Abstract

A method of high-speed holographic microscopy is developed to take three successive microscopic photographs of a crack tip propagating in a transparent poly(methyl methacrylate) specimen at a speed of several hundred meters per second. When a crack is propagating in a specimen, three Q-switched ruby lasers emit three laser pulses successively. The time interval between each laser pulse and the next is 1 µs or longer. An optical system of angle-multiplexing holography records the crack as three successive holograms on one photographic plate. Crack images are reconstructed and photographed through a conventional microscope. The spatial resolution of the reconstructed images is approximately 114 lines/mm. From the photographs, one can measure crack speed, crack opening displacement, and the dynamic stress intensity factor. The high-speed holographic microscopy makes it possible to study rapid crack propagation in microseconds.

© 1997 Optical Society of America

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References

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  1. P. Manogg, “Schattenoptische messung der spezifischen bruchenergie wahrend des bruchvorgangs bei plexiglas,” in Proceedings of the International Conference on Physics of Non-Crystalline Solids, Delft, Netherlands, 1964 (North-Holland, Amsterdam, 1964), pp. 481–490.
  2. J. Beinert, J. F. Kalthoff, M. Maier, “Neuere ergebnisse zur anwendung des schattenfleckverfahrens auf stehende und schnell-laufende bruche,” in Proceedings of the 6th International Conference on Experimental Stress Analysis, Munich, Germany, 1978, VDI-Report No. 313 (VDI-Verlag, Dusseldorf, Germany, 1978), pp. 791–798.
  3. P. S. Theocaris, F. Katsamanis, “Response of cracks to impact by caustics,” Eng. Fract. Mech. 10, 197–210 (1978).
    [CrossRef]
  4. J. F. Kalthoff, “Shadow optical method of caustics”, in Handbook on Experimental Mechanics, A. S. Kobayashi, ed., (Prentice-Hall, Englewood Cliffs, N.J., 1987), pp. 430–500.
  5. A. J. Rosakis, “Two optical techniques sensitive to gradients of optical path difference: the method of caustics and the coherent gradient sensor (CGS),” in Experimental Techniques in Fracture, J. S. Epstein, ed. (VCH, New York, 1993), pp. 327–425.
  6. H. V. Tippur, S. Krishnaswamy, A. J. Rosakis, “Optical mapping of crack tip deformations using the methods of transmission and reflection coherent gradient sensing: a study of crack tip K-dominance,” Int. J. Fract. 52, 91–117 (1991).
  7. R. P. Singh, A. Shukla, “Mechanics of dynamic crack propagation along bimaterial interfaces: the intersonic regime,” in Abstract Proceedings of 8th International Congress on Experimental Mechanics, Nashville, Tennessee, 1996 (Society for Experimental Mechanics, Bethel, Conn., 1996), pp. 314–315.
  8. P. D. Washabaugh, W. G. Knauss, “Non-steady periodic behavior in the dynamic fracture of PMMA,” Int. J. Fract. 59, 189–197 (1993).
    [CrossRef]
  9. D. C. Holloway, “Application of holographic interferometry to stress wave and crack propagation problems,” Opt. Eng. 21 (3), 468–473 (1982).
    [CrossRef]
  10. S. Suzuki, H. Homa, R. Kusaka, “Pulsed holographic microscopy as a measurement method of dynamic fracture toughness for fast propagating cracks,” J. Mech. Phys. Solids 36 (3), 631–659 (1988).
    [CrossRef]
  11. S. Suzuki, “Measurement of crack and craze opening displacement of rapidly propagating cracks by means of pulsed holographic microscopy,” in Proceedings of the 9th International Conference on Experimental Mechanics (Permanent Committee for Stress Analysis, Copenhagen, 1990), Vol. 5, pp. 1833–1842.
