Advertisement

Dynamic Crack Initiation, Some Experimental Methods and Modelling

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

Abstract

The main purpose of this part of the book is to review new experimental methods which are useful and effective in determination of resistance to fracture under fast and impact conditions of loading. In recent decade a substantial progress has been made in this domain.

The first part concentrates on loading rate effects in fracture initiation and its theoretical basis. In general, the small scale yielding is considered, however, some cases of the large scale yielding are also discussed.

The loading rate spectrum is thoroughly analyzed. Experimental techniques and some results obtained within the low and medium loading rate are both considered. Over the region of higher loading rates application of elastic waves for testing fracture resistance is discussed. An emphasis is placed on application of Split Hopkinson Bar (SHB) to fracture dynamics (Modes I and III are discussed).

In the final part attention is being given to experimental results in crack initiation over a wide range of loading rates and temperatures. A modelling of the loading rate spectra is attempted. A generalized model for quasi-static, fast and impact loading of a stationary crack has been developed and discussed. The experimental results are presented in such a way to be useful in practical applications. It is believed that a better understanding of the nature of the loading rate effects in metallic materials can be useful in preventing catastrophic failures under impact.

Keywords

Fracture Toughness Compact Tension Specimen Small Scale Yielding Dynamic Fracture Toughness Master Plot 
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.
    Irwin, G. R.: Plastic zone near a crack and fracture toughness, in: Proc. 7th Sagamore Conf. 1960, IV-63.Google Scholar
  2. 2.
    Huit, J. A. H. and F. A. Mc Clintock: Elastic-Plastic Stress and Strain Distributions Around Sharp Notches Under Repeated Shear, in: Proc. of the Ninth Int. Congr. of Appl. Mech., University of Brussels, Brussels 1957, 8, 51.Google Scholar
  3. 3.
    Mc Clintock, F. A. and G. R. Irwin: Plasticity Aspects of Fracture Mechanics, in: Fracture Toughness Testing and Its Applications, ASTM STP 381, American Society for Testing and Materials, Philadelphia 1965, 84.Google Scholar
  4. 4.
    Begley, J. D. and J. A. Landes: The J integral as a fracture criterion, in: ASTM STP 514, American Society for Testing and Materials, Philadelphia 1972, 1.Google Scholar
  5. 5.
    Landes, J. D. and J. A. Begley: The effect of specimen geometry on JIc, in: ASTM STP 514, American Society for Testing and Materials, Philadelphia 1972, 24.Google Scholar
  6. 6.
    Bui, H. D.: Dual path independent integrals in the boundary-value problems of cracks, Engng. Fracture Mech., 6 (1974), 287.Google Scholar
  7. 7.
    Nakamura, T., C.F. Shih and L. B. Freund: Computational methods based on an energy integral in dynamic fracture, Int. J. Fract., 27 (1985), 229.Google Scholar
  8. 8.
    Atkinson, C. and J. D. Eshelby: The flow of energy into the tip of a moving crack: Int. J. Fract., 4 (1968), 3.Google Scholar
  9. 9.
    Freund, L. B.: Crack propagation in an elastic solid subjected to general loading, I. Constant rate of extension, J. Mech. Phys. Solids, 21 (1973), 47.MATHGoogle Scholar
  10. 10.
    Wells, A. A.: Application of fracture mechanics at and beyond general yielding, British Welding J., 10 (1963), 563.Google Scholar
  11. 11.
    Dugdale, D. S.: Yielding of steel containing slits, J. Mech. Phys. Solids, 8 (1960), 8.Google Scholar
  12. 12.
    Klepaczko, J. R.: A general approach to rate sensitivity and constitutive modelling of FCC and BCC metals, in: Impact: Effects of Fast Transient Loadings (Eds. W. J. Amman et al.), A. A. Balkema, Rotterdam, 1988, 3.Google Scholar
  13. 13.
    Campbell, J. D. and W. G. Ferguson: The temperature and strain-rate dependence of the shear strength of mild steel, Phil. Mag., 81 (1970), 63.Google Scholar
  14. 14.
    Hahn, G. T., B. L. Averbach, W. S. Owen and M. Cohen: Initiation of cleavage microcracks in polycrystalline iron and steel, in: Fracture (Eds. B. L. Avervbach et al.), The Technology Press of MIT and J. Wiley, Cambridge/New York 1960, 91.Google Scholar
  15. 15.
    Louat, N. and H. L. Wain: Brittle fracture and the yield-point phenome non, in: Fracture (Eds. B. L. Averbach et al.), The Technology Press of MIT and J. Wiley, Cambridge/New York 1960, 161.Google Scholar
  16. 16.
