Probability distribution of energetic-statistical size effect in quasibrittle fracture

Probabilistic Engineering Mechanics

Volumn 19, Issue 4, 2004, Pages 307-319

  Bažant, Zdeněk P ^a  

^a Northwestern University   (United States)

Author keywords

Asymptotic analysis; Extreme value statistics; Failure; Fracture mechanics; Nonlocal continuum; Probability distribution; Quasibrittle materials; Size effect; Weakest link model

Indexed keywords

ASYMPTOTIC STABILITY; BRITTLE FRACTURE; COMPUTER SIMULATION; CRACKS; MONTE CARLO METHODS; RANDOM PROCESSES; WEIBULL DISTRIBUTION;

ASYMPTOTIC ANALYSIS; EXTREME VALUE STATISTICS; FAILURE; NONLOCAL CONTINUUM; QUASIBRITTLE MATERIALS; SIZE EFFECT; WEAKEST LINK MODEL;

PROBABILITY DISTRIBUTIONS;

EID: 4644335245     PISSN: 02668920     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.probengmech.2003.09.003     Document Type: Article

References (58)

1. Bažant Z.P., Planas J. Fracture and size effect in concrete and other quasibrittle materials. 1998;CRC Press, Boca Raton, FL.
2. Bažant Z.P. Scaling of structural strength. 2002;Hermes Penton Science (Kogan Page Science), London, UK.
3. Bažant Z.P. Scaling of quasibrittle fracture: asymptotic analysis. Int J Fract. 83:(1):1997;19-40.
4. Bažant Z.P. Size effects in quasibrittle fracture: apercu of recent results. de Borst R., Mazars J., Pijandier-Cabot J., van Mier J.G.M. Fracture mechanics of concrete structures (Proceedings, FraMCoS-4 International Conference, Paris). 2001;651-658 Balkema, Lisse, Netherlands.
5. Bažant Z.P., Chen E.-P. Scaling of structural failure. Appl Mech Rev ASME. 50:(10):1997;593-627.
6. Bažant Z.P., Li Z. Modulus of rupture: size effect due to fracture initiation in boundary layer. J Struct Engng ASCE. 121:(4):1995;739-746.
7. Bažant Z.P., Li Z. Zero-brittleness size-effect method for one-size fracture test of concrete. J Engng Mech ASCE. 122:(5):1996;458-468.
8. Bažant Z.P. Size effect in tensile and compression fracture of concrete structures: computational modeling and design. Mihashi H., Rokugo K. Fracture mechanics of concrete structures (Third International Conference, FraMCoS-3, Gifu, Japan). 1998;1905-1922 Aedificatio Publishers, Freiburg, Germany.
9. Bažant Z.P. Size effect in blunt fracture: concrete, rock, metal. J Engng Mech, ASCE. 110:1984;518-535.
10. Bažant Z.P., Kazemi M.T. Size effect in fracture of ceramics and its use to determine fracture energy and effective process zone length. J Am Ceram Soc. 73:(7):1990;1841-1853.
11. Bažant Z.P., Daniel I.M., Li Z. Size effect and fracture characteristics of composite laminates. ASME J Engng Mater Technol. 118:(3):1997;317-324.
12. Bažant Z.P., Kim J.-J.H., Daniel I.M., Becq-Giraudon E., Zi G. Size effect on compression strength of fiber composites failing by kink band propagation. Int J Fract. 95:1999;103-141.
13. Fisher R.A., Tippett L.H.C. Limiting forms of the frequency distribution of the largest and smallest member of a sample. Proc Camb Philosoph Soc. 24:1928;180-190.
14. Weibull W. The phenomenon of rupture in solids. Proc R Swedish Inst Engng Res (Ingenioersvetenskaps Akad. Handl.), Stockholm. 153:1939;1-55.
15. Weibull W. A statistical representation of fatigue failures in solids. Proc R Inst Tech No. 27. 1949.
16. Weibull W. A statistical distribution function of wide applicability. J Appl Mech ASME. 1951;18.
17. Epstein B. Statistical aspects of fracture problems. J Appl Phys. 19:1948;140-147.
18. Freudenthal A.M. Physical and statistical aspects of fatigue. In: Advance in applied mechanics. vol. 4:1956;Academic Press, London. p. 117-57.
19. Freudenthal A.M., Gumbel E.J. On the statistical interpretation of fatigue tests. Proc R Soc (Lond) A. 216:1953;309-332.
20. Gumbel E.J. Statistics of extremes. 1958;Columbia University Press, New York.
21. Saibel E. Size effect in structural safety. Proceedings of the International Conference on Structure, Solid Mechanics and Engineering Design in Civil Engineering Materials, Southampton, Part I. 1969;. p. 125-30.
22. Daniels H.E. The statistical theory of the strength of bundles and threads. Proc R Soc Lond. A183:1945;405-435.
23. Harlow D.G., Phoenix S.L. The chain-of-bundles probability model for the strength of fibrous materials. I. Analysis and conjectures. J Compos Mater. 12:1978;195-214.
24. Harlow D.G., Phoenix S.L. The chain-of-bundles probability model for the strength of fibrous materials. ii. A numerical study of convergence. J Compos Mater. 12:1978;314-334.
25. Smith R.L., Phoenix S.L. Asymptotic distributions for the failure of fibrous materials under series-parallel structure and equal load-sharing. J Appl Mech. 48:1981;75-81.
26. Smith R.L. The asymptotic distribution of the strength of a series-parallel system with equal load sharing. Ann Probab. 10:(1):1982;137-171.
27. Phoenix S.L., Smith R.L. A comparison of probabilistic techniques for the strength of fibrous materials under local load-sharing among fibers. Int J Solids Struct. 19:(6):1983;479-496.
28. McCartney L.N., Smith R.L. Statistical theory of the strength of fiber bundles. J Appl Mech. 50:1983;601-608.
29. Phoenix S.L. The stochastic strength and fatigue of fiber bundles. Int J Fract. 14:1983;327-344.
30. Phoenix S.L., Ibnabdeljalil M., Hui C.-Y. Size effects in the distribution for strength of brittle matrix fibrous composites. Int J Solids Struct. 34:(5):1997;545-568.
31. Phoenix S.L., Beyerlein I.J. Distribution and size scalings for strength in a one-dimensional random lattice with load redistribution to nearest and next nearest neighbors. Phys Rev E. 62:(2):2000;1622-1645.
32. Mahesh S., Phoenix S.L., Beyerlein I.J. Strength distributions and size effects for 2D and 3D composites with Weibull fibers in an elastic matrix. Int J Fract. 115:2002;41-85.
33. Bažant Z.P., Novák D. Probabilistic nonlocal theory for quasibrittle fracture initiation and size effect. I. Theory. J Engng Mech ASCE. 126:(2):2000;166-174.
34. Bažant Z.P., Novák D. Probabilistic nonlocal theory for quasibrittle fracture initiation and size effect. II. Application. J Engng Mech ASCE. 126:(2):2000;175-185.
35. Bažant Z.P. Probabilistic modeling of quasibrittle fracture and size effect. Corotis R.B. Proceedings of the Eighth Internationsl Conference on Structural Safety and Reliability (ICOSSAR), Newport Beach, CA. Proceedings of the Eighth Internationsl Conference on Structural Safety and Reliability (ICOSSAR), Newport Beach, CA. 2001:2001;1-23 Swets & Zeitinger/Balkema, Lisse, The Netherlands.
36. Barenblatt G.I. Similarity, self-similarity and intermediate asymptotics. 1979;Consultants Bureau, New York.
37. Barenblatt G.I. Scaling, self-similarity, and intermediate asymptotics. 1996;Cambridge University Press, Cambridge.
38. Bender M.C., Orszag S.A. Advanced mathematical methods for scientists and engineers. 1978;McGraw-Hill, New York. [chapters 9-11].
39. Bažant Z.P., Novák D. Energetic-statistical size effect in quasibrittle failure at crack initiation. ACI Mater J. 97:(3):2000;381-392.
40. Bažant Z.P., Zhou Y., Novák D., Daniel I.M. Size effect in fracture of sandwich structure components: foam and laminate. Proceedings of the ASME International Mechanical Engineering Congress, New York). vol. AMD-TOC:2001;American Society of Mechanical Engineers, New York. (paper 25413), p. 1-12.
41. Freudenthal A.M. Statistical approach to brittle fracture. Liebowitz H. Fracture. vol. 2:1968;591-619 Academic Press, London. [chapter 6].
42. Bažant Z.P., Zhou Y., Novák D., Daniel I.M. Size effect on flexural strength of fiber-composite laminate. ASME J Mater Technol. 2003;. in press.
43. Jackson K.E. Scaling effects in the flexural response and failure of composite beams. AIAA J. 30:(8):1992;2099-2105.
44. Johnson D.P., Morton J., Kellas S., Jackson K.E. Size effect in scaled fiber composites under four-point flexural loading. AIAA J. 38:(6):2000;1047-1054.
45. Wisnom M.R. The effect of specimen size on the bending strength of unidirectional carbon fiber-epoxy. Compos Struct. 18:1991.
46. Wisnom M.R., Atkinson J.A. Reduction in tensile and flexural strength of unidirectional glass fiber-epoxy with increasing specimen size. Compos Struct. 38:1997;405-412.
47. Cottrell A.H. Iron Steel Inst Spec Rep. 69:1963;281.
48. Jirásek M., Bažant Z.P. Inelastic analysis of structures. 2002;Wiley, Chichester, UK.
49. Zech B., Wittmann F.H. A complex study on the reliability assessment of the containment of a PWR. Part II. Probabilistic approach to describe the behavior of materials. Jaeger T.A., Boley T.A. Transaction of the Fourth International Conference on Structural Mechanics in Reactor Technology. vol. H, J1/11:1977;1-14 European Communities, Brussels, Belgium.
50. Bažant Z.P. Energetic and statistical size effects in fiber composites and sandwich structures. A précis of recent progress. Hui D. Proceedings of the 10th International Conference on Composites/Nano Engineering (ICCE-10). 2003;869-872 University of New Orleans.
51. Bažant ZP, Xi Y. Statistical size effect in quasibrittle structures. II. Nonlocal theory. ASCE J of Engineering Mechanics 117(11):2623-2640.
52. Ang A.H.-S., Tang W.H. Probability concepts in engineering planning and design. vol. II. Decision, risk and reliability. 1984;Wiley, New York.
53. Bouchaud J.-P., Potters M. Theory of financial risks: from statistical physics to risk management. 2000;Cambridge University Press, Cambridge.
54. Freudenthal A.M., Garrelts J.M., Shinozuka M. The analysis of structural safety. J Struct Div ASCE. 92:(ST1):1966;619-677.
55. Weibull W. Basic aspects of fatigue. Proceedings of the Colloquium on Fatigue, Stockholm. 1956;Springer, Berlin.
56. Bažant ZP, Yu Q. Designing against size effect on shear strength of reinforced concrete beams without stirrups. Structural engineering report No. 03-02/A466s. Northwestern University, Evanston, Illinois; 2003.
57. Haldar A., Mahadevan S. Probability, reliability and statistical methods in engineering design. 2000;Wiley, New York.
58. Bažant Z.P., Yu Q., Zi G. Choice of standard fracture test for concrete and its statistical evaluation. Intern, J. of Fracture. 128:(11):2002;1331-1336.