Abstract

In combination with known thermomechanical-fatigue data for Mo, we have conducted transient photothermal deflection (TPD) measurements to develop a model for the multipulse laser damage of Mo mirrors to predict their lifetimes. In laser-damage experiments to verify the model, Mo mirrors were irradiated with 10-ns Nd:YAG laser pulses at 1064 nm at a 10-Hz repetition rate. Digitized TPD waveforms indicated peak surface angular deflection that could then be converted into surface displacement. Numerical modeling of the vertical heat distribution enabled the peak surface-deflection signal to be converted into peak surface temperature. The thermomechanical model was verified by both the experimental and the numerical results. Conventional mechanical-fatigue data for Mo were used to derive a predictive equation for the laser-accumulation lifetime of Mo mirrors. Experiments were performed with 1–104 pulses per site, yielding laser-damage thresholds and accumulation curves. The accumulation behavior predicted from measurements of mechanical fatigue was in excellent agreement with the measured behavior. Thus a single-pulse TPD measurement of peak deformation at a subthreshold laser fluence, in conjunction with mechanical-fatigue data, may be used to estimate the safe operating fluence for a component in a multipulse laser environment.

© 1991 Optical Society of America

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References

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  1. H. M. Musal, “Thermomechanical stress degradation of metal mirror surfaces under pulsed-laser irradiation,” in Laser Induced Damage in Optical Materials: 1979, NBS Spec. Publ. 568, 159–173 (1980).
  2. N. Koumvakalis, C. S. Lee, M. Bass, “Single and multiple pulse catastrophic damage in diamond-turned Cu and Ag mirrors, at 10.6, 1.06, and 0.532 μm,” Opt. Eng. 22, 419–423 (1983).
    [CrossRef]
  3. C. S. Lee, N. Koumvakalis, M. Bass, “A theoretical model for multiple-pulse laser-induced damage to metal mirrors,” J. Appl. Phys. 54, 5727–5731 (1983).
    [CrossRef]
  4. Y. Jee, M. F. Becker, R. M. Walser, “Laser-induced damage on single-crystal metal surfaces,” J. Opt. Soc. Am. B 5, 648–659 (1988).
    [CrossRef]
  5. M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, A. C. Boccara, “Photothermal displacement spectroscopy: an optical probe for solids and surfaces,” Appl. Phys. A 32, 141–154 (1983).
    [CrossRef]
  6. C. Karner, A. Mandel, F. Trager, “Pulsed-laser photothermal displacement spectroscopy for surface studies,” Appl. Phys. A 38, 19–21 (1985).
    [CrossRef]
  7. J. Opsal, A. Rosencwaig, D. L. Willenborg, “Thermal-wave detection and thin-film thickness measurements with laser beam deflection,” Appl. Opt. 22, 3169–3176 (1983).
    [CrossRef] [PubMed]
  8. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in Pascal (Cambridge U. Press, New York, 1989).
  9. M. R. Mitchell, “Fundamentals of modern fatigue analysis for design,” in Fatigue and Microstructure (American Society for Metals, Metals Park, Ohio, 1979).
  10. P. Beardmore, P. H. Thorton, “The relationship between discontinuous yielding and cyclic behavior in polycrystalline molybdenum,” Metall. Trans. 1, 775–779 (1970).
  11. K. Furuya, N. Nagata, R. Watanabe, H. Yoshida, “Effect of low cycle fatigue on the ductile-brittle transition in molybdenum,” J. Nucl. Mater. 103–104, 937–941 (1981).
    [CrossRef]
  12. K. Furuya, T. Kainuma, “Effects of alloying and heat treatment on the endurance limit of molybdenum in high cycle fatigue tests,” J. Nucl. Mater. 122–123, 754–758 (1984).
    [CrossRef]
  13. H. Nishi, T. Oku, T. Kodaira, “Low cycle fatigue behavior of titanium carbide coated molybdenum,” J. Nucl. Mater. 141–143, 152–155 (1986).
    [CrossRef]
  14. An estimate for dA/dT is made on the basis of values given for Ag, Au, Cu, and Al in M. Sparks, E. Loh, “Temperature dependence of absorptance in laser damage of metallic mirrors: I melting,” J. Opt. Soc. Am. 69, 847–858 (1979).
    [CrossRef]
  15. ASM Handbook Committee, Metals Handbook, 9th ed. (American Society for Metals, Metals Park, Ohio, 1979).

