, P. Berger, R. Weber, N. Speker, B. Sommer, and T. Graf, “Calibrated heat flow model for the determination of different heat-affected zones in single-pass laser-cut CFRP using a cw CO2-Laser,” Appl. Phys., A Mater. Sci. Process. 118(4), 1509–1516 (2015).
[Crossref]

J. Appl. Phys. (1)

T. V. Kononenko, C. Freitag, M. S. Komlenok, V. Onuseit, R. Weber, T. Graf, and V. I. Konov, “Heat accumulation effects in short-pulse multi-pass cutting of carbon fiber reinforced plastics,” J. Appl. Phys. 118(10), 103105 (2015).
[Crossref]

J. Opt. Soc. Am. B (1)

Laser Phys. Lett. (1)

T. Graf, P. Berger, R. Weber, H. Hügel, A. Heider, and P. Stritt, “Analytical expressions for the threshold of deep-penetration laser welding,” Laser Phys. Lett. 12(5), 056002 (2015).
[Crossref]

Opt. Express (1)

Opt. Lasers Eng. (1)

L. Romoli, F. Fischer, and R. Kling, “A study on UV laser drilling of PEEK reinforced with carbon fibers,” Opt. Lasers Eng. 50(3), 449–457 (2012).
[Crossref]

Opt. Lett. (1)

Phys. Procedia (1)

R. Weber, M. Hafner, A. Michalowksi, and T. Graf, “Minimum damage in CFRP laser processing,” Phys. Procedia 12(2), 307–310 (2011).
[Crossref]

Proc. SPIE (1)

D. Hellrung, A. Gillner, and R. Poprawe, “Laser beam removal of micro-structures with Nd: YAG lasers,” Proc. SPIE 3097, 267–273 (1997).
[Crossref]

Prog. Quantum Electron. (1)

E. G. Gamaly and A. V. Rode, “Physics of ultra-short laser interaction with matter: From phonon excitation to ultimate transformations,” Prog. Quantum Electron. 37(5), 215–323 (2013).
[Crossref]

Quantum Electron. (1)

T. Kononenko, V. Konov, S. Garnov, R. Danielius, A. Piskarskas, G. Tamoshauskas, and 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]

Other (4)

R. Weber, T. Graf, P. Berger, V. Onuseit, M. Wiedenmann, C. Freitag, and A. Feuer, “Heat accumulation during pulsed laser materials processing,” Opt. Express 22(9), 11312 (2014).
[Crossref]

N. N. Rykalin, Die Wärmegrundlagen des Schweißvorgangs (VEB Verlag Technik Berlin, 1957).

D. Radaj, Heat Effects of Welding, Temperature Field, Residual Stress, Distortion (Springer Verlag, 1992).

H. Hügel and T. Graf, Laser in der Fertigung 3rd Ed., (Vieweg + Teubner, 2014).

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Figures (6)

Fig. 1
Fig. 1

A typical example for heat accumulation showing the evolution of the temperature as a function of time at the origin of the beam on the surface of the material which is processed with a pulsed laser. The second pulse arrives, before the surface has cooled down to the original ambient temperature (left arrow). In the case of metals a significant change of the process occurs, when the subsequent pulses are incident on the still molten surface (right arrow), which usually significantly decreases the resulting process quality.

Fig. 2
Fig. 2

Typical geometries for the heat flow in one dimension (1D) with an area on the surface as heat source, in two dimensions (2D) with a line inside the material as heat source and in three dimensions (3D) with a point on the surface as heat source.

Fig. 3
Fig. 3

Relative deviation of the integral approximation for the three dimensions (1D, 2D, and 3D) with respect to the original sum which is <10% for NHeatInp >3 in any case.

Fig. 4
Fig. 4

(Left and Center) Microscope images of the grooves created with 39 pulses/spot at two different average laser powers. Clear, shiny looking re-solidified liquid is visible inside the groove produced with 610 W of average power (Center). The corresponding height-plot below the image shows a deep groove and a solidified melt-wall on the right side. (Right) Number of pulses after which the surface is still liquid when the next pulse arrives. The squares are the experimental values, the line is a fit of Eq. (9a) to the experimental data using the parameters which are described in the text.

