Advertisement

Experimental Fracture Dynamics

  • J. F. Kalthoff
Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 310)

Abstract

This chapter considers the fracture behaviour of propagating and subsequently arresting cracks and of cracks under impact loading. Loading techniques and measuring methodologies for determining the crack arrest toughness KIc and the impact fracture toughness KId are discussed. Conventional measuring procedures are outlined; the validity and the applicability range of these procedures are critically examined. Furthermore, the physical processes that control the various dynamic events are analyzed by means of a special optical technique which determines the dynamic stress intensity factor directly from the local stress strain field at the crack tip. On the basis of the established results, improved measuring techniques are developed that are capable of determining true dynamic material strength properties at arbitrary test conditions without any restrictions in crack propagation velocity, loading rate, load duration, etc.

Keywords

Stress Intensity Factor Crack Length Crack Arrest Dynamic Stress Intensity Factor Shadow Pattern 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    P. Manogg, “Anwendung der Schattenoptik zur Untersuchung des Zerreissvorgangs von Platten”, Dissertation, Freiburg, Germany. 1964.Google Scholar
  2. 2.
    P. Manogg, “Schattenoptische Messung der spezifischen Bruchenergie wahrend des Bruchvorgangs bei Plexiglas”, Proc. Int. Conf. Phys. Non-Crystalline Solids, Delft, The Netherlands, 1964, 481–490.Google Scholar
  3. 3.
    P. S. Theocaris and N. Joakimides, “Some Properties of Generalized Epicycloids Applied to Fracture Mechanics”, J. Appl. Mech., 22. 1971, 876–890.MATHGoogle Scholar
  4. 4.
    P. S. Theocaris, “The Reflected Caustic Method for the Evaluation of Mode III Stress Intensity Factor”, Intern. J. Mech. Sci., 23, 1981, 105–117.CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    P. S. Theocaris, “Stress Concentrations at Concentrated Loads”, Exp. Mech., 13, 1973, 511–528.CrossRefGoogle Scholar
  6. 6.
    A. J. Rosakis, and L. B. Freund, “Optical Measurement of the Plastic Strain Concentration at a Tip in a Ductile Plate”, J. Eng. Mater. Technol., 104, 1982, 115–125CrossRefGoogle Scholar
  7. 7.
    A. J. Rosakis, C. C. Ma, and L. B. Freund, “Analysis of the Optical Shadow Spot Method for a Tensile Crack in a Power-Law Hardening Material”, J. Appl. Mech., 50, 1983, 777–782.CrossRefGoogle Scholar
  8. 8.
    J. F. Kalthoff, J. Beinert, and S. Winkler, “Analysis of Fast Running Arresting Cracks by the Shadow-Optical Method of Caustics”, TITAM Symp. Opt. Methods Mech. Solids (A. Lagarde, Ed.), University of Poitiers, France, Sept. 10–14, 1979, Sijthoff-Noordhoff, Alphen aari den Rijn, The Netherlands, 1980, 497–508.Google Scholar
  9. 9.
    J. Beinert, and J. F. Kalthoff, “Experimental Determination of Dynamic Stress Intensity Factors by Shadow Patterns”, in Mechanics of Fracture Vol. 7, Experimental Fracture Mechanics (G. C. Sih, Ed.), Marti nus Nijhoff Publishers, Hingham, Mass. 1981, 280–330.Google Scholar
  10. 10.
    J. F. Kalthoff, “Stress Intensity Factor Determination by Caustics”, Proc. Int. Conf. on Experimental Stress Analysis, organized by Japan Society of Mechanical Engineers (JSME) and American Society for Experimental Stress Analysis (SESA), Honolulu-Maui, Hawaii, May 23–29, 1982, 1119–1126.Google Scholar
  11. 11.
    J. F. Kalthoff, W. Boehme, and S. Winkler, “Analysis of Impact Fracture Phenomenon by Means of the Shadow Optical Method of Caustics”, Proc. 7th Int. Conf. Exp. Stress Anal., organized by SESA, Haifa, Israel, Aug. 23–27, 1982, 148–160Google Scholar
  12. 12.
    J. F. Kalthoff, “Shadow Optical Method of Caustics”, in “Handbook on Experimental Mechanics”, Ed. A. S. Kobayashi, Prentice Hall, Englewood Cliffs, N. Y. 1987, 430–500.Google Scholar
  13. 13.
    J. F. Kalthoff, “D 2. 9 Schattenoptisches Kaustikenverfahren”, in “Handbuch der experimentellen Spannungsanalyse”, Hrsg. Ch. Rohrbach, N. Czaika, VDI-Verlag, Duesseldorf, 1988.Google Scholar
  14. 14.
    M. Born, and F. Wolf, “Principles of Optics”, Pergamon Press, New York, 1970.Google Scholar
  15. 15.
    P. S. Theocaris, “Complex Stress Intensity Factors of Bifurcation Cracks”. J. Mech. Phys. Solids, 210, 1972, 265–279.CrossRefGoogle Scholar
  16. 16.
    II. Seidelmann, “Anwendung des schattenoptischen Kaustikenverfahrens zur Bestimmung bruchmechanischer Kennwerte bei ueberlagerter Normal- und Scherbeanspruchung”, Bericht 2/76 des Fraunhofer-Instituts fuer Festkoerpermechanik, Freiburg, 1976.Google Scholar
  17. 17.
    G. C. Sih. “Handbook of Stress Intensity Factors”, Institute of Frac lure und Solid Mechanics, Lehigh University, Bethlehem, Pa., 1973.Google Scholar
  18. 18.
    L. R. Freund. “Crack Propagation in an Elastic Solid Subjected to General Loading — I. Constant Rate of E. xtension”, J. Mech. Phys. Solids. 20. 1972. 129–140.CrossRefMATHMathSciNetGoogle Scholar
  19. 19.
    J. F. Kalt hoff. “Zur Ausbreitung und Arretierung schnell laufender Risse”, Fortschritt-Berichte der VDI-Zeitsehriften, Reihe 18, 4, VDI-lag. Duesseldorf. 1978, 1–95.Google Scholar
  20. 20.
    vI. W. Hutchinson. “Singular Behavior at the End of a Tensile Crack in a Hardening Material”, J. Mech. Phys. Solids, 16, 1986, 13–31.CrossRefGoogle Scholar
  21. 21.
    J. R. Rice, and G. F. Rosengreen, “Plane Strain Deformation Near a Crack Tip in a Power-Law Hardening Material”, J. Mech. Phys. Solids, 16, 1968. 1–12.CrossRefMATHGoogle Scholar
  22. 22.
    J. W. Hutchinson, “Plastic Stress and Strain Fields at a Crack Tip”, J. Mech. Phys. Solids, 165. 1968, 337–347.CrossRefGoogle Scholar
  23. 20.
    J. F. Kalthoff, Fortschritt-Berichte der VDI-Zeitschriften, Reihe 18, 4, VDI-Verlag, Duesseldorf, 1978, 1–95.Google Scholar
  24. 21.
    J. F. Kalthoff. “Bruchdynamik laufender und arretierender Risse”, in “Grundlagen der Bruchmechanik”, Hrsg. H.-P. Rossmanith, Springer-Verlag, Wien, New York, 1982, 191–219.CrossRefGoogle Scholar
  25. 25.
    M. Yoshiki, T. Kanazawa, and S. Machida, “Some Basic Considerations on Crack Arresting Mechanisms in Welded Steel Structures”, Fac. of Fngineering, Dept. of Naval Architecture, University of Tokyo, Japan, 1965.Google Scholar
  26. 26.
    J. I. Bluhm, “Fracture Arrest”, Chapter 1 in Vol. V of Fracture, An Advanced Treatise, ed. by H. Liebowitz, Academic Press, New York, London, 1969.Google Scholar
  27. 27.
    H. Kihara, and K. Ikeda, “Technische Anwendung der Bruchmechanik auf duennwandige Bauteile”, Archiv fuer das Eisenhuettenwesen, Bd. 45, 1974, 413.Google Scholar
  28. 28.
    ASTM, “Fast Fracture and Crack Arrest”, ASTM STP 627, American Society for Testing and Materials, Philadelphia, 1977.Google Scholar
  29. 29.
    ASTM, “Crack Arrest Methodology and Applications”, ASTM STP 711. American Society for Testing and Materials, Philadelphia, 1980.Google Scholar
  30. 30.
    Robertson T., Journal of the Iron and Steel Institute, 1953, 306–312.Google Scholar
  31. 31.
    ASTM E 1221, “Standard Test Method for Determining Plain-Strain Crack-Arrest Fracture Toughness, KIc, of Ferritic Steels”, Annual Book of ASTM Standards, Vol. 03. 01, American Society for Testing and Materials, Philadelphia, 1988 (see Appendix I)Google Scholar
  32. 32.
    P. B. Crosley, and E. J. Ripling, “Crack Arrest Toughness of Pressure Vessel Steels”, Nuclear Engineering and Design, 17, 1971, 32–45.CrossRefGoogle Scholar
  33. 33.
    P. B. Crosley, and E. J. Ripling, Towards Development of a Standard Test for Measuring KIc, in “Fast Fracture and Crack Arrest”, ASTM STP 627, American Society for Testing and Materials, Philadelphia, 1977. 372–391.CrossRefGoogle Scholar
  34. 34.
    J. F. Kalthoff, J. Beinert, and S. Winkler, “Measurements of Dynamic Stress Intensity Factors for Fast Running and Arresting Cracks in Double-Cantilever-Beam Specimens”, in “Fast Fracture and Crack Arrest”, ASTM STÜP 627, (G. T. Hahn and M. F. Kanninen, Eds.), American Society for Testing and Materials, Philadelphia, 1977, 161–176.CrossRefGoogle Scholar
  35. 35.
    J. F. Kalthoff, J. Beinert, S. Winkler, and W. Klemm, “Experimental Analysis of Dynamic Effects in Different Crack Arrest Test Specimens”, in “Crack Arrest Methodology and Applications”, ASTM STP 711 (G. T. Hahn and M. F. Kanninen, Eds.), American Society for Testing and Materials, Philadelphia, 1980, 109–127.CrossRefGoogle Scholar
  36. 36.
    G. T. Hahn, R. G. Hoagland, M. F. Kanninen, and A. R. Rosenfield, “A Preliminary Study of Fast Fracture and Arrest in the DCB Test Specimen”, Proc. Int. Conf. Dynamic Crack Propagation, Ed. G. C. Sih, Lehigh University, Bethlehem, Pa., U. S. A., July 10–12, 1972.Google Scholar
  37. 37.
    G. T. Hahn, P. C. Gehlen, R. G. Hoagland, M. F. Kanninen, C. Popelar, A. R. Rosenfield, et al., “Critical Experiments, Measurements and Analyses to Establish a Crack Arrest Methodology for Nuclear Pressure Vessel Steels”, Reports BMI-1937, 1959, 1965, Battelle Columbus Laboratories, Columbus, Ohio, 1975, 1976, 1978.Google Scholar
  38. 38.
    J. F. Kalthoff, “Crack Arrest Toughness Measurement”, Proc. CSNI-Workshop on Application of Crack Arrest Concepts, U. S. Nuclear Regulatory-Commission Report, Fraunhofer-Institut fur Werkstoffmechanik, Freiburg F. R. of Germany, June 4–5, 1984, 1–14.Google Scholar
  39. 39.
    ASMF Boiler and Pressure Vessel Code, Section XI, A 4000, A 5000. The American Society of Mechanical Engineers, New York, 1974.Google Scholar
  40. 40.
    J. F. Kalthoff, and J. Beinert, “Bericht uber die Ergebnisse des ASTM-Round-Robin-Tests zur Messung der Rissarrestzaehigkeit”, 18. Sitzung des Arbeitskreises Bruchvorgaenge im DVM, Aachen, 18/19. 2. 1986, 183–190.Google Scholar
  41. 41.
    J. Beinert, and J. F. Kalthoff, “ The Development of a Crack Arrest Test Specimen with Reduced Dynamic Effects”, Proc. Int. Conf. on Application of Fracture Mechanics to Materials and Structures, Eds. G. C. Sih, E. Sommer, W. Dahl, Freiburg, F. R. G., June 20–24, 1983, 493–507.Google Scholar
  42. 42.
    ASTM, Round Robin Test Program of Crack Arrest, Ed. W. Corwin, American Society for Testing and Materials, Philadelphia 1988.Google Scholar
  43. 43.
    J. F. Kalthoff, J. Beinert, and S. Winkler, “Einfluss dynamischer Effekte auf die Bestimmung von Rissarrestzaehigkeiten und auf die Anwendung von Rissarrestsicherheitsanalysen”, 8. Sitzung des Arbeitskreises Bruchvorgaenge im DVM, Koln, 1976, 138.Google Scholar
  44. 44.
    J. F. Kalthoff, and A. P. Reisch, “Instrumentierter Kerbschlagbiegeversuch zur Ermittlunhg bruchmechanischer Kennwerte”, Vortragsband der Tagung Werkstoffpruefung 1984, Deutscher Verband fuer Materialpruefung e. V., Rad Nauheim, 6./7. Dezember 1984, 1–10.Google Scholar
  45. 45.
    DVM, “Messtechnische Anforderungen beim instrumentierten Kerbschlagbiegeversuch”, DVM-Merkblatt 0001, Deutscher Verband fuer Materialpruefung, Berlin, 1986, 1–11, (see Appendix II).Google Scholar
  46. 46.
    VDEh, “Kerbschlagbiegeversuch mit Ermittlung von Kraft und Weg”, STAHL-EISEN-Pruefblaetter (SEP-1315) des Vereins Deutscher Fisenhuettenleute, Verlag Stahleisen, Duesseldorf, 1987, (see Appendix II)Google Scholar
  47. 47.
    ASTM E 24. 03. 03, “Proposed Standard Method of Tests for Instrumented Impact Testing of Precracked Charpy Specimens of Metallic Materials”, Draft 2d, American Society for Testing and Materials, Philadelphia, U. S. A., 1981.Google Scholar
  48. 48.
    D. R. Ireland, “Critical Review of Instrumented Impact Testing”, Proc. Int. Conf. Dynamic Fracture Toughness, London, July 5–7, 1976.Google Scholar
  49. 49.
    J. F. Kalthoff, W. Boehme, S. Winkler, and W. Klemm, “Measurements of Dynamic Stress Intensity Factors in Impacted Bend Specimens”, C. S. N. I. Specialist Meeting on Instrumented Precracked Charpy Testing, Palo Alto, Calif., Dec. 1–3, 1980, EPRI NP-2102-LD, Electric Power Research Institute, Nov. 1981, 1–17.Google Scholar
  50. 50.
    A. Krisch, “Anforderungen an Kraft und Durchbiegungsmessungen beim Kerbschlagbiegeversuch”, Archiv Eisenhuettenwesen, Vol. 43, 1972, 901–905.Google Scholar
  51. 51.
    C. E. Turner, “Dynamic Fracture Toughness Measurements by Instrumented Impact Testing”, Advanced Seminar on Fracture Mechanics, Oct. 20–24, 1975, Commission of European Communities, Joint Research Centre, ISPRA, Italy.Google Scholar
  52. 52.
    W. Boehme, and J. F. Kalthoff, “The Behaviour of Notched Bend Specimens in Impact Testing”, Int. Journal of Fracture, Vol. 20, 1982, 139–193.CrossRefGoogle Scholar
  53. 53.
    S. Venzi, A. H. Priest, and J. J. May, “Impact Testing of Metals”, ASTM STP 466, The American Society for Testing and Materials, Philadelphia, 1970, 165–180.Google Scholar
  54. 54.
    W. Goldsmith, “Impact”, Edward Arnold Ltd., London, 1960.MATHGoogle Scholar
  55. 55.
    D. M. Norris, “Engineering Fracture Mechanics”, 11, 1979, 261–274.Google Scholar
  56. 56.
    J. F. Kalthoff, S. Winkler, W. Boehme, and W. Klemm, “Determination of the Dynamic Fracture Toughness Kid in Impact Tests by Means of Response Curves”, Proc. 5th Int. Conf. on Fracture, Cannes, March 29 — April 3, 1981, in “Advances in Fracture Research”, Pergamon Press, Oxford, New York, 1980, 363–373.Google Scholar
  57. 57.
    J. F. Kalthoff, “The Concept of Impact Response Curves”, in “Metals Handbook — Vol. 8, Mechanical Testing”, American Society for Metals, Metals Park, Ohio, 1985, 272.Google Scholar
  58. 58.
    J. F. Kalthoff, S. Winkler, and W. Boehme, “A Novel Procedure for Measuring the Impact Fracture Toughness KIc with Precracked Charpy Specimens”, Proc. Int. Conf. on Mechanical and Physical Behaviour of Materials under Dynamic Loading, Paris, Sept. 2–5, 1985, Journal de Physique, Tome 46, Colloque C5, supplement au n° 8, 1985, 179–186.Google Scholar
  59. 59.
    F. J. Loss, “Dynamic Toughness Analysis of Pressure Vessel Steels”, Third Water Reactor Safety Research Information Meeting, organized by U. S. Nuclear Regulatory Commission at National Bureau of Standards, Gaithersburg, Md., Oct. 1, 1975.Google Scholar
  60. 60.
    W. Boehme, “Eine einfache Methode zur Bestimmung der dynamischen Rissspitzenbeanspruchung bei schlagbelasteten Dreipunktbiegeprpoben”, IWM-Report Z 2/84, Fraunhofer-Institut fuer Werkstoffmechanik, Freiburg, F. R. of Germany, March, 1984.Google Scholar
  61. 61.
    D. R. Ireland, “Procedures and Problems Associated with Reliable Control of the Instrumented Impact Test”, in “Instrumented Impact Testing”, ASTM STP 563, American Society for Testing and Materials, Philadelphia, 1974, 3–29.CrossRefGoogle Scholar
  62. 62.
    J. F. Kalthoff, and S. Winkler, “Vorrichtung zur Erfassung des Rissstarts bei einer Bruchmechanikprobe”, Patentanmeldung P 33 34 570. 8, Deutsches Patentamt, Muenchen, Sept. 24, 1983, and “Instrument for Detecting the Instant of which a Crack Begins in a Mechanical Strength Test of a Ferromagnetic Metal”, U. S. Patent and Trademark Office, Washington, Patent application. Serial No. 06/652 320, Filed Sept. 19, 1984.Google Scholar
  63. 63.
    J. F. Kalthoff, S. Winkler, W. Boehme, and D. A. Shockey, “Mechanical Response of Cracks to Impact Loading”, Proc. Int. Conf. on Dynamical Mechanical Properties and Fracture Dynamics of Engineering Materials, Ed. Z. Bilek, Czechoslovak Academy of Sciences, Brno-Valtice, June 16–18, 1983, 1–16.Google Scholar
  64. 64.
    J. Eftis, and J. M. Krafft, “A Comparison of the Initiation with the Rapid Propagation of a Crack in a Mild Steel Plate”, J. Basic Engineering, Trans. ASME, March, 1965, 257–263. 1CrossRefGoogle Scholar
  65. 65.
    G. C. Sih “Handbook of Stress Intensity Factors”, Institute of Fracture and Solid Mechanics, Lehigh University, Bethlehem, Pa., 1973.Google Scholar
  66. 66.
    D. A. Shockey, and D. R. Curran, “A Method for Measuring Kic at Very High Strain Rates”, in “Progress in Flow Growth and Fracture Toughness Testing”, ASTM STP 536, 1973, 297–311.Google Scholar
  67. 67.
    D. A. Shockey, J. F. Kalthoff, and D. C. Ehrlich,” Evaluation of Dynamic Instability Criteria”, Int. J. Fracture 22, 1983, 217–279.CrossRefGoogle Scholar
  68. 68.
    L. S. Costin, J. Duffy, and L. B. Freund, “Fracture Initiation in Metals Under Stress Wave Loading Conditions”, in “Fast Fracture and Crack Arrest”, (G. T. Hahn and M. F. Kanninen, Eds.), ASTM STP 627, 1977, 301–308.Google Scholar
  69. 69.
    J. R. Klepaczko, “Applications of the Split-Hopkinson Pressure Bar to Fracture Dynamics”, in Proc. 2nd Conf. Mech. Prop. High Rates of Strain (J. Harding, ed.), Oxford, 201–204, The Institute of Physics, Conf. Ser. No. 45, Bristol, London, 1979.Google Scholar
  70. 70.
    J. R. Klepaczko, “Loading Rate Spectra for Fracture Initiation in Metals”, Theoretical and Applied Fracture Mechanics, 1, 1984, 181–191.CrossRefGoogle Scholar
  71. 71.
    K. Ravi-Chandar, and W. G. Knauss, “An Experimental Investigation Into Dynamic Fracture: 1. Crack Initiation and Arrest,” Int. J. Fracture, 25, 1984, 247–262.CrossRefGoogle Scholar
  72. 72.
    J. F. Kalthoff, “Fracture Behaviour Under High Rates of Loading”, Proc. Int. Conf. on Dynamic Fracture Mechanics, San Antonio, Texas, Nov. 7–9, 1984, Eng. Frac. Mech., Vol. 23, 1986, 289–298.Google Scholar
  73. 73.
    J. F. Kalthoff, and S. Winkler, “Fracture Behavior Under Impact”, First and Second Anual Reports (W8/83 and W10/83) and Final Report (W10/86) on the Project DAJA 37–81-C-0013 prepared for ERO of ARO, London, Fraunhofer-Institut fuer Werkstoffmechanik, Freiburg 1982, 1983, 1985.Google Scholar
  74. 74.
    W. Boehme, and J. F. Kalthoff, “Der Einfluss der Probengroesse auf dynamische Effekte bei der Kid-Bestimmung im Kerbschlagbiegetest”, Report W3/83 on the Project Ka 443–7 prepared for Deutsche Forschungsgemeinschaft, Fraunhofer-Institut fuer Werkstoffmechanik, Freibürg, 1983.Google Scholar
  75. 75.
    J. F. Kalthoff, “Shadow Optical Analysis of Dynamic Shear Fracture”, Proc. Int. Conf. on Photomechanics and Speckle Metrology, (SPIE), San Diego, Calif., Aug. 16 21, 1987, 531–538, and Optical Engineering, 27, 1988, 835–840.Google Scholar
  76. 76.
    J. F. Kalthoff, “Failure Mode Transition at High Rates of Shear Loading”, Int. Conf. on Impact Loading and Dynamic Behaviour of Materials, Bremen, May 18–22, 1987, Deutsche Gesellschaft fuer Metallkunde (DGM), 185–196.Google Scholar
  77. 77.
    ft. Dormeval, “Adiabatic Shear Phenomenon”, Proc. Int. Conf. on Impact Loading and Dynamic Behaviour of Materials, Bremen, May 18–22, 1987, Deutsche Gesellschaft fuer Metallkunde (DGM).Google Scholar
  78. 78.
    D. R. Curran, L. Seaman, and D. A. Shockey, “Dynamic Failure of Solids”, Physics Reports (Review Section of Physics Letters), 147, Nos. 5,6, 1987, 253–388, North Holland, Amsterdam.Google Scholar
  79. 79.
    H. Neuber, “Kerbspannungslehre”, Springer-Verlalg, 1958.CrossRefMATHGoogle Scholar
  80. 80.
    D. A. Shockey, J. F. Kalthoff, and D. C. Ehrlich, “Evaluation of Dynamic Crack Instability Criteria”, Int. Journ. of Fracture 22, 1983, 217–229.CrossRefGoogle Scholar
  81. 81.
    H. Homma, D. A. Shockey, and Y. Murayama, “Response of Cracks in Structural Materials to Short Pulse Loads”, J. Mech. Phys. Solids, 1983.Google Scholar
  82. 82.
    D. A. Shockey, J. F. Kalthoff, H. Homma, and D. C. Ehrlich, “Criterion for Crack Instability under Short Pulse Loads”, Proc. Int. Conf. on Fraoture, Cannes, March 29 — April 3, 1981, in “Advances in Fracture Research”, Pergamon Press, Oxford, New York, 1980, 415–423.Google Scholar
  83. 83.
    J. D. Achenbach, “Dynamic Effects in Brittle Fracture”, in Mechanics Today, I. ed. S. Nemat-Nasser, Oxford: Pergamon-Press, 1972, 1–57.Google Scholar
  84. 84.
    L. B. Freund, “Crack Propagation in an Elastic Solid Subjected to General Loading III. Stress Wave Loading”, J. Mech. Phys. Solids, 21, 1973, 47–61.CrossRefMATHGoogle Scholar
  85. 85.
    O. Sih, “Handbook of Stress Intensity Factors” Inst. of Fracture and Solid Mechanics, Lehigh University, Bethlehem, Pa., 1973.Google Scholar
  86. 86.
    J. F. Kalthoff, and D. A. Shockey, “On the Instabillity of Cracks Loaded by Tensile Stress Pulses of Short Duration”, Stanford Research Institute, Poulter Laboratory Technical Report 001–75, 1975.Google Scholar
  87. 87.
    J. F. Kalthoff, and D. A. Shockey, “Instability of Cracks under Impulse Loads”, J. Appl. Phys., Vol. 48, No. 3, 1977, 986–993.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 1990

Authors and Affiliations

  • J. F. Kalthoff
    • 1
  1. 1.University of BochumBochumGermany

Personalised recommendations