  12. S. Suzuki, “Three-dimensional measurement of opening displacement of rapidly propagating cracks in PMMA,” in Applied Stress Analysis, T. H. Hyde, E. Ollerton, eds. (Elsevier Applied Science, New York, 1990), pp. 26–35.
    [CrossRef]
  13. S. Suzuki, S. Fukuchi, “Some experiments on measurement of dynamic stress intensity factor of fast propagating cracks,” in Dynamic Failure of Materials: Theory, Experiments and Numerics, H. P. Rossmanith, A. J. Rosakis, eds. (Elsevier Applied Science, New York, 1991), pp. 219–231.
    [CrossRef]
  14. S. Suzuki, T. Takeichi, “Measurement of craze stress and dynamic fracture toughness of PMMA by means of pulsed holographic microscopy,” in Proceedings of the International Symposium on Advanced Techniques in Experimental Mechanics (Japan Society of Mechanical Engineering, Tokyo, 1995), pp. 311–316.
  15. S. Suzuki, “A method of pulsed holographic microscopy to photograph fast propagating cracks with higher spatial resolution,” in Post-Conference Proceedings of the 1996 8th International Congress on Experimental Mechanics, Nashville, Tennessee (Society for Experimental Mechanics, Bethel, Conn., 1996), pp. 229–236.
  16. W. Lauterborn, K. J. Ebeling, “High-speed holography of laser-induced breakdown in liquids,” Appl. Phys. Lett. 31, 663–664 (1977).
    [CrossRef]
  17. L. O. Heflinger, G. L. Stewart, C. R. Booth, “Holographic motion pictures of microscopic plankton,” Appl. Opt. 17, 951–954 (1978).
    [CrossRef] [PubMed]
  18. M. J. Ehrlich, J. S. Steckenrider, J. W. Wagner, “System for high-speed time-resolved holography of transient events,” Appl. Opt. 31, 5947–5951 (1992).
    [CrossRef] [PubMed]
  19. K. J. Ebeling, W. Lauterborn, “Acoustooptic beam deflection for spatial frequency multiplexing in high speed holocinematography,” Appl. Opt. 17, 2071–2076 (1978).
    [CrossRef] [PubMed]
  20. W. Hentschel, W. Lauterborn, “High-speed holographic movie camera,” Opt. Eng. 24, 687–691 (1985).
  21. R. G. Racca, J. M. Dewey, “Time-resolved holography for the study of shock waves,” in 18th International Congress on High Speed Photography and Photonics, W. Daheng, ed., Proc. SPIE1032, 578–586 (1988).
    [CrossRef]
  22. R. G. Racca, J. M. Dewey, “High speed time-resolved holographic interferometer using solid-state shutters,” Opt. Laser Technol. 22, 199–204 (1990).
    [CrossRef]
  23. R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, San Diego, Calif., 1971).
  24. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), p. 418.
  25. E. B. Champagne, “Nonparaxial imaging, magnification, and aberration properties in holography,” J. Opt. Soc. Am. 57, 51–55 (1967).
    [CrossRef]
  26. R. P. Kambour, “Mechanism of fracture in glassy polymers. III. Direct observation of the craze ahead of the propagating crack in poly(methyl methacrylate) and polystyrene,” J. Polym. Sci. Part A 4, 349–358 (1966).
    [CrossRef]
  27. H. R. Brown, I. M. Ward, “Craze shape and fracture in poly(methyl methacrylate),” Polymer 14, 469–475 (1973).
    [CrossRef]
  28. Y. Imai, I. M. Ward, “A study of craze deformation in the fatigue fracture of polymethylmethacrylate,” J. Mater. Sci. 20, 3842–3852 (1985).
    [CrossRef]
  29. K. Takahashi, “Dynamic fracture instability in glassy polymers as studied by ultrasonic fractography,” Polym. Eng. Sci. 27, 25–32 (1987).
    [CrossRef]
  30. L. B. Freund, Dynamic Fracture Mechanics (Cambridge U. Press, Cambridge, England, 1990).
    [CrossRef]
  31. H. I. Bjelkhagen, Silver-Halide Recording Materials for Holography and Their Processing, Vol. 66 of Optical Sciences (Springer-Verlag, New York, 1993), p. 155.

1993 (1)

P. D. Washabaugh, W. G. Knauss, “Non-steady periodic behavior in the dynamic fracture of PMMA,” Int. J. Fract. 59, 189–197 (1993).
[CrossRef]

1992 (1)

1991 (1)

H. V. Tippur, S. Krishnaswamy, A. J. Rosakis, “Optical mapping of crack tip deformations using the methods of transmission and reflection coherent gradient sensing: a study of crack tip K-dominance,” Int. J. Fract. 52, 91–117 (1991).

1990 (1)

R. G. Racca, J. M. Dewey, “High speed time-resolved holographic interferometer using solid-state shutters,” Opt. Laser Technol. 22, 199–204 (1990).
[CrossRef]

1988 (1)

S. Suzuki, H. Homa, R. Kusaka, “Pulsed holographic microscopy as a measurement method of dynamic fracture toughness for fast propagating cracks,” J. Mech. Phys. Solids 36 (3), 631–659 (1988).
[CrossRef]

1987 (1)

K. Takahashi, “Dynamic fracture instability in glassy polymers as studied by ultrasonic fractography,” Polym. Eng. Sci. 27, 25–32 (1987).
[CrossRef]

1985 (2)

Y. Imai, I. M. Ward, “A study of craze deformation in the fatigue fracture of polymethylmethacrylate,” J. Mater. Sci. 20, 3842–3852 (1985).
[CrossRef]

W. Hentschel, W. Lauterborn, “High-speed holographic movie camera,” Opt. Eng. 24, 687–691 (1985).

1982 (1)

D. C. Holloway, “Application of holographic interferometry to stress wave and crack propagation problems,” Opt. Eng. 21 (3), 468–473 (1982).
[CrossRef]

1978 (3)

1977 (1)

W. Lauterborn, K. J. Ebeling, “High-speed holography of laser-induced breakdown in liquids,” Appl. Phys. Lett. 31, 663–664 (1977).
[CrossRef]

1973 (1)

H. R. Brown, I. M. Ward, “Craze shape and fracture in poly(methyl methacrylate),” Polymer 14, 469–475 (1973).
[CrossRef]

1967 (1)

1966 (1)

R. P. Kambour, “Mechanism of fracture in glassy polymers. III. Direct observation of the craze ahead of the propagating crack in poly(methyl methacrylate) and polystyrene,” J. Polym. Sci. Part A 4, 349–358 (1966).
[CrossRef]

Beinert, J.

J. Beinert, J. F. Kalthoff, M. Maier, “Neuere ergebnisse zur anwendung des schattenfleckverfahrens auf stehende und schnell-laufende bruche,” in Proceedings of the 6th International Conference on Experimental Stress Analysis, Munich, Germany, 1978, VDI-Report No. 313 (VDI-Verlag, Dusseldorf, Germany, 1978), pp. 791–798.

Bjelkhagen, H. I.

H. I. Bjelkhagen, Silver-Halide Recording Materials for Holography and Their Processing, Vol. 66 of Optical Sciences (Springer-Verlag, New York, 1993), p. 155.

Booth, C. R.

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), p. 418.

Brown, H. R.

H. R. Brown, I. M. Ward, “Craze shape and fracture in poly(methyl methacrylate),” Polymer 14, 469–475 (1973).
[CrossRef]

Burckhardt, C. B.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, San Diego, Calif., 1971).

Champagne, E. B.

Collier, R. J.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, San Diego, Calif., 1971).

Dewey, J. M.

R. G. Racca, J. M. Dewey, “High speed time-resolved holographic interferometer using solid-state shutters,” Opt. Laser Technol. 22, 199–204 (1990).
[CrossRef]

R. G. Racca, J. M. Dewey, “Time-resolved holography for the study of shock waves,” in 18th International Congress on High Speed Photography and Photonics, W. Daheng, ed., Proc. SPIE1032, 578–586 (1988).
[CrossRef]

Ebeling, K. J.

K. J. Ebeling, W. Lauterborn, “Acoustooptic beam deflection for spatial frequency multiplexing in high speed holocinematography,” Appl. Opt. 17, 2071–2076 (1978).
[CrossRef] [PubMed]

W. Lauterborn, K. J. Ebeling, “High-speed holography of laser-induced breakdown in liquids,” Appl. Phys. Lett. 31, 663–664 (1977).
[CrossRef]

Ehrlich, M. J.

Freund, L. B.

L. B. Freund, Dynamic Fracture Mechanics (Cambridge U. Press, Cambridge, England, 1990).
[CrossRef]

Fukuchi, S.

S. Suzuki, S. Fukuchi, “Some experiments on measurement of dynamic stress intensity factor of fast propagating cracks,” in Dynamic Failure of Materials: Theory, Experiments and Numerics, H. P. Rossmanith, A. J. Rosakis, eds. (Elsevier Applied Science, New York, 1991), pp. 219–231.
[CrossRef]

Heflinger, L. O.

Hentschel, W.

W. Hentschel, W. Lauterborn, “High-speed holographic movie camera,” Opt. Eng. 24, 687–691 (1985).

Holloway, D. C.

D. C. Holloway, “Application of holographic interferometry to stress wave and crack propagation problems,” Opt. Eng. 21 (3), 468–473 (1982).
[CrossRef]

Homa, H.

S. Suzuki, H. Homa, R. Kusaka, “Pulsed holographic microscopy as a measurement method of dynamic fracture toughness for fast propagating cracks,” J. Mech. Phys. Solids 36 (3), 631–659 (1988).
[CrossRef]

Imai, Y.

Y. Imai, I. M. Ward, “A study of craze deformation in the fatigue fracture of polymethylmethacrylate,” J. Mater. Sci. 20, 3842–3852 (1985).
[CrossRef]

Kalthoff, J. F.

J. Beinert, J. F. Kalthoff, M. Maier, “Neuere ergebnisse zur anwendung des schattenfleckverfahrens auf stehende und schnell-laufende bruche,” in Proceedings of the 6th International Conference on Experimental Stress Analysis, Munich, Germany, 1978, VDI-Report No. 313 (VDI-Verlag, Dusseldorf, Germany, 1978), pp. 791–798.

J. F. Kalthoff, “Shadow optical method of caustics”, in Handbook on Experimental Mechanics, A. S. Kobayashi, ed., (Prentice-Hall, Englewood Cliffs, N.J., 1987), pp. 430–500.

Kambour, R. P.

R. P. Kambour, “Mechanism of fracture in glassy polymers. III. Direct observation of the craze ahead of the propagating crack in poly(methyl methacrylate) and polystyrene,” J. Polym. Sci. Part A 4, 349–358 (1966).
[CrossRef]

Katsamanis, F.

P. S. Theocaris, F. Katsamanis, “Response of cracks to impact by caustics,” Eng. Fract. Mech. 10, 197–210 (1978).
[CrossRef]

Knauss, W. G.

P. D. Washabaugh, W. G. Knauss, “Non-steady periodic behavior in the dynamic fracture of PMMA,” Int. J. Fract. 59, 189–197 (1993).
[CrossRef]

Krishnaswamy, S.

H. V. Tippur, S. Krishnaswamy, A. J. Rosakis, “Optical mapping of crack tip deformations using the methods of transmission and reflection coherent gradient sensing: a study of crack tip K-dominance,” Int. J. Fract. 52, 91–117 (1991).

Kusaka, R.

S. Suzuki, H. Homa, R. Kusaka, “Pulsed holographic microscopy as a measurement method of dynamic fracture toughness for fast propagating cracks,” J. Mech. Phys. Solids 36 (3), 631–659 (1988).
[CrossRef]

Lauterborn, W.

W. Hentschel, W. Lauterborn, “High-speed holographic movie camera,” Opt. Eng. 24, 687–691 (1985).

K. J. Ebeling, W. Lauterborn, “Acoustooptic beam deflection for spatial frequency multiplexing in high speed holocinematography,” Appl. Opt. 17, 2071–2076 (1978).
[CrossRef] [PubMed]

W. Lauterborn, K. J. Ebeling, “High-speed holography of laser-induced breakdown in liquids,” Appl. Phys. Lett. 31, 663–664 (1977).
[CrossRef]

Lin, L. H.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, San Diego, Calif., 1971).

Maier, M.

J. Beinert, J. F. Kalthoff, M. Maier, “Neuere ergebnisse zur anwendung des schattenfleckverfahrens auf stehende und schnell-laufende bruche,” in Proceedings of the 6th International Conference on Experimental Stress Analysis, Munich, Germany, 1978, VDI-Report No. 313 (VDI-Verlag, Dusseldorf, Germany, 1978), pp. 791–798.

Manogg, P.

P. Manogg, “Schattenoptische messung der spezifischen bruchenergie wahrend des bruchvorgangs bei plexiglas,” in Proceedings of the International Conference on Physics of Non-Crystalline Solids, Delft, Netherlands, 1964 (North-Holland, Amsterdam, 1964), pp. 481–490.

Racca, R. G.

R. G. Racca, J. M. Dewey, “High speed time-resolved holographic interferometer using solid-state shutters,” Opt. Laser Technol. 22, 199–204 (1990).
[CrossRef]

R. G. Racca, J. M. Dewey, “Time-resolved holography for the study of shock waves,” in 18th International Congress on High Speed Photography and Photonics, W. Daheng, ed., Proc. SPIE1032, 578–586 (1988).
[CrossRef]

Rosakis, A. J.

H. V. Tippur, S. Krishnaswamy, A. J. Rosakis, “Optical mapping of crack tip deformations using the methods of transmission and reflection coherent gradient sensing: a study of crack tip K-dominance,” Int. J. Fract. 52, 91–117 (1991).