    Kocks, U. F., A. S. Argon and M. F. Ashby: Thermodynamics and Kinetics of Slip, Pergamon Press, Oxford 1975.Google Scholar
  17. 17.
    Wilson, M. L., R. H. Hawley and J. Duffy: The effect of loading rate and temperature on fracture initiation in 1020 hot-rolled steel, Engng. Fract. Mech., 13 (1980), 371.Google Scholar
  18. 18.
    Krasovsky, A. J., Yu. A. Kashtalyan and V. N. Krasiko: Brittle-to-ductile transition in steels and the critical transition temperature, Int. J. Fract., 23 (1983), 297.Google Scholar
  19. 19.
    Marandet, B., G. Phellipeau and G. Sanz: Experimental Determination of Dynamic Fracture Toughness by J-Integral Method, in: Advances in Frac ture Research (Ed. D. François), Proc. ICF-5, Pergamon Press, Oxford 1981, 375.Google Scholar
  20. 20.
    Krabiell, A. and W. Dahl: Influence of Strain Rate and Temperature on the Tensile and Fracture Properties of Structural Steels, in: Advances in Fracture Research (Ed. D. François), Proc. ICF-5, Pergamon Press, Oxford 1981, 393.Google Scholar
  21. 21.
    Kussmaul, K., C. Zimmermann, T. Demier and D. Kraemer: On the Use of Opto-electronic Components for the Registration of Crack Tip Behaviour Under Dynamical Loading Conditions, in: Proc. Conf. DYMAT 85, Les éditions de physique, Les Ulis, France 1985, C5–219.Google Scholar
  22. 22.
    Klepaczko, J. R.: Displacement gauge with a photodiode, J. of Measurements, Automatics and Control, 12 (1966), 466, (in Polish).Google Scholar
  23. 23.
    Klepaczko, J. R.: An extensometric gauge, Patent of Poland No 54728, 1967.Google Scholar
  24. 24.
    Shoemaker, A. K. and S. T. Rolfe: Static and dynamic low-temperature KIc behavior of steels, J. Basic Engng, Trans. ASME Ser. D., (1969), 512 1.Google Scholar
  25. 25.
    Madison, R. B. and G. R. Irwin: Dynamic KIc testing of structural steel, J. of the Struct. Div., ASCE, 100, No ST 7, Proc. Paper 10653n, (1974), 1331.Google Scholar
  26. 26.
    Kalthoff, J. F., S. Winkler, W. Böhme and W. Klemm: Determination of the dynamic fracture toughness KId in impact test by means of impact response curves, in: Advances in Fracture Research (Ed. D. François), Proc. ICF-5, Pergamon Press, Oxford 1981, 368.Google Scholar
  27. 27.
    Kalthoff, J. F., S. Winkler and W. Böhme: A novel procedure for measuring the impact fracture toughness KId with precracked Charpy specimens, in: Proc. Conf. DYMAT 85, Les éditions de physique, Les Ulis, France 1985, C5–179.Google Scholar
  28. 28.
    Klepaczko, J. R.: Loading rate spectra for fracture initiation in metals, Theoretical and Applied Fracture Mechanics, 1 (1984), 181.Google Scholar
  29. 29.
    Klepaczko, J. R.: Fracture initiation under impact, Int. J. Impact Engng., 3 (1985), 191.Google Scholar
  30. 30.
    Klepaczko, J. R.: Fracture initiation of metals over a wide range of loading rates, loading rate spectra, presented on IUTAM Symposium on Macro and Micro Mechanics of High Velocity Deformation and Fracture, Aug. (1985), Tokyo, Japan.Google Scholar
  31. 31.
    Nunomura, S., T. Kashiwamura, K. Machida and S. Sakui: Fracture toughness of ball bearing steel, in: Fracture Mechanics and Technologyf (eds. G. C. Sih and Y. A. Chow), Sijthoff and Noordhoff, Leyden, 1977, 553.Google Scholar
  32. 32.
    Kanninen, M. F. and C. H. Popelar, Advanced Fracture Mechanics, Oxford University Press, New York 1985.MATHGoogle Scholar
  33. 33.
    Holtzman, M., B. Vlach and Z. Bilek: The effect of microstructure on the fracture toughness of structural steels, Int. J. Press. Ves. Piping, 9 (1981), 284.Google Scholar
  34. 34.
    Klepaczko, J. R. and G. Pluvinage: Fracture Toughness of Some Structural Steels at High Loading Rates and Different Temperatures, in: Proc. Conf. DYMAT 85, Les éditions de physique, Les Ulis, France 1985, C5–145.Google Scholar
  35. 35.
