Problems with hu-duan boundary effect model and its comparison to size-shape effect law for quasi-brittle fracture

Journal of Engineering Mechanics

Volumn 136, Issue 1, 2010, Pages 40-50

  Yu, Qiang ^a   Le, Jia Liang ^a   Hoover, Christian G ^a   Bažant, Zdeněk P ^a  

^a NORTHWESTERN UNIVERSITY   (United States)

Author keywords

Asymptotics of fracture; Cohesive cracks; Concrete; Evaluation of experimental data; Failure of structures; Fracture energy; Fracture scaling

Indexed keywords

ASYMPTOTICS; ASYMPTOTICS OF FRACTURE; COHESIVE CRACKS; CONCRETE EVALUATION; EXPERIMENTAL DATA; FAILURE OF STRUCTURES;

ASYMPTOTIC ANALYSIS; BOUNDARY ELEMENT METHOD; BRITTLENESS; CRACKS; FRACTURE ENERGY; STRUCTURAL DESIGN; TENSILE STRENGTH;

BRITTLE FRACTURE;

BRITTLE FRACTURE; COHESIVE SOIL; CONCRETE STRUCTURE; CRACK; FAILURE MECHANISM; FRACTURE GEOMETRY; NUMERICAL MODEL; TENSILE STRENGTH;

EID: 77950985916     PISSN: 07339399     EISSN: None     Source Type: Journal    
DOI: 10.1061/(ASCE)EM.1943-7889.89     Document Type: Article

References (49)

1. Barenblatt G.I. The formation of equilibrium cracks during brittle fracture, general ideas and hypotheses, axially symmetric cracks. Prikl. Mat. Mech. 1959, 23(3):434-444
2. Barenblatt G.I. Scaling, selfsimilarity, and intermediate asymptotics 1996, Cambridge University Press, Cambridge, U.K.
3. Barenblatt G.I. Scaling 2003, ambridge University Press, Cambridge, U.K.
4. Bažant Z.P. Size effect in blunt fracture: Concrete, rock, metal. J. Eng. Mech. 1984, 110(4):518-535. JENMDT, 0733-9399, 10.1061/(ASCE)0733-9399(1984)110:4(518)
5. Bažant Z.P. Analysis of work-of-fracture method for measuring fracture energy of concrete. J. Eng. Mech. 1996, 122(2):138-144. JENMDT, 0733-9399, 10.1061/(ASCE)0733-9399(1996)122:2(138)
6. Bažant Z.P. Scaling of quasibrittle fracture: Asymptotic analysis. Int. J. Fract. 1997, 83(1):19-40. IJFRAP, 0376-9429, 10.1023/A:1007387823522
7. Bažant Z.P. Size effects in quasibrittle fracture: Apercu of recent results. Proc., FraMCoS-4 Int. Conf. 2001, 651-658. R. de Borst, J. Mazars, G. Pijaudier-Cabot, J. G. M. van Mier, eds., Balkema, Rotterdam, The Netherlands
8. Bažant Z.P. Scaling theory of quaisbrittle structural failure. Proc. Natl. Acad. Sci. U.S.A. 2004, 101(37):13400-13407. PNASA6, 0027-8424, 10.1073/pnas.0405856101
9. Bažant Z.P. Scaling of structural strength 2005, 2nd Ed. Elsevier, London.
10. Bažant Z.P. Becq-Giraudon E. Statistical prediction of fracture parameters of concrete and implication for choice of testing standard. Cem. Concr. Res. 2002, 32(4):529-556. CCNRAI, 0008-8846, 10.1016/S0008-8846(01)00723-2
11. Bažant Z.P. Kazemi M.T. Determination of fracture energy, process zone length, and brittleness number from size effect, with application to rock and concrete. Int. J. Fract. 1990a, 44:111-131. IJFRAP, 0376-9429, 10.1007/BF00047063
12. 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. 1990b, 73(7):1841-1853. JACTAW, 0002-7820, 10.1111/j.1151-2916.1990.tb05233.x
13. Bažant Z.P. Le J.-.L. Bazant M.Z. Scaling of strength and lifