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Fracture testing and design

  • Chapter
Mechanical damage and crack growth in concrete

Part of the book series: Engineering Application of Fracture Mechanics ((EAFM,volume 5))

Abstract

Preliminary remarks. One of the major problems in analyzing the strength of materials is the so-called ‘size effect’. Despite the numerous research efforts, this effect is still not completely understood. Two important aspects of size effects are:

  1. (1)

    Uncracked structures show an increase in brittleness when their size is increased, and

  2. (2)

    Notched (or cracked) structures become less sensitive to the presence of mechanical imperfections when their size is decreased and they tend to behave in a more ductile fashion.

These two effects have been known for a long time, but it is only recently that a consistent explanation could be given in terms of Fracture Mechanics concepts. The two fundamental failure modes known classically are brittle fracture and plastic collapse both of which may occur depending on the combination of the load and geometric variables. Although Plastic Limit Analysis can be applied to treat the failure of structures due to excessive distortion and Linear Elastic Fracture Mechanics to the onset of rapid fracture, both of these disciplines apply only at the global scale level. They cannot address failure by yielding and fracture [1–9] that is the rule in practice rather than the exception.

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References

  1. Carpinteri, A., Size effect in fracture toughness testing: a dimensional analysis approach, Analytical and Experimental Fracture Mechanics, edited by G.C. Sih and M. Mirabile, Sijthoff and Noordhoff, pp. 785–797 (1981).

    Google Scholar 

  2. Carpinteri, A., Notch sensitivity in fracture testing of aggregative materials, Engineering Fracture Mechanics, 16, pp. 467–481 (1982).

    Article  Google Scholar 

  3. Carpinteri, A., Static and energetic fracture parameters for rocks and concretes, Materials and Structures (RILEM), 14, pp. 151–162 (1981).

    Google Scholar 

  4. Carpinteri, A., Application of fracture mechanics to concrete structures, Journal of the Structural Division, American Society of Civil Engineers, 108, pp. 833–848 (1982).

    Google Scholar 

  5. Carpinteri, A., Plastic flow collapse versus separation collapse in elastic-plastic strain-hardening structures, Materials and Structures (RILEM), 16, pp. 85–96 (1983).

    Google Scholar 

  6. Carpinteri, A., Size effects in solid mechanics due to topology transformation during crack growth, Application of Fracture Mechanics to Materials and Structures, edited by G.C. Sih, E. Sommer and W. Dahl, Martinus Nijhoff Publishers, pp. 281–293 (1984).

    Google Scholar 

  7. Carpinteri, A., Marega, C. and Savadori, A., Ductile-brittle transition by varying structural size, Engineering Fracture Mechanics, 21, pp. 263–271 (1985).

    Article  Google Scholar 

  8. Carpinteri, A., Size effects in material strength due to crack growth and material non-linearity, Theoretical and Applied Fracture Mechanics, 1, pp. 39–46 (1984).

    Article  Google Scholar 

  9. Carpinteri, A., Scale effects in fracture of plain and reinforced concrete structures, Fracture Mechanics of Concrete: Structural Application and Numerical Calculation, edited by G.C. Sih and A. DiTommaso, Martinus Nijhoff Publishers, The Hague, pp. 95–140 (1984).

    Google Scholar 

  10. Peterson, R.E., Model testing as applied to strength of materials, Journal of Applied Mechanics, 1, pp. 79–85 (1933).

    Google Scholar 

  11. Standard Method of Test for Plane Strain Fracture Toughness of Metallic Materials, E 399-74, ASTM.

    Google Scholar 

  12. Carpinteri, A. and Sih, G.C., Damage accumulation and crack growth in bilinear materials with softening: Application of Strain Energy Density Theory, Journal of Theoretical and Applied Fracture Mechanics, Vol. 1, No. 2, pp. 145–160 (1984).

    Article  Google Scholar 

  13. Sih, G.C., Mechanics of material damage in concrete, Fracture Mechanics of Concrete: Material Characterization and Testing, edited by A. Carpinteri and A.R. Ingraffea, Martinus Nijhoff Publishers, The Hague, pp. 1–29 (1984).

    Google Scholar 

  14. Sih, G.C., Non-linear response of concrete: Interaction of size, loading step and material property, Applications of Fracture Mechanics to Cementitious Composites, edited by S.P. Shah, Martinus Nijhoff Publishers, The Hague, pp. 3–23 (1984).

    Google Scholar 

  15. Dugdale, D.S., Yielding of steel sheets containing slits, Journal of Mechanics and Physics of Solids, 8, pp. 100–104 (1960).

    Article  ADS  Google Scholar 

  16. Irwin, G.R., Analysis of stresses and strains near the end of a crack traversing a plate, Journal of Applied Mechanics, 24, pp. 361–364 (1957).

    Google Scholar 

  17. Nadai, A., Theory of flow and fracture of solids, McGraw-Hill Book Co., New York, Vol. I and II (1950).

    Google Scholar 

  18. Sih, G.C., Introductory chapters of mechanics of fracture, Vol. I to VII, edited by G.C. Sih, Martinus Nijhoff Publishers, The Hague (1973)–1981).

    Google Scholar 

  19. Sih, G.C., Mechanics and Physics of Energy Density Theory, J of Theoretical and Applied Fracture Mechanics, Vol. 4, No. 3 pp. 157–173 (1985).

    Article  MathSciNet  Google Scholar 

  20. Glucklich, J. and Cohen, L.J., Size as a factor in the brittle-ductile transition and the strength of some materials, International Journal of Fracture Mechanics, 3, pp. 278–289 (1967).

    Article  Google Scholar 

  21. Kaplan, M.F., Crack propagation and the fracture of concrete, Journal of the American Concrete Institute, 58, pp. 591–610 (1961).

    Google Scholar 

  22. Romualdi, J.P. and Batson, G.B., Mechanics of crack arrest in concrete, Journal of the Engineering Mechanics Division, American Society of Civil Engineers, 89, pp. 147–168 (1963).

    Google Scholar 

  23. Glucklich, J., Fracture of plain concrete, Journal of the Engineering Mechanics Division, American Society of Civil Engineers, 89, pp. 127–136 (1963).

    Google Scholar 

  24. Naus, D.J. and Lott, J.L., Fracture toughness of Portland cement concretes, Journal of the American Concrete Institute, 66, pp. 481–489 (1969).

    Google Scholar 

  25. Welch, G.B. and Haisman, B., The application of fracture mechanics to concrete and the measurement of fracture toughness, Materials and Structures (RILEM), 2, pp. 171–177 (1969).

    Google Scholar 

  26. Moavenzadeh, F. and Kuguel, R., Fracture of concrete, Journal of Materials, 4, pp. 497–519 (1969).

    Google Scholar 

  27. Desayi, P., Fracture of concrete in compression, Materials and Structures (RILEM), 10, pp. 139–144 (1969).

    Google Scholar 

  28. Shah, S.P. and McGarry, F.J., Griffith fracture criterion and concrete, Journal of the Engineering Mechanics Division, American Society of Civil Engineers, 97, pp. 1663–1675 (1971).

    Google Scholar 

  29. Brown, J.H., Measuring the fracture toughness of cement paste and mortar, Magazine of Concrete Research, 24, pp. 185–196 (1972).

    Google Scholar 

  30. Brown, J.H., The failure of glass-fibre-reinforced notched beams in flexure, Magazine of Concrete Research, 25, pp. 31–38 (1973).

    Google Scholar 

  31. Brown, J.H. and Pomeroy, C.D., Fracture toughness of cement paste and mortars, Cement and Concrete Research, 3, pp. 475–480 (1973).

    Article  Google Scholar 

  32. Naus, D.J., Batson, G.B. and Lott, J.L., Fracture mechanics of concrete, Fracture Mechanics of Ceramics, edited by R.C. Bradt, D.P.H. Hasselman and F.F. Lange, Vol. 2, Plenum Press, pp. 469–481 (1974).

    Google Scholar 

  33. Walsh, P.F., Crack initiation in plain concrete, Magazine of Concrete Research, 28, pp. 37–41 (1976).

    Article  ADS  Google Scholar 

  34. Higgins, D.D. and Bailey, J.E., Fracture measurements on cement paste, Journal of Materials Science, 11, pp. 1995–2003 (1976).

    Article  ADS  Google Scholar 

  35. Schmidt, R.A., Fracture-toughness testing of limestone, Experimental Mechanics, 16, pp. 161–167 (1976).

    Article  Google Scholar 

  36. Evans, A.G., Clifton, J.R. and Anderson, E., The fracture mechanics of mortars, Cement and Concrete Research, 6, pp. 535–548 (1976).

    Article  Google Scholar 

  37. Mindess, S. and Nadeau, J.S., Effect of notch width on K IC for mortar and concrete, Cement and Concrete Research, 6, pp. 529–534 (1976).

    Article  Google Scholar 

  38. Bear, T.J. and Barr, B., Fracture toughness tests for concrete, International Journal of Fracture, 13, pp. 92–96 (1977).

    Article  Google Scholar 

  39. Barr, B. and Bear, T.J., A simple test of fracture toughness, Concrete, 10, pp. 25–27 (1976).

    Google Scholar 

  40. Barr, B. and Bear, T.J., Fracture toughness, Concrete, 11, pp. 30–32 (1977).

    Google Scholar 

  41. Henry, J.P. and Paquet, J., La ténacité des roches calcaires: influence des paramètres microstructuraux et de l’environment, Mechanics Research Communications, 4, pp. 193–198 (1977).

    Article  Google Scholar 

  42. Henry, J.P., Paquet, J. and Tancrez, J.P., Experimental study of crack propagation in calcite rocks, International Journal of Rock Mechanics, Mining Science and Geomechanics, 14, pp. 85–91 (1977).

    Article  Google Scholar 

  43. Henry, J.P. and Paquet, P., Résistance des Matériaux, C.R. Acad. Sc., Paris, 284, pp. 511–514 (1977).

    Google Scholar 

  44. Hillemeier, B. and Hilsdorf, H.K., Fracture mechanics studies on concrete compounds, Cement and Concrete Research, 7, pp. 523–536 (1977).

    Article  Google Scholar 

  45. Gjørv, O.E., Sørensen, S.I. and Arnesen, A., Notch sensitivity and fracture toughness of concrete, Cement and Concrete Research, 7, pp. 333–344 (1977).

    Article  Google Scholar 

  46. Cook, D.J. and Crookham, G.D., Fracture toughness measurements of polymer concrete, Magazine of Concrete Research, 30, pp. 205–214 (1978).

    Article  Google Scholar 

  47. Swartz, S.E., Hu, K.K. and Jones, G.L., Compliance monitoring of crack growth in concrete, Journal of the Engineering Mechanics Division, American Society of Civil Engineers, 104, pp. 789–800 (1978).

    Google Scholar 

  48. Strange, P.C. and Bryant, A.H., Experimental tests on concrete fracture, Journal of the Engineering Mechanics Division, American Society of Civil Engineers, 105, pp. 337–342 (1979).

    Google Scholar 

  49. Sok, C. and Baron, J., Mécanique de la rupture appliquée au béton hydraulique, Cement and Concrete Research, 9, pp. 641–648 (1979).

    Article  Google Scholar 

  50. Swamy, R.N., Fracture mechanics applied to concrete, Developments in Concrete Technology, Vol. 1, edited by F.D. Lydon, Applied Science Publishers LTD, pp. 221–281 (1979).

    Google Scholar 

  51. Ziegeldorf, S., Müller, H.S. and Hilsdorf, H.K., A model law for the notch sensitivity of brittle materials, Cement and Concrete Research, 10, pp. 589–599 (1980).

    Article  Google Scholar 

  52. Ziegeldorf, S., Müller, H.S. and Hilsdorf, H.K., Effect of aggregate particle size on mechanical properties of concrete, Proceedings of the 5th International Conference on Fracture, Cannes, pp. 2243–2251 (1981).

    Google Scholar 

  53. Carpinteri, A., Experimental determination of fracture toughness parameters K IC and J IC for aggregative materials, Proceedings of the 5th International Conference on Fracture, Cannes, pp. 1491–1498 (1981).

    Google Scholar 

  54. Saouma, V.E., Ingraffea, A.R. and Catalano, D.M., Fracture toughness of concrete — K IC revisited, Report 80-9, Department of Structural Engineering, Cornell University (1980).

    Google Scholar 

  55. Kesler, C., Naus, D. and Lott, J., Fracture mechanics — Its applicability to concrete, Proceedings of the International Conference on Mechanical Behavior of Materials, Vol. IV, pp. 113–124 (1971).

    Google Scholar 

  56. Mai, Y.W., Foote, R.M.L. and Cotterell, B., Size effects and scaling laws of fracture in asbestos cement, The International Journal of Cement Composites, 2, pp. 23–34 (1980).

    Google Scholar 

  57. Mai, Y.W. and Atkins, A.G., Scale effects and crack propagation in non-linear elastic structures, International Journal of Mechanical Science, 17, pp. 673–675 (1975).

    Article  MATH  Google Scholar 

  58. Mai, Y.W. and Atkins, A.G., Crack propagation in nonproportionally scaled elastic structures, International Journal of Mechanical Science, 20, pp. 437–449 (1978).

    Article  MATH  Google Scholar 

  59. Visalvanich, K. and Naaman, A.E., Fracture methods in cement composites, Journal of the Engineering Mechanics Division, American Society of Civil Engineers, 107, pp. 1155–1171 (1981).

    Google Scholar 

  60. Petersson, P.E., Crack growth and development of fracture zones in plain concrete and similar materials, Report TVBM-1006, Division of Building Materials, Lund Institute of Technology (1981).

    Google Scholar 

  61. Arrea, M. and Ingraffea, A.R., Mixed mode crack propagation in mortar and concrete, Report 81-13, Department of Structural Engineering, Cornell University (1982).

    Google Scholar 

  62. Hillerborg, A. and Petersson, P.E., Determination of the fracture energy of mortar and concrete by use of three-point bend tests on notched beams, Proposed RILEM Recommendation, 29th January, 1982.

    Google Scholar 

  63. Hillerborg, A., Concrete fracture energy tests performed by 9 laboratories according to a draft RILEM recommendation, Report TVBM-3015, Division of Building Materials, Lund Institute of Technology (1983).

    Google Scholar 

  64. Ferrara, G. and Imperato, L., Il parametro G F nella meccania della frattura del calcestruzzo; influenza della geometria di prova e del tipo di aggregato, XI Congresso AIAS, Torino, pp. 189–200 (1983).

    Google Scholar 

  65. Carpinteri, An., Dimensional analysis implications of the fictitious crack model, Engineering Fracture Mechanics, 22, pp. 327–333 (1985).

    Article  Google Scholar 

  66. Hillerborg, A., Additional concrete fracture energy tests performed by 6 laboratories according to a draft RILEM recommendation, Report TVBM-3017, Division of Building Materials, Lund Institute of Technology (1984).

    Google Scholar 

  67. Mindess, S., The cracking and fracture of concrete: an annotated bibliography, Fracture Mechanics of Concrete, edited by F.H. Wittmann, Elsevier Science Publishers B.V., pp. 539–661 (1983).

    Google Scholar 

  68. Mindess, S., Fracture toughness testing of cement and concrete, Fracture Mechanics of Concrete: Material Characterization and Testing, edited by A. Carpinteri and A.R. Ingraffea, Martinus Nijhoff Publishers, pp. 67–110 (1984).

    Google Scholar 

  69. Weibull, W., A statistical theory of the strength of materials, Swedish Royal Institute for Engineering Research, Stockholm (1939).

    Google Scholar 

  70. Jayatilaka, A.S., Fracture of Engineering Brittle Materials, Applied Science Publishers LTD, London (1979).

    Google Scholar 

  71. Freudenthal, A.M., Statistical approach to brittle fracture, Fracture: An Advanced Treatise, edited by H. Liebowitz, Vol. II, pp. 592–619 (1968).

    Google Scholar 

  72. Leicester, R.H., Effect of size on the strength of structures, Paper No. 71, Division of Building Research, Forest Products Laboratory, C.S.I.R.O., Melbourne (1973).

    Google Scholar 

  73. Bazant, Z.P., Size effect in blunt fracture: concrete, rock, metal, Journal of Engineering Mechanics, American Society of Civil Engineers, 110, pp. 518–535 (1984).

    Google Scholar 

  74. Sih, G.C., Handbook of Stress-Intensity Factors for Researchers and Engineers, Lehigh University (1973).

    Google Scholar 

  75. Carpinteri, A., DiTommaso, A. and Viola, E., Collinear stress effect on the crack branching phenomenon, Materials and Structures (RILEM), 12, pp. 439–446 (1979).

    Google Scholar 

  76. DiLeonardo, G., Fracture toughness characterization of materials under multiaxial loading, International Journal of Fracture, 15, pp. 537–552 (1979).

    Article  Google Scholar 

  77. Williams, M.L., Stress singularities resulting from various boundary conditions in angular corners of plates in extension, Journal of Applied Mechanics, 19, pp. 526–528 (1952).

    Google Scholar 

  78. Viola, E. and Piva, A., Two arc cracks around a circular rigid inclusion, Meccanica, 15, pp. 166–176 (1980).

    Article  MATH  Google Scholar 

  79. Hatano, T., Theory of failure of concrete and similar brittle solid on the basis of strain, International Journal of Fracture Mechanics, 5, pp. 73–79 (1969).

    Article  Google Scholar 

  80. Hutchinson, J.W., Singular behavior at the end of a tensile crack in a hardening material, Journal of the Mechanics and Physics of Solids, 16, pp. 13–31 (1968).

    Article  ADS  MATH  Google Scholar 

  81. Rice, J.R. and Rosengren, G.F., Plane strain deformation near a crack tip in a power-law hardening material, Journal of the Mechanics and Physics of Solids, 16, pp. 1–12 (1968).

    Article  ADS  MATH  Google Scholar 

  82. Comben, A.J., The effect of depth on the strength properties of timber beams, Special Report No. 12, Department of Scientific and Industrial Research, London (1957).

    Google Scholar 

  83. Richards, C.W., Size effect in the tension test of mild steel, Proceedings of the American Society for Testing and Materials, 54, pp. 995–1000 (1954).

    Google Scholar 

  84. Sabnis, G.M. and Mirza, S.M., Size effects in model concretes? Journal of the Structural Division, American Society of Civil Engineers, 105, pp. 1007–1020 (1979).

    Google Scholar 

  85. Hauser, F.E., Landon, P.R. and Dorn, J.E., Fracture of magnesium alloys at low temperature, Journal of Metals, pp. 589–593 (1956).

    Google Scholar 

  86. Hillerborg, A., Modeer, M. and Petersson, P.E., Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements, Cement and Concrete Research, 6, pp. 773–782 (1976).

    Article  Google Scholar 

  87. Heilmann, H.G., Hilsdorf, H.H. and Finsterwalder, K., Festigkeit und Verformung von Beton unter Zugspannungen, Deutscher Ausschuss für Stahl-beton, 203 (1969).

    Google Scholar 

  88. Rice, J.R., The localization of plastic deformation, Theoretical and Applied Mechanics, Proceedings of the 14th IUTAM Congress, Delft, pp. 207–220 (1976).

    Google Scholar 

  89. Needleman, A. and Rice, J.R., Limits to ductility set by plastic flow localization, Mechanics of Sheet Metal Forming, edited by Donald P. Koistinen and Neng-Ming Wang, Plenum Publishing Corporation, pp. 237–265 (1978).

    Google Scholar 

  90. Bazant, Z.P. and Oh, B.H., Concrete fracture via stress-strain relations, Report 81-10/665c, Center for Concrete and Geomaterials, Northwestern University (1981).

    Google Scholar 

  91. Carpinteri, A., Interpretation of the Griffith instability as a bifurcation of the global equilibrium, Application of Fracture Mechanics to Cementitious Composites, NATO-ARW, Sept. 4–7, 1984. Northwestern University, edited by S.P. Shah, Martinus Nijhoff Publishers, pp. 287–316 (1985).

    Google Scholar 

  92. Maier, G., On structural instability due to strain-softening, IUTAM Symposium on Instability of Continuous Systems, Herrenhalb (Germany), Springer Verlag, pp. 411–417 (1971).

    Google Scholar 

  93. Maier, G., Zavelani, A. and Dotreppe, J.C., Equilibrium branching due to flexural softening, Journal of the Engineering Mechanics Division, American Society of Civil Engineers, 99, pp. 897–901 (1973).

    Google Scholar 

  94. Bazant, Z.P., Instability, ductility and size effect in strain-softening concrete, Journal of the Engineering Mechanics Division, American Society of Civil Engineers, 102, pp. 331–344 (1976).

    Google Scholar 

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  1. Istituto di Scienza delle Costruzioni, University of Bologna, Bologna, Italy

    Alberto Carpinteri

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© 1986 Martinus Nijhoff Publishers, Dordrecht

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Carpinteri, A. (1986). Fracture testing and design. In: Mechanical damage and crack growth in concrete. Engineering Application of Fracture Mechanics, vol 5. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4350-6_8

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  • DOI: https://doi.org/10.1007/978-94-009-4350-6_8

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8434-5

  • Online ISBN: 978-94-009-4350-6

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