    Hopkinson, B.: A method of measuring the pressure produced in the detonation of high explosives and by the impact of bullets, Phil. Trans. Roy. Soc. (London), Ser. A, 213 (1914), 437.Google Scholar
  36. 36.
    Hopkinson, B.: Collected Scientific Papers, University Press, Cambridge 1921.MATHGoogle Scholar
  37. 37.
    Davies, R. M.: A critical study of the Hopkinson pressure bar, Phil. Trans. Roy. Soc. (London), Ser. A, 240 (1948), 375.MATHGoogle Scholar
  38. 38.
    Kolsky, H.: An investigation of the mechanical properties of materials at very high rates of strain, Proc. Phys. Soc. (London), Ser. B, 62 (1949), 676.Google Scholar
  39. 39.
    Klepaczko, J. R.: The modified Hopkinson bar, Theoretical and Applied Mechanics, 9 (1971), 479; (in Polish).Google Scholar
  40. 40.
    Hauser, F. E., J. A. Simmons and J. E. Dorn, Strain rate effects in plastic wave propagation, in: Response of Metals to High Velocity Deformation, Interscience, New York 1960.Google Scholar
  41. 41.
    Lindholm, U. S.: Some experiments with the split Hopkinson pressure bar, J. Mech. Phys. Solids, 12 (1964), 317.Google Scholar
  42. 42.
    Duffy, J., J. D. Campbell and R. H. Hawley: On the use of a torsional split Hopkinson bar to study rate effects in 1100–0 aluminum, Brown Univ. Rep. NSF-GK-4242/1, Providence 1970.Google Scholar
  43. 43.
    Campbell, J. D. and J. L. Lewis: The development and use of a torsional split Hopkinson bar for testing materials at shear strain rates up to 15000 sec−1, Univ. of Oxford Rep. No 1080/69, Oxford 1969.Google Scholar
  44. 44.
    Klepaczko, J. R.: Application of the split Hopkinson pressure bar for impact testing of rocks, Engineering Transactions, 28 (1980), 381 (in Polish).Google Scholar
  45. 45.
    Kolsky, H.: Stress Waves in Solids, Dover Publications, Inc., New York 1963.Google Scholar
  46. 46.
    Achenbach, J. D.: Wave Propagation in Elastic Solids, North Holland, Amsterdam 1976.Google Scholar
  47. 47.
    Follansbee, P. S. and C. Frantz: Wave propagation in the split Hopkinson pressure bar, J. Engng. Materials and Technology, 105 (1983), 61.Google Scholar
  48. 48.
    Kolsky, H.: Experimental Studies in Stress Wave Propagation, in Proc. 5-th U. S. Natl. Congr. of Appl. Mech., ASME, New York, 1966, 21.Google Scholar
  49. 49.
    Klepaczko, J. R. and R. J. Clifton: The Propagation of Plastic Wave Fronts in a Plastically Deforming Aluminum Alloy, Techn. Report ARO-D-G182/9, Brown University, Providence, 1974.Google Scholar
  50. 50.
    Malinowski, J. Z. and J. R. Klepaczko: A unified analytic and numerical approach to specimen behaviour in the split Hopkinson pressure bar, Int. J. Mech. Sci., 28 (1986), 381.Google Scholar
  51. 51.
    Costin, L. S., E. E. Crisman, R. H. Hawley and J. Duffy: On the localisation of plastic flow in mild steel tubes under dynamic torsional loading, in: Mechanical Properties at High Strain Rates of Strain 1979 (Ed. J. Harding), The Institute of Physics, Bristol 1979, 90.Google Scholar
  52. 52.
    Hartley, K. A., J. Duffy and R. H. Hawley: Measurement of the temperature profile during shear band formation in steels deforming at high strain rates, Brown University Report No DAAG 29–85-K-0003/2, Providence 1986.Google Scholar
  53. 53.
    Klepaczko, J. R.: Application of the split Hopkinson pressure bar to fracture dynamics, in: Mechanical Properties at High Rates of Strain 1979 (Ed. J. Harding), The Institute of Physics, Bristol 1979, 201.Google Scholar
  54. 54.
    Gambin, W., P. Lipinski and G. Pluvinage: A singular element for a new experimental method of fracture toughness determination, Engng. Fract. Mech., 18 (1983), 567.Google Scholar
  55. 55.
    Klepaczko, J. R.: Discussion of a new experimental method in measuring fracture toughness initiation at high loading rates by stress waves, J. Engng. Materials and Technology, 104 (1982), 29.Google Scholar
  56. 56.