A. J. Rosakis, “Two optical techniques sensitive to gradients of optical path difference: the method of caustics and the coherent gradient sensor (CGS),” in Experimental Techniques in Fracture, J. S. Epstein, ed. (VCH, New York, 1993), pp. 327–425.

Shukla, A.

R. P. Singh, A. Shukla, “Mechanics of dynamic crack propagation along bimaterial interfaces: the intersonic regime,” in Abstract Proceedings of 8th International Congress on Experimental Mechanics, Nashville, Tennessee, 1996 (Society for Experimental Mechanics, Bethel, Conn., 1996), pp. 314–315.

Singh, R. P.

R. P. Singh, A. Shukla, “Mechanics of dynamic crack propagation along bimaterial interfaces: the intersonic regime,” in Abstract Proceedings of 8th International Congress on Experimental Mechanics, Nashville, Tennessee, 1996 (Society for Experimental Mechanics, Bethel, Conn., 1996), pp. 314–315.

Steckenrider, J. S.

Stewart, G. L.

Suzuki, S.

S. Suzuki, H. Homa, R. Kusaka, “Pulsed holographic microscopy as a measurement method of dynamic fracture toughness for fast propagating cracks,” J. Mech. Phys. Solids 36 (3), 631–659 (1988).
[CrossRef]

S. Suzuki, T. Takeichi, “Measurement of craze stress and dynamic fracture toughness of PMMA by means of pulsed holographic microscopy,” in Proceedings of the International Symposium on Advanced Techniques in Experimental Mechanics (Japan Society of Mechanical Engineering, Tokyo, 1995), pp. 311–316.

S. Suzuki, “A method of pulsed holographic microscopy to photograph fast propagating cracks with higher spatial resolution,” in Post-Conference Proceedings of the 1996 8th International Congress on Experimental Mechanics, Nashville, Tennessee (Society for Experimental Mechanics, Bethel, Conn., 1996), pp. 229–236.

S. Suzuki, “Measurement of crack and craze opening displacement of rapidly propagating cracks by means of pulsed holographic microscopy,” in Proceedings of the 9th International Conference on Experimental Mechanics (Permanent Committee for Stress Analysis, Copenhagen, 1990), Vol. 5, pp. 1833–1842.

S. Suzuki, “Three-dimensional measurement of opening displacement of rapidly propagating cracks in PMMA,” in Applied Stress Analysis, T. H. Hyde, E. Ollerton, eds. (Elsevier Applied Science, New York, 1990), pp. 26–35.
[CrossRef]

S. Suzuki, S. Fukuchi, “Some experiments on measurement of dynamic stress intensity factor of fast propagating cracks,” in Dynamic Failure of Materials: Theory, Experiments and Numerics, H. P. Rossmanith, A. J. Rosakis, eds. (Elsevier Applied Science, New York, 1991), pp. 219–231.
[CrossRef]

Takahashi, K.

K. Takahashi, “Dynamic fracture instability in glassy polymers as studied by ultrasonic fractography,” Polym. Eng. Sci. 27, 25–32 (1987).
[CrossRef]

Takeichi, T.

S. Suzuki, T. Takeichi, “Measurement of craze stress and dynamic fracture toughness of PMMA by means of pulsed holographic microscopy,” in Proceedings of the International Symposium on Advanced Techniques in Experimental Mechanics (Japan Society of Mechanical Engineering, Tokyo, 1995), pp. 311–316.

Theocaris, P. S.

P. S. Theocaris, F. Katsamanis, “Response of cracks to impact by caustics,” Eng. Fract. Mech. 10, 197–210 (1978).
[CrossRef]

Tippur, H. V.

H. V. Tippur, S. Krishnaswamy, A. J. Rosakis, “Optical mapping of crack tip deformations using the methods of transmission and reflection coherent gradient sensing: a study of crack tip K-dominance,” Int. J. Fract. 52, 91–117 (1991).

Wagner, J. W.

Ward, I. M.

Y. Imai, I. M. Ward, “A study of craze deformation in the fatigue fracture of polymethylmethacrylate,” J. Mater. Sci. 20, 3842–3852 (1985).
[CrossRef]

H. R. Brown, I. M. Ward, “Craze shape and fracture in poly(methyl methacrylate),” Polymer 14, 469–475 (1973).
[CrossRef]

Washabaugh, P. D.