1988 (1)

1986 (1)

H. Nishi, T. Oku, T. Kodaira, “Low cycle fatigue behavior of titanium carbide coated molybdenum,” J. Nucl. Mater. 141–143, 152–155 (1986).
[CrossRef]

1985 (1)

C. Karner, A. Mandel, F. Trager, “Pulsed-laser photothermal displacement spectroscopy for surface studies,” Appl. Phys. A 38, 19–21 (1985).
[CrossRef]

1984 (1)

K. Furuya, T. Kainuma, “Effects of alloying and heat treatment on the endurance limit of molybdenum in high cycle fatigue tests,” J. Nucl. Mater. 122–123, 754–758 (1984).
[CrossRef]

1983 (4)

J. Opsal, A. Rosencwaig, D. L. Willenborg, “Thermal-wave detection and thin-film thickness measurements with laser beam deflection,” Appl. Opt. 22, 3169–3176 (1983).
[CrossRef] [PubMed]

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, A. C. Boccara, “Photothermal displacement spectroscopy: an optical probe for solids and surfaces,” Appl. Phys. A 32, 141–154 (1983).
[CrossRef]

N. Koumvakalis, C. S. Lee, M. Bass, “Single and multiple pulse catastrophic damage in diamond-turned Cu and Ag mirrors, at 10.6, 1.06, and 0.532 μm,” Opt. Eng. 22, 419–423 (1983).
[CrossRef]

C. S. Lee, N. Koumvakalis, M. Bass, “A theoretical model for multiple-pulse laser-induced damage to metal mirrors,” J. Appl. Phys. 54, 5727–5731 (1983).
[CrossRef]

1981 (1)

K. Furuya, N. Nagata, R. Watanabe, H. Yoshida, “Effect of low cycle fatigue on the ductile-brittle transition in molybdenum,” J. Nucl. Mater. 103–104, 937–941 (1981).
[CrossRef]

1980 (1)

H. M. Musal, “Thermomechanical stress degradation of metal mirror surfaces under pulsed-laser irradiation,” in Laser Induced Damage in Optical Materials: 1979, NBS Spec. Publ. 568, 159–173 (1980).

1979 (1)

1970 (1)

P. Beardmore, P. H. Thorton, “The relationship between discontinuous yielding and cyclic behavior in polycrystalline molybdenum,” Metall. Trans. 1, 775–779 (1970).

Amer, N. M.

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, A. C. Boccara, “Photothermal displacement spectroscopy: an optical probe for solids and surfaces,” Appl. Phys. A 32, 141–154 (1983).
[CrossRef]

Bass, M.

N. Koumvakalis, C. S. Lee, M. Bass, “Single and multiple pulse catastrophic damage in diamond-turned Cu and Ag mirrors, at 10.6, 1.06, and 0.532 μm,” Opt. Eng. 22, 419–423 (1983).
[CrossRef]

C. S. Lee, N. Koumvakalis, M. Bass, “A theoretical model for multiple-pulse laser-induced damage to metal mirrors,” J. Appl. Phys. 54, 5727–5731 (1983).
[CrossRef]

Beardmore, P.

P. Beardmore, P. H. Thorton, “The relationship between discontinuous yielding and cyclic behavior in polycrystalline molybdenum,” Metall. Trans. 1, 775–779 (1970).

Becker, M. F.

Boccara, A. C.

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, A. C. Boccara, “Photothermal displacement spectroscopy: an optical probe for solids and surfaces,” Appl. Phys. A 32, 141–154 (1983).
[CrossRef]

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in Pascal (Cambridge U. Press, New York, 1989).

Fournier, D.

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, A. C. Boccara, “Photothermal displacement spectroscopy: an optical probe for solids and surfaces,” Appl. Phys. A 32, 141–154 (1983).
[CrossRef]

Furuya, K.

K. Furuya, T. Kainuma, “Effects of alloying and heat treatment on the endurance limit of molybdenum in high cycle fatigue tests,” J. Nucl. Mater. 122–123, 754–758 (1984).
[CrossRef]

K. Furuya, N. Nagata, R. Watanabe, H. Yoshida, “Effect of low cycle fatigue on the ductile-brittle transition in molybdenum,” J. Nucl. Mater. 103–104, 937–941 (1981).
[CrossRef]

Jee, Y.

Kainuma, T.

K. Furuya, T. Kainuma, “Effects of alloying and heat treatment on the endurance limit of molybdenum in high cycle fatigue tests,” J. Nucl. Mater. 122–123, 754–758 (1984).
[CrossRef]

Karner, C.

C. Karner, A. Mandel, F. Trager, “Pulsed-laser photothermal displacement spectroscopy for surface studies,” Appl. Phys. A 38, 19–21 (1985).
[CrossRef]

Kodaira, T.

