Probability distribution of energetic-statistical size effect in quasibrittle fracture

Bažant, 1998 Bažant, 2002 Bažant, 1997, Scaling of quasibrittle fracture: asymptotic analysis, Int J Fract, 83, 19, 10.1023/A:1007387823522 Bažant, 2001, Size effects in quasibrittle fracture: apercu of recent results, 651 Bažant, 1997, Scaling of structural failure, Appl Mech Rev ASME, 50, 593, 10.1115/1.3101672 Bažant, 1995, Modulus of rupture: size effect due to fracture initiation in boundary layer, J Struct Engng ASCE, 121, 739, 10.1061/(ASCE)0733-9445(1995)121:4(739) Bažant, 1996, Zero-brittleness size-effect method for one-size fracture test of concrete, J Engng Mech ASCE, 122, 458, 10.1061/(ASCE)0733-9399(1996)122:5(458) Bažant, 1998, Size effect in tensile and compression fracture of concrete structures: computational modeling and design, 1905 Bažant, 1984, Size effect in blunt fracture: concrete, rock, metal, J Engng Mech, ASCE, 110, 518, 10.1061/(ASCE)0733-9399(1984)110:4(518) Bažant, 1990, Size effect in fracture of ceramics and its use to determine fracture energy and effective process zone length, J Am Ceram Soc, 73, 1841, 10.1111/j.1151-2916.1990.tb05233.x Bažant, 1997, Size effect and fracture characteristics of composite laminates, ASME J Engng Mater Technol, 118, 317, 10.1115/1.2806812 Bažant, 1999, Size effect on compression strength of fiber composites failing by kink band propagation, Int J Fract, 95, 103, 10.1023/A:1018640015465 Fisher, 1928, Limiting forms of the frequency distribution of the largest and smallest member of a sample, Proc Camb Philosoph Soc, 24, 180, 10.1017/S0305004100015681 Weibull, 1939, The phenomenon of rupture in solids, Proc R Swedish Inst Engng Res (Ingenioersvetenskaps Akad. Handl.), Stockholm, 153, 1 Weibull, 1949, A statistical representation of fatigue failures in solids, Proc R Inst Tech No. 27 Weibull, 1951, A statistical distribution function of wide applicability, J Appl Mech ASME, 18 Epstein, 1948, Statistical aspects of fracture problems, J Appl Phys, 19, 140, 10.1063/1.1698380 Freudenthal, 1956, vol. 4 Freudenthal, 1953, On the statistical interpretation of fatigue tests, Proc R Soc (Lond) A, 216, 309, 10.1098/rspa.1953.0024 Gumbel, 1958 Saibel, 1969 Daniels, 1945, The statistical theory of the strength of bundles and threads, Proc R Soc Lond, A183, 405, 10.1098/rspa.1945.0011 Harlow, 1978, The chain-of-bundles probability model for the strength of fibrous materials. I. Analysis and conjectures, J Compos Mater, 12, 195, 10.1177/002199837801200207 Harlow, 1978, The chain-of-bundles probability model for the strength of fibrous materials. ii. A numerical study of convergence, J Compos Mater, 12, 314, 10.1177/002199837801200308 Smith, 1981, Asymptotic distributions for the failure of fibrous materials under series–parallel structure and equal load-sharing, J Appl Mech, 48, 75, 10.1115/1.3157595 Smith, 1982, The asymptotic distribution of the strength of a series–parallel system with equal load sharing, Ann Probab, 10, 137, 10.1214/aop/1176993919 Phoenix, 1983, A comparison of probabilistic techniques for the strength of fibrous materials under local load-sharing among fibers, Int J Solids Struct, 19, 479, 10.1016/0020-7683(83)90086-0 McCartney, 1983, Statistical theory of the strength of fiber bundles, J Appl Mech, 50, 601, 10.1115/1.3167097 Phoenix, 1983, The stochastic strength and fatigue of fiber bundles, Int J Fract, 14, 327, 10.1007/BF00034692 Phoenix, 1997, Size effects in the distribution for strength of brittle matrix fibrous composites, Int J Solids Struct, 34, 545, 10.1016/S0020-7683(96)00034-0 Phoenix, 2000, 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, 1622, 10.1103/PhysRevE.62.1622 Mahesh, 2002, Strength distributions and size effects for 2D and 3D composites with Weibull fibers in an elastic matrix, Int J Fract, 115, 41, 10.1023/A:1015729607223 Bažant, 2000, Probabilistic nonlocal theory for quasibrittle fracture initiation and size effect. I. Theory, J Engng Mech ASCE, 126, 166, 10.1061/(ASCE)0733-9399(2000)126:2(166) Bažant, 2000, Probabilistic nonlocal theory for quasibrittle fracture initiation and size effect. II. Application, J Engng Mech ASCE, 126, 175, 10.1061/(ASCE)0733-9399(2000)126:2(175) Bažant, 2001, Probabilistic modeling of quasibrittle fracture and size effect, 2001, 1 Barenblatt, 1979 Barenblatt, 1996 Bender, 1978 Bažant, 2000, Energetic-statistical size effect in quasibrittle failure at crack initiation, ACI Mater J, 97, 381 Bažant, 2001, vol. AMD-TOC Freudenthal, 1968, Statistical approach to brittle fracture, vol. 2, 591 Bažant, 2003, Size effect on flexural strength of fiber-composite laminate, ASME J Mater Technol Jackson, 1992, Scaling effects in the flexural response and failure of composite beams, AIAA J, 30, 2099, 10.2514/3.11186 Johnson, 2000, Size effect in scaled fiber composites under four-point flexural loading, AIAA J, 38, 1047, 10.2514/2.1066 Wisnom, 1991, The effect of specimen size on the bending strength of unidirectional carbon fiber-epoxy, Compos Struct, 18, 10.1016/0263-8223(91)90013-O Wisnom, 1997, Reduction in tensile and flexural strength of unidirectional glass fiber-epoxy with increasing specimen size, Compos Struct, 38, 405, 10.1016/S0263-8223(97)00075-5 Cottrell, 1963, Iron Steel Inst Spec Rep, 69, 281 Jirásek, 2002 Zech, 1977, A complex study on the reliability assessment of the containment of a PWR. Part II. Probabilistic approach to describe the behavior of materials, vol. H, J1/11, 1 Bažant, 2003, Energetic and statistical size effects in fiber composites and sandwich structures. A précis of recent progress, 869 Bažant ZP, Xi Y. Statistical size effect in quasibrittle structures. II. Nonlocal theory. ASCE J of Engineering Mechanics 117(11):2623–2640. Ang, 1984 Bouchaud, 2000 Freudenthal, 1966, The analysis of structural safety, J Struct Div ASCE, 92, 619 Weibull, 1956 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. Haldar, 2000 Bažant, 2002, Choice of standard fracture test for concrete and its statistical evaluation, Intern, J. of Fracture, 128, 1331