P. D. Washabaugh, W. G. Knauss, “Non-steady periodic behavior in the dynamic fracture of PMMA,” Int. J. Fract. 59, 189–197 (1993).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), p. 418.

Appl. Opt. (3)

Appl. Phys. Lett. (1)

W. Lauterborn, K. J. Ebeling, “High-speed holography of laser-induced breakdown in liquids,” Appl. Phys. Lett. 31, 663–664 (1977).
[CrossRef]

Eng. Fract. Mech. (1)

P. S. Theocaris, F. Katsamanis, “Response of cracks to impact by caustics,” Eng. Fract. Mech. 10, 197–210 (1978).
[CrossRef]

Int. J. Fract. (2)

H. V. Tippur, S. Krishnaswamy, A. J. Rosakis, “Optical mapping of crack tip deformations using the methods of transmission and reflection coherent gradient sensing: a study of crack tip K-dominance,” Int. J. Fract. 52, 91–117 (1991).

P. D. Washabaugh, W. G. Knauss, “Non-steady periodic behavior in the dynamic fracture of PMMA,” Int. J. Fract. 59, 189–197 (1993).
[CrossRef]

J. Mater. Sci. (1)

Y. Imai, I. M. Ward, “A study of craze deformation in the fatigue fracture of polymethylmethacrylate,” J. Mater. Sci. 20, 3842–3852 (1985).
[CrossRef]

J. Mech. Phys. Solids (1)

S. Suzuki, H. Homa, R. Kusaka, “Pulsed holographic microscopy as a measurement method of dynamic fracture toughness for fast propagating cracks,” J. Mech. Phys. Solids 36 (3), 631–659 (1988).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Polym. Sci. Part A (1)

R. P. Kambour, “Mechanism of fracture in glassy polymers. III. Direct observation of the craze ahead of the propagating crack in poly(methyl methacrylate) and polystyrene,” J. Polym. Sci. Part A 4, 349–358 (1966).
[CrossRef]

Opt. Eng. (2)

W. Hentschel, W. Lauterborn, “High-speed holographic movie camera,” Opt. Eng. 24, 687–691 (1985).

D. C. Holloway, “Application of holographic interferometry to stress wave and crack propagation problems,” Opt. Eng. 21 (3), 468–473 (1982).
[CrossRef]

Opt. Laser Technol. (1)

R. G. Racca, J. M. Dewey, “High speed time-resolved holographic interferometer using solid-state shutters,” Opt. Laser Technol. 22, 199–204 (1990).
[CrossRef]

Polym. Eng. Sci. (1)

K. Takahashi, “Dynamic fracture instability in glassy polymers as studied by ultrasonic fractography,” Polym. Eng. Sci. 27, 25–32 (1987).
[CrossRef]

Polymer (1)

H. R. Brown, I. M. Ward, “Craze shape and fracture in poly(methyl methacrylate),” Polymer 14, 469–475 (1973).
[CrossRef]

Other (15)

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, San Diego, Calif., 1971).

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), p. 418.

L. B. Freund, Dynamic Fracture Mechanics (Cambridge U. Press, Cambridge, England, 1990).
[CrossRef]

H. I. Bjelkhagen, Silver-Halide Recording Materials for Holography and Their Processing, Vol. 66 of Optical Sciences (Springer-Verlag, New York, 1993), p. 155.

R. P. Singh, A. Shukla, “Mechanics of dynamic crack propagation along bimaterial interfaces: the intersonic regime,” in Abstract Proceedings of 8th International Congress on Experimental Mechanics, Nashville, Tennessee, 1996 (Society for Experimental Mechanics, Bethel, Conn., 1996), pp. 314–315.

J. F. Kalthoff, “Shadow optical method of caustics”, in Handbook on Experimental Mechanics, A. S. Kobayashi, ed., (Prentice-Hall, Englewood Cliffs, N.J., 1987), pp. 430–500.

A. J. Rosakis, “Two optical techniques sensitive to gradients of optical path difference: the method of caustics and the coherent gradient sensor (CGS),” in Experimental Techniques in Fracture, J. S. Epstein, ed. (VCH, New York, 1993), pp. 327–425.

P. Manogg, “Schattenoptische messung der spezifischen bruchenergie wahrend des bruchvorgangs bei plexiglas,” in Proceedings of the International Conference on Physics of Non-Crystalline Solids, Delft, Netherlands, 1964 (North-Holland, Amsterdam, 1964), pp. 481–490.

J. Beinert, J. F. Kalthoff, M. Maier, “Neuere ergebnisse zur anwendung des schattenfleckverfahrens auf stehende und schnell-laufende bruche,” in Proceedings of the 6th International Conference on Experimental Stress Analysis, Munich, Germany, 1978, VDI-Report No. 313 (VDI-Verlag, Dusseldorf, Germany, 1978), pp. 791–798.

R. G. Racca, J. M. Dewey, “Time-resolved holography for the study of shock waves,” in 18th International Congress on High Speed Photography and Photonics, W. Daheng, ed., Proc. SPIE1032, 578–586 (1988).
[CrossRef]

S. Suzuki, “Measurement of crack and craze opening displacement of rapidly propagating cracks by means of pulsed holographic microscopy,” in Proceedings of the 9th International Conference on Experimental Mechanics (Permanent Committee for Stress Analysis, Copenhagen, 1990), Vol. 5, pp. 1833–1842.

S. Suzuki, “Three-dimensional measurement of opening displacement of rapidly propagating cracks in PMMA,” in Applied Stress Analysis, T. H. Hyde, E. Ollerton, eds. (Elsevier Applied Science, New York, 1990), pp. 26–35.
[CrossRef]

S. Suzuki, S. Fukuchi, “Some experiments on measurement of dynamic stress intensity factor of fast propagating cracks,” in Dynamic Failure of Materials: Theory, Experiments and Numerics, H. P. Rossmanith, A. J. Rosakis, eds. (Elsevier Applied Science, New York, 1991), pp. 219–231.
[CrossRef]

S. Suzuki, T. Takeichi, “Measurement of craze stress and dynamic fracture toughness of PMMA by means of pulsed holographic microscopy,” in Proceedings of the International Symposium on Advanced Techniques in Experimental Mechanics (Japan Society of Mechanical Engineering, Tokyo, 1995), pp. 311–316.

S. Suzuki, “A method of pulsed holographic microscopy to photograph fast propagating cracks with higher spatial resolution,” in Post-Conference Proceedings of the 1996 8th International Congress on Experimental Mechanics, Nashville, Tennessee (Society for Experimental Mechanics, Bethel, Conn., 1996), pp. 229–236.

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Figures (13)

Fig. 1
Fig. 1

Recording of three objects on one photographic plate by angle-multiplexing holography.

Fig. 2
Fig. 2

Reconstruction of three object images from the superimposed holograms.

Fig. 3
Fig. 3

PMMA specimen.

Fig. 4
Fig. 4

(a) Optical system for high-speed holographic recording of fast-propagating cracks. (b) Propagation of light in the PMMA specimen.

Fig. 5
Fig. 5

Reflection and refraction of rays at a surface of PMMA.

Fig. 6
Fig. 6

Reconstruction and microscopic photographing of crack images: (a) the first frame, (b) the second frame, and (c) the third frame.

Fig. 7
Fig. 7

Three successive photographs of a rapidly propagating crack. The frame interval is approximately 2.2 µs, and the crack speed is approximately 198 m/s.

Fig. 8
Fig. 8

Schema of crack tip in PMMA.

Fig. 9
Fig. 9

Signal of three laser pulses and signal of conducting strips that were cut by the crack shown in Fig. 7.

Fig. 10
Fig. 10

Crack opening displacement of the crack shown in Fig. 7.

Fig. 11
Fig. 11

Three successive photographs of a rapidly propagating crack. The frame interval is approximately 1.0 µs, and the crack speed is approximately 245 m/s.

Fig. 12
Fig. 12

Three successive photographs of a rapidly propagating crack. The frame interval is approximately 5.0 µs, and the crack speed is approximately 321 m/s.

Fig. 13
Fig. 13

Dynamic stress intensity factor versus crack speed.

Tables (2)

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Table 1 Resolution of Reconstructed Imagesa

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Table 2 Resolution of Reconstructed Imagesa

Equations (4)

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sin β=n sin α n=1.49,
sin θi=λHλRsin θi i=1, 2, or 3,
COD=8π1/2KIvG1-ν1Lvr,
Lv=2α1α12-α224α1α2-1+α222,α1=1-v/c121/2, α2=1-v/c221/2, c1=2G1-ν1ρ1-2ν11/2,c2=Gρ1/2,ν1=νplane strainν/1+ρplane stress,

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