H. Nishi, T. Oku, T. Kodaira, “Low cycle fatigue behavior of titanium carbide coated molybdenum,” J. Nucl. Mater. 141–143, 152–155 (1986).
[CrossRef]

Kohn, S.

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, A. C. Boccara, “Photothermal displacement spectroscopy: an optical probe for solids and surfaces,” Appl. Phys. A 32, 141–154 (1983).
[CrossRef]

Koumvakalis, N.

C. S. Lee, N. Koumvakalis, M. Bass, “A theoretical model for multiple-pulse laser-induced damage to metal mirrors,” J. Appl. Phys. 54, 5727–5731 (1983).
[CrossRef]

N. Koumvakalis, C. S. Lee, M. Bass, “Single and multiple pulse catastrophic damage in diamond-turned Cu and Ag mirrors, at 10.6, 1.06, and 0.532 μm,” Opt. Eng. 22, 419–423 (1983).
[CrossRef]

Lee, C. S.

N. Koumvakalis, C. S. Lee, M. Bass, “Single and multiple pulse catastrophic damage in diamond-turned Cu and Ag mirrors, at 10.6, 1.06, and 0.532 μm,” Opt. Eng. 22, 419–423 (1983).
[CrossRef]

C. S. Lee, N. Koumvakalis, M. Bass, “A theoretical model for multiple-pulse laser-induced damage to metal mirrors,” J. Appl. Phys. 54, 5727–5731 (1983).
[CrossRef]

Loh, E.

Mandel, A.

C. Karner, A. Mandel, F. Trager, “Pulsed-laser photothermal displacement spectroscopy for surface studies,” Appl. Phys. A 38, 19–21 (1985).
[CrossRef]

Mitchell, M. R.

M. R. Mitchell, “Fundamentals of modern fatigue analysis for design,” in Fatigue and Microstructure (American Society for Metals, Metals Park, Ohio, 1979).

Musal, H. M.

H. M. Musal, “Thermomechanical stress degradation of metal mirror surfaces under pulsed-laser irradiation,” in Laser Induced Damage in Optical Materials: 1979, NBS Spec. Publ. 568, 159–173 (1980).

Nagata, N.

K. Furuya, N. Nagata, R. Watanabe, H. Yoshida, “Effect of low cycle fatigue on the ductile-brittle transition in molybdenum,” J. Nucl. Mater. 103–104, 937–941 (1981).
[CrossRef]

Nishi, H.

H. Nishi, T. Oku, T. Kodaira, “Low cycle fatigue behavior of titanium carbide coated molybdenum,” J. Nucl. Mater. 141–143, 152–155 (1986).
[CrossRef]

Oku, T.

H. Nishi, T. Oku, T. Kodaira, “Low cycle fatigue behavior of titanium carbide coated molybdenum,” J. Nucl. Mater. 141–143, 152–155 (1986).
[CrossRef]

Olmstead, M. A.

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, A. C. Boccara, “Photothermal displacement spectroscopy: an optical probe for solids and surfaces,” Appl. Phys. A 32, 141–154 (1983).
[CrossRef]

Opsal, J.

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in Pascal (Cambridge U. Press, New York, 1989).

Rosencwaig, A.

Sparks, M.

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in Pascal (Cambridge U. Press, New York, 1989).

Thorton, P. H.

P. Beardmore, P. H. Thorton, “The relationship between discontinuous yielding and cyclic behavior in polycrystalline molybdenum,” Metall. Trans. 1, 775–779 (1970).

Trager, F.

C. Karner, A. Mandel, F. Trager, “Pulsed-laser photothermal displacement spectroscopy for surface studies,” Appl. Phys. A 38, 19–21 (1985).
[CrossRef]

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in Pascal (Cambridge U. Press, New York, 1989).

Walser, R. M.

Watanabe, R.

K. Furuya, N. Nagata, R. Watanabe, H. Yoshida, “Effect of low cycle fatigue on the ductile-brittle transition in molybdenum,” J. Nucl. Mater. 103–104, 937–941 (1981).
[CrossRef]

Willenborg, D. L.

Yoshida, H.