Fig. 5
Fig. 5

Sketch of the cutting kerf during multi scan ablation. 1D-heat flow, represented by the red arrows, is assumed to be established after a large number of scans and sufficiently high scan speed.

Fig. 6
Fig. 6

Limiting number of scans when cutting CFRP at which the matrix damage significantly increases as a function of the average laser power (left) and as a function of the feed rate (right). The squares are the experimental results. The lines are the results from the model using the identical material constant for both graphs as described in the text.

Tables (1)

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Table 1 Laser parameters used for processing of CrNi steel and CFRP

Equations (31)

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Δ T HA,nD ( t= N HeatInp f HeatInp )= Q nD ρ c p ( 4πκ f HeatInp ) nD N=1 N HeatInp 1 N nD .
1D Q 1 =σ Q Heat /A (inJ/ m 2 ),
2D Q 2 =σ Q Heat / (inJ/m), and
3D Q 3 =σ Q Heat   (inJ),
n=1 N HeatInp 1 N nD 1 N HeatInp 1 N nD dN + C nD .
1D 1 N HeatInp 1 N dN+ C 1 2 N HeatInp + C 1 ,
2D 1 N HeatInp 1 N dN+ C 2 ln( N HeatInp )+ C 2 ,
3D 1 N HeatInp 1 N 3 dN+ C 3 2 N HeatInp + C 3 .
1D Δ T HA,1D Q 1 ρ c p 4πκ f HeatInp ( 2 N HeatInp + C 1 ),
2D Δ T HA,2D Q 2 ρ c p 4πκ f HeatInp ( ln( N HeatInp )+ C 2 ),
3D Δ T HA,3D Q 3 ρ c p ( 4πκ f HeatInp ) 3 ( 2 N HeatInp + C 3 ),
Q Heat = η Heat η abs E inc = η Heat η abs P Inc,av f HeatInp .
C Mat,nD = ρ c p ( 4πκ ) nD η Heat η abs = ( ρ c p ) 2nD ( 4π λ th ) nD η Heat η abs .
1D P Inc,Limit,1 C Mat,1 Δ T Limit σ A f HeatInp 2 N tot + C 1 ,
2D P Inc,Limit,2 C Mat,2 Δ T Limit σ ln( N tot )+ C 2 , and
3D P Inc,Limit,3 C Mat,3 Δ T Limit σ N tot f HeatInp ( N tot C 3 2 ) .
1D N Limit,1 ( C Mat,1 Δ T Limit σ A f HeatInp 2 P Inc,av C 1 2 ) 2 ,
2D N Limit,2 e C Mat,2 Δ T Limit σ P Inc,av C 2 , and
3D N Limit,3 ( 2 P Inc,av f HeatInp P Inc,av f HeatInp C 3 C Mat,3 Δ T Limit σ ) 2 .
t Pause,nD = N tot f HeatInp n Pauses,nD ( P Inc,av P Inc,Limit,nD 1 ),
n Pauses,nD = N tot / N Limit,nD .
N tot = V Proc h Proc η Proc E Inc = V Proc h Proc f HeatInp η Proc P Inc,av ,
f HeatInp = f Laser and P Inc,av = P Laser = E Pulse f Laser .
f HeatInp = v Feed Contour + v Feed t Pos .
P Inc,av = P Laser f HeatInp Contour v Feed = P Laser Contour Contour + v Feed t Pos .
Diff = 4κ N Pules f laser ,
Diff = 4κ t Proc >> d Mat ,
P Inc,Limit,1 C Mat,1 Δ T Limit Contour d Mat v Feed Contour + v Feed t Pos ( 2 d Focus d Mat h Proc v Feed η Proc P Inc,Limit,1 + C 1 ) ,
N Scans,Limit,1 ( C Mat,1 Δ T Limit 2 d Mat v Feed ( Contour + v Feed t Pos ) P Laser C 1 2 ) 2 .
P Inc,Limit,1 C Mat,1 2 Δ T Limit 2 η Proc 4 h Proc d Mat Contour d Focus ,
N Scans,Limit,1 C Mat,1 2 Δ T Limit 2 4 d Mat 2 v Feed Contour P Laser 2 .

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