    Klepaczko, J. R. and A. Andrzejewski: Fracture toughness of some aluminum alloys at low and high loading rates, IFTR Rep. No 39/1979, Warsaco, 1979.Google Scholar
  57. 57.
    Klepaczko, J. R.: Determination of the critical value of the J-integral at high loading rates using the wedge-loaded specimen, J. of Testing and Evaluation, 13 (1985), 441.Google Scholar
  58. 58.
    Klepaczko, J. R. and J. Z. Malinowski: Dynamic frictional effects as measured from the split Hopkinson pressure bar, in: High Velocity Deformation of Solids (eds. K. Kawata and J. Shioiri), Springer-Verlag, Berlin 1979, 403.Google Scholar
  59. 59.
    Priest, A. H.: Influence of strain rate and temperature on the fracture and tensile properties of several metallic materials, in: Proc. Conf. on Dynamic Fracture Toughness, Welding Institute and ASM, London 1979, 95.Google Scholar
  60. 60.
    Dambrine, B., P. Lipinski, G. Pluvinage: Mesure de la ténacité en dynamique d’aciers pour rails, Mémoires et Etudes Scientifiques Revue de Métallurgie (1982), 329.Google Scholar
  61. 61.
    Shabbits, W. O.: Dynamic fracture toughness properties of heavy section A533 grade B Class 1 steel plate, Westinghouse Report, WCAP-7623, Dec. 1973.Google Scholar
  62. 62.
    Costin, L. S., J. Duffy and L. B. Freund: Fracture initiation in metals under stress wave loading conditions, in: Fast Fracture and Crack Arrest, ASTM STP 627, American Society for Testing and Materials, Philadelphia, 1977, 301.Google Scholar
  63. 63.
    Eftis, J. and J. M. Krafft: A comparison of the initiation with the rapid propagation of a crack in a mild steel plate, J. of Basic Engng., 87 (1965), 257.Google Scholar
  64. 64.
    Rice, J. R.: A path independent integral and the approximate analysis of strain concentration by notches and cracks, J. Appl. Mech., 35 (1968), 379.Google Scholar
  65. 65.
    Rice, J. R.: Mathematical analysis in the mechanics of fracture, in: Fractu re (Ed. H. Liebowitz), Vol. II, Academic Press, New York, 1968, 191.Google Scholar
  66. 66.
    Knott, J. F.: Fundamentals of Fracture Mechanics, J. Wiley, New York 1979; (3-rd. ed.).Google Scholar
  67. 67.
    Broberg, K. B.: Crack growth criteria and non-linear fracture mechanics, J. Mech. Phys. Solids, 19 (1971), 407.Google Scholar
  68. 68.
    Rice, J. R., P. C. Paris and J. G. Merkle: Some further results of J-integral, analysis and estimates, ASTM STP 536, 1973, 231.Google Scholar
  69. 69.
    Merkle, J. G. and H. T. Corten: A J-integral analysis for compact specimen, considering axial force as well as bending effects, J. Press. Vessel Techn., Trans. ASME, J 96 (1974), 286.Google Scholar
  70. 70.
    Kanazawa, T., D. Machida, M. Onozuka and S. Kaneda: A preliminary study on the J-integral fracture criterion, Report of the University of Tokyo, IIW X-779–75, Tokyo 1975.Google Scholar
  71. 71.
    ASTM Standard: Standard Test for JIc, A Measure of Fracture Toughness, E813–81, ASTM, 1981.Google Scholar
  72. 72.
    Clarke, G. A. and J. D. Landes: Evaluation of J for the compact specimen, J. of Testing and Evaluation, Philadelphia, 7 (1979), 264.Google Scholar
  73. 73.
    Klepaczko, J. R.: Loading rate spectra for fracture initiation in metals, Theoretical and Applied Fracture Mechanics, 1 (1984), 181.Google Scholar
  74. 74.
    Klepaczko, J. R.: Fracture initiation under impact, Int. J. Impact. Engng., 3 (1985), 191.Google Scholar
  75. 75.
    Bui, H. D.: Mécanique de la Rupture Fragile, Masson, Paris 1978.Google Scholar
  76. 76.
    Ehrlacher, A.: Path independent integral for the calculation of the energy release rate in elastodynamics, in: Advances in Fracture Research, (Ed. D. François), Pergamon Press, Oxford 1981, 2187.Google Scholar
  77. 77.
    Mall, S.: A finite element analysis of transient crack problems with a path-independent integral, in: Advances in Fracture Research, (Ed. D. François), Pergamon Press, Oxford 1981, 2171.Google Scholar
  78. 78.
    Klepaczko, J. R.: An experimental procedure to determine J-integral under high loading rates, in: Mechanical Properties at High Rates of Strain, 1979 (Ed. J. Harding), The Inst. of Physics, Bristol 1979, 201.Google Scholar
  79. 79.
    Klepaczko, J. R., P. Lipinski and G. Pluvinage: A numerical analysis of yield stress and strain hardening effects on elastic-plastic zone growth around crack tip, unpublished report, Metz University, Metz 1984.Google Scholar
  80. 80.
    Bagoumi, M. R. and M. N. Bassim: Experimental correlation between ductility and J-integral in the transition region of 1045 steel, Engng. Fract. Mech. 18 (1983), 468.Google Scholar
  81. 81.
    Klepaczko, J. R.: Quasi-static and dynamic compression behavior of materials, Technical Report No 1, Dept. of Mech. Engng., The University of Manitoba, Winnipeg 1982.Google Scholar
  82. 82.
    Costin, L. S.: The effect of loading rate and temperature on the initiation of fracture in a mild, rate sensitive steel, Brown University Report No NSF ENG77–07798/2, Providence 1978.Google Scholar
  83. 83.
    Dormeval, R., J. M. Chevalier and M. Stelly: Fracture initiation of metals at high loading rates, in: Advances in Fracture Research, (Ed. D. François), Pergamon Press, Oxford 1981, 355.Google Scholar
  84. 84.
    Couque H., J. Duffy and R. J. Asaro: Effects of prior austenite and ferrite grain size on fracture properties of a plain carbon steel, Brown University Report No DAAG 29 81-K-0121/7, Providence 1984.Google Scholar
  85. 85.
    Ohlson, N. G.: Determination of crack initiation at high strain rates, in: Mechanical Properties at High Rates of Strain, (Ed. J. Harding) 1979, The Institute of Physics, Bristol 1979, 215.Google Scholar
  86. 86.
    Kishida, K., T. Yokoyama and M. Nakano: Measurement of dynamic fracture toughness based on the split Hopkinson bar technique, in: Mechanical Properties at High Rates of Strain, 1984 (Ed. J. Harding), The Institute of Physics, Bristol 1984, 221.Google Scholar
  87. 87.
    Lindholm, U. S. and L. M. Yakley: High strain-rate testing: tension and compression, Exp. Mech., 8 (1968), 1.Google Scholar
  88. 88.
    Corran, R. S. J., F. G. Benitez, J. Harding and C. Ruiz: A discussion of pro blems encountered in the dynamic fracture toughness, in: Mechanical Properties at High Rates of Strain, 1984 (Ed. J. Harding), The Institute of Physics, Bristol 1984, 253.Google Scholar
  89. 89.
    Couque, H., S. J. Hudak and U. S. Lindholm: On the use of coupled pressure bars to measure the dynamic fracture initiation and crack propagation toughness of pressure vessel steels, in: Proc. Int. Conf. on Mech. and Phys. Behaviour of Materials Under Dynamic Loading, Les éditions de physique 1988, C3–347.Google Scholar
  90. 90.
    Lipinski, P. and J. R. Klepaczko: A new experimental method in determining crack propagation transition temperature in steel, Int. J. Solids and Struct., 18 (1982), 1129.Google Scholar
  91. 91.
    Bensussan, Ph.: Fracture dynamics of 35 NCD 16 steel, in: Proc. Int. Conf. on Mech. and Phys. Behaviour of Materials Under Dynamic Loading, Les éditions de physique 1988, C3–199, (in French).Google Scholar
  92. 92.
    Dharan, C. K. H. and F. E. Hauser: Determination of stress-strain characteristics at very high strain rates, Exp. Mech., 10 (1970), 370.Google Scholar
  93. 93.
    Tobota, A., J. R. Klepaczko and J. Gronostajski: Application of the rotational hammer for dynamic tensile tests, Theoretical and Applied Mechanics, 18 (1980), 258.Google Scholar
  94. 94.
    Kawata, K., S. Hashimoto, K. Kurokawa and N. Kanayama: A new testing method for the characterization of materials in high-velocity tension, in: Mechanical Properties at High Rates of Strain, 1979 (Ed. J. Harding), The Institute of Physics, Bristol 1979, 71.Google Scholar
  95. 95.
    Lipinski, P.: Propagation transition temperature and crack dynamics in structural steel, Report of Institute Fundamental Technological Research, Warsaw 1980, (in Polish).Google Scholar
  96. 96.
    Nadai, A.: Theory of Flow and Fracture of Solids, McGraw-Hill, New York 1950, 81.Google Scholar
  97. 97.
    Nicholas, T.: Instrumented impact testing using a Hopkinson bar apparatus, Technical Report AFML-TR-7554, Wright-Patterson AFB, Ohio 1975.Google Scholar
  98. 98.
    Nicholas, T.: Notched bend behavior of beryllium over a wide range of strain rates, Technical Report AFML-TR-75–177, Wright-Patterson AFB, Ohio 1975.Google Scholar
  99. 99.
    Mines, R. A. W. and C. Ruiz: The dynamic beheviour of the instrumented Charpy test, in: Proc. Int. Conf. on Mech. and Phys. Behaviour of Materials Under Dynamic Loading, Les éditions de physique 1985, C5–187.Google Scholar
  100. 100.
    Tanaka, K. and T. Kagatsume: Impact bending test on steel at low temperatures, Bull. JSME, 23 (1980), 1736.Google Scholar
  101. 101.
    Yokoyama, T. and K. Kishida: A novel impact three-point bend test method for determining dynamic fracture initiation toughness, Proc. Int. Conf. on Fracture and Fracture Mechanics, Shangai 1987, 553.Google Scholar
  102. 102.
    Yokoyama, T. and K. Kishida: Measurement of dynamic fracture initiation toughness by a novel impact three-point bend test technique using Hopkinson pressure bars, in: Impact Loading and Dynamic Behaviour of Materials, DGM Informationsgesellschaft Verlag, Oberursel 1988, 273.Google Scholar
  103. 103.
    Hurd, N. J. and P. E. Irwing: A comparison of Mode HI and Mode I toughness in quenched and tempered steels, in: Fracture and Fatigue, Proc. 3rd Colloquium on Fracture (Ed. J. C. Radon), Pergamon Press, Oxford 1980, 239.Google Scholar
  104. 104.
    Tsangarakis, S.: Fracture behavior of 4340 steel under Mode III loading, Engng. Fract. Mech., 16 (1982), 569.Google Scholar
  105. 105.
    Tsangarakis, S.: The dependence of Mode III fracture initiation toughness on strength and microstructure, Engng. Fract. Mech., 19 (1984), 903.Google Scholar
  106. 106.
    Gupte, K. A. and S. Banerjee: Fracture of round bars loaded in Mode III and a procedure for KIIIc determination, Engng. Fract. Mech., 19 (1984), 919.Google Scholar
  107. 107.
    Tada, H.: The Stress Analysis of Cracks Handbook, Del Res. Corp., Heller-town 1973.Google Scholar
  108. 108.
    Hult, J. A. H. and F. A. McClintock: Elastic-plastic stress and strain distributions around sharp notches under repeated shear, Proc. 9thf IUTAM Int. Congress, University of Brussels, 8 (1957), 51.Google Scholar
  109. 109.
    Yates, J. R.: Crack tip plastic zone sizes in cylindrical bars subjected to torsion, Fatigue Fract. Engng Mater. Struct., 10 (1987), 471.Google Scholar
  110. 110.
    Nkule, L.: Tests on Fracture Toughness in Mode HI at High Rate for XC48 Steel, Ph. D. Thesis, ENSM Nantes 1985; (in French).Google Scholar
  111. 111.
    Klepaczko, J. R. and L. Nkule: A new experimental test method for dynamic fracture initiation in Mode HI, in preparation.Google Scholar
  112. 112.
    Charpy, G.: On testing metals by the bending of notched bars (translation of the original paper from Mémoires de la Société des Ingénieurs Civils de France, 1904, p. 468), Int. J. Fract., 25 (1984), 287.Google Scholar
  113. 113.
    Impact Testing of Materials, ASTM STP 466, American Society for Testing and Materials, Philadelphia 1969.Google Scholar
  114. 114.
    Instrumented Impact Testing, ASTM STP 563, American Society for Testing and Materials, Philadelphia 1974.Google Scholar
  115. 115.
    Ireland, D. R.: Procedures and problems associated with reliable control of the instrumented impact test, ASTM STP 563, Philadelphia 1974, 3.Google Scholar
  116. 116.
    Barsom, J. M. and S. T. Rolfe: Fracture Fatigue Control in Structures, Prentice-Hall, Englewood Cliffs 1987.Google Scholar
  117. 117.
    Barsom, J. M. and S. T. Rolfe: Correlations between KIc and Charpy V-notch test results in the transition temperature range, ASTM STP 466, American Society for Testing and Materials, Philadelphia 1969, 281.Google Scholar
  118. 118.
    Norris, D. M.: Computer simulation of the Charpy V-notch toughness test, Engng. Fract. Mech., 11 (1979), 261.Google Scholar
  119. 119.
    Kalthoff, J. F.: Determination of the dynamic fracture toughness KId in impact tests by means of response curve, in: Advances in Fracture Research, (Ed. D. François), Pergamon Press, Oxford 1981, 363.Google Scholar
  120. 120.
    Rintamaa, R. and C. Zimmermann: Advanced instrumented impact testing facility for characterization of dynamic fracture behavior, Nucl. Engng. and Design, 96 (1986), 159.Google Scholar
  121. 121.
    Rintamaa, R., K. Rahka, K. Wallin, K. Ikonen, H. Talja, H. Kotilainen and E. Sirkkola: Instrumented impact testing machine with reduced specimen oscillation effects, Research Report of Technical Research Centre of Finland, Espoo 1984.Google Scholar
  122. 122.
    Williams, J. G.: The analysis of dynamic fracture using lumped mass-spring models, Int. J. Fract., 33 (1987), 47.Google Scholar
  123. 123.
    Williams, J. G. and G. C. Adams: The analysis of instrumented impact tests using a mass-spring model, Int. J. Fract., 33 (1987), 209.Google Scholar
  124. 124.
    Williams J. G. and M. N. M. Badi: The effect of damping on the spring-mass dynamic fracture model, Int. J. Fract., 39 (1989), 147.Google Scholar
  125. 125.
    Kishimoto, K., S. Akoi and M. Sakata: Simple formula for dynamic stress intensity factor of precracked Charpy specimen, Engng. Fract. Mech., 13 (1980), 501.Google Scholar
  126. 126.
    Kishimoto, K., S. Akoi and M. Sakata: Dynamic fracture mechanics parameter estimation for three-point bend specimen in large scale yielding, in: Impact Loading and Dynamic Behaviour of Materials, DGM Informationsgesellschaft Verlag, Oberursel 1988, 129.Google Scholar
  127. 127.
    Nash, G.: An analysis of the force and bending moments generated during the notched beam impact test, Int. J. Fract. Mech., 5 (1969), 269.Google Scholar
  128. 128.
    Macke, T.: Development and analysis of a method for material characterization under impact; Application for testing of fracture toughness of composites with ceramic or metallic matrix, Ph. D. Thesis, University of Bordeaux, Talence 1988; (in French).Google Scholar
  129. 129.
    Macke, T., J. J. Balette and J. M. Quenisset: A method for evaluation of dynamic toughness and impact loading resistance, in: Impact Loading and Dynamic Behaviour of Materials, DGM Informationsgesellschaft Verlag, Oberursel 1988, 289.Google Scholar
  130. 130.
    Tvergard, V. and A. Needleman: Effect of material rate sensitivity on failure modes in the Charpy V-notch test, J. Mech. Phys. Solids, 34 (1986), 213.Google Scholar
  131. 131.
    Theocaris, P. S. and G. A. Papadopoulos: Interrelation between static and dynamic stress intensity factors and their evaluation by caustics, J. of Strain Analysis, 19 (1984), 127.Google Scholar
  132. 132.
    Kalthoff, J. F.: The shadow optical method of caustics, in: Handbook on Experimental Mechanics, Ch. 9, (Ed. A. S. Kobayashi), Prentice Hall, Engle-wood Cliffs, 1985.Google Scholar
  133. 133.
    Rosakis, A. J. and A. T. Zehner: Caustics by reflection and their application to elastic-plastic and dynamic fracture mechanics, in: Proc. SPIE Conference on Photomechanics and Speckle Metrology, San Diego, 1987.Google Scholar
  134. 134.
    Zehner, A. T. and A. J. Rosakis: Dynamic fracture initiation and propagation in 4340 steel under impact loading, Calif. Inst. of Technology, GAL, SM Report 86–6, 1986.Google Scholar
  135. 135.
    Klepaczko, J. R. and A. Solecki: Effect of tempering on quasi-static and impact fracture toughness and mechanical properties for 5110 H steel, Met. Trans. A, 15A (1984), 901.Google Scholar
  136. 136.
    Zhurkov, S. N.: Kinetic concept of the strongth of solids, Int. J. Fracture, 1 (1965), 311.Google Scholar
  137. 137.
    Dahl, W., W. Hesse, A. Krabiell and H. J. Rosezin: Influence of yielding behaviour and stress-strain law on the failure analysis, Nucl. Engng. Design, 76 (1983), 309.Google Scholar
  138. 138.
    McGregor, C. W. and J. C. Fisher: A velocity-modified temperature for the plastic flow of metals, J. Appl. Mech., 68 (1946), A11.Google Scholar
  139. 139.
    Hahn, G. T., R. G. Hoagland and A. R. Rosenfield: The variation of KIc with temperature and loading rate, Met. Trans., 2 (1971), 537.Google Scholar
  140. 140.
    Ritchie, R. O., W. L. Server and R. A. Wullaert: Critical fracture stress and fracture strain models for the prediction of lower and upper shelf toughness in nuclear pressure vessel steels, Met. Trans. A, 10A (1979), 1557.Google Scholar
  141. 141.
    Ritchie, R. O., J. F. Knott and J. R. Rice: On the relationship between critical tensile stress and fracture toughness in mild steel, J. Mech. Phys. Solids, 21 (1973), 395.Google Scholar
  142. 142.
    Rice, J. R. and G. F. Rosengreen: Plane strain deformation near a crack tip in a power-law hardening material, J. Mech. Phys. Solids, 16 (1968), 1.MATHGoogle Scholar
  143. 143.
    Hutchinson, J. W.: Singular behavior at the end of a tensile crack in a hardening material, J. Mech. Phys. Solids, 16 (1968), 13.MATHGoogle Scholar
  144. 144.
    McClintock, F. A.: Plasticity aspects of fracture, in: Fracture, An Advanced Treatise (Ed. H. Liebowitz), Vol. III, Academic Press, New York 1971, 48.Google Scholar
  145. 145.
    Kalthoff, J. F.: Fracture behavior under high rate of loading, Rep. Z5/85 Fraunhofer-Institut für Werkstoffmechanik, Freiburg 1985.Google Scholar
  146. 146.
    Rosenfield, A. R. and G. T. Hahn: Numerical description of the ambient low-temperature, and high-strain rate flow and fracture behavior of plain carbon steel, Trans. ASM, 59 (1966), 962.Google Scholar
  147. 147.
    Hahn, G. T.: The influence of microstructure on brittle fracture toughness, Met. Trans. A, 15A (1984), 947.Google Scholar
  148. 148.
    Krafft, J. M. and G. Irwin: Crack velocity considerations, in: Fracture Toughness Testing and Its Applications, ASTM STP 381, American Society for Testing and Materials, Philadelphia 1965, 84.Google Scholar
  149. 149.
    Krafft, J. M.: Correlation of plane strain crack toughness with strain hardening characteristics of a low, a medium and a high strength steel, Appl. Mat. Res., 3 (1964), 88.Google Scholar
  150. 150.
    Campbell, J. D.: Dynamic Plasticity, CISM Udine, 1997.Google Scholar
  151. 151.
    Broek, D.: Elementary Engineering Fracture Mechanics, Martinus Nij-hoff Publ., Dordrecht 1987.MATHGoogle Scholar
  152. 152.
    Campbell, J. D.: The dynamic yielding of mild steel, Acta Metall., 1 (1953), 706.Google Scholar
  153. 153.
    Shockey, D. A., J. F. Kalthoff and D. C. Erlich: Evaluation of dynamic crack instability criteria, Int. Journ. of Fracture, 22 (1983), 217.Google Scholar
  154. 154.
    Shockey, D. A., J. F. Kalthoff, H. Homma and D. C. Erlich: Short pulse fracture mechanics, in: Dynamic Fracture (Eds. W. G. Knauss, K. Ravi-Chandar and A. J. Rosakis) Caltech, Pasadena 1983, 57.Google Scholar
  155. 155.
    Homma, H., D. A. Shockey and Murayama: Response of cracks in structural materials to short pulse loads, J. Mech. Phys. Solids, 31 (1983), 261.Google Scholar
  156. 156.
    Buchar, J.: The effect of strain rate sensitivity on crack initiation under dynamic loading, in: IUTAM Symposium (Eds. K. Kawata and J. Shioiri) Springer Verlag, Berlin 1985, 428.Google Scholar
  157. 157.
    Kalthoff, J. F., D. A. Shockey and H. Homma: Short pulse fracture mecha nics, in: Mechanical Properties at High Rates of Strain, 1984 (Ed. J. Har ding), The Institute of Physics, Bristol 1984, 205.Google Scholar
  158. 158.
    Freund, L. B.: Crack propagation in an elastic solid subjected to general loading, III stress wave loading, J. Mech. Phys. Solids, 21 (1973), 47.MATHGoogle Scholar
  159. 159.
    Tuler, F. R. and B. M. Butcher: A criterion for the time dependence of dynamic fracture, Int. J. Fract. Mech., 4 (1968), 431.Google Scholar

Copyright information

© Springer-Verlag Wien 1990

Authors and Affiliations

  • J. R. Klepaczko
    • 1
  1. 1.University of MetzMetzFrance

Personalised recommendations