K. Furuya, N. Nagata, R. Watanabe, H. Yoshida, “Effect of low cycle fatigue on the ductile-brittle transition in molybdenum,” J. Nucl. Mater. 103–104, 937–941 (1981).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. A (2)

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, A. C. Boccara, “Photothermal displacement spectroscopy: an optical probe for solids and surfaces,” Appl. Phys. A 32, 141–154 (1983).
[CrossRef]

C. Karner, A. Mandel, F. Trager, “Pulsed-laser photothermal displacement spectroscopy for surface studies,” Appl. Phys. A 38, 19–21 (1985).
[CrossRef]

J. Appl. Phys. (1)

C. S. Lee, N. Koumvakalis, M. Bass, “A theoretical model for multiple-pulse laser-induced damage to metal mirrors,” J. Appl. Phys. 54, 5727–5731 (1983).
[CrossRef]

J. Nucl. Mater. (3)

K. Furuya, N. Nagata, R. Watanabe, H. Yoshida, “Effect of low cycle fatigue on the ductile-brittle transition in molybdenum,” J. Nucl. Mater. 103–104, 937–941 (1981).
[CrossRef]

K. Furuya, T. Kainuma, “Effects of alloying and heat treatment on the endurance limit of molybdenum in high cycle fatigue tests,” J. Nucl. Mater. 122–123, 754–758 (1984).
[CrossRef]

H. Nishi, T. Oku, T. Kodaira, “Low cycle fatigue behavior of titanium carbide coated molybdenum,” J. Nucl. Mater. 141–143, 152–155 (1986).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Laser Induced Damage in Optical Materials: 1979, NBS Spec. Publ. (1)

H. M. Musal, “Thermomechanical stress degradation of metal mirror surfaces under pulsed-laser irradiation,” in Laser Induced Damage in Optical Materials: 1979, NBS Spec. Publ. 568, 159–173 (1980).

Metall. Trans. (1)

P. Beardmore, P. H. Thorton, “The relationship between discontinuous yielding and cyclic behavior in polycrystalline molybdenum,” Metall. Trans. 1, 775–779 (1970).

Opt. Eng. (1)

N. Koumvakalis, C. S. Lee, M. Bass, “Single and multiple pulse catastrophic damage in diamond-turned Cu and Ag mirrors, at 10.6, 1.06, and 0.532 μm,” Opt. Eng. 22, 419–423 (1983).
[CrossRef]

Other (3)

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in Pascal (Cambridge U. Press, New York, 1989).

M. R. Mitchell, “Fundamentals of modern fatigue analysis for design,” in Fatigue and Microstructure (American Society for Metals, Metals Park, Ohio, 1979).

ASM Handbook Committee, Metals Handbook, 9th ed. (American Society for Metals, Metals Park, Ohio, 1979).

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Figures (7)

Fig. 1
Fig. 1

a, Sample data for multipulse metal surface damage thresholds for Cu and Al: E-P, electropolished; D-T, diamond turned. b, Initially predicted behavior of Mo based on the results for Cu and Al.

Fig. 2
Fig. 2

Experimental setup for laser-damage and TPD experiments. B.S., beam splitter; F.L., focal length; HWP, half-wave plate; Pol., polarizer; DCS, digital camera system.

Fig. 3
Fig. 3

a, Experimental data for surface displacement of a Mo surface versus laser fluence obtained from TPD experiments. b, Surface temperature rise versus laser fluence determined from the data in a.

Fig. 4
Fig. 4

Typical numerical model result showing Mo temperature as a function of time and depth for a pulse whose fluence is just at the melting threshold, 1.30 J/cm2.

Fig. 5
Fig. 5

Numerical model results for peak surface displacement versus time for the same case as in Fig. 4.

Fig. 6
Fig. 6

Comparison of numerical model results (solid curves) with experimental data (filled diamonds) for a, surface temperature rise versus laser fluence and b, surface displacement versus laser fluence.

Fig. 7
Fig. 7

Experimental data (open squares) for normalized damage fluence versus number of laser pulses, and linear-regression fit (solid curve).

Tables (2)

Tables Icon

Table I Constants and Parameters for Molybdenum

Tables Icon

Table II Mechanical Fatigue Data for Annealed Recrystallized Molybdenum

Equations (10)

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F N = F 1 N s 1 .
Δ h = ( 1 + ν ) ( 1 ν ) α 0 Δ T ( x , t ) d x ,
L eff = ( π k th t p 4 ρ C υ ) 1 / 2 ,
Δ h = ( 1 + ν ) ( 1 ν ) α L eff Δ T = 6.35 × 10 3 ( nm / K ) Δ T .
P = f N c ,
σ = σ f N b ,
N = 1 + ν 1 ν α Δ T .
total = N b ,
F N = F 1 N s 1 ,
F y = ( 1 υ ) ( π k th ρ C ν t p ) 1 / 2 Y 2 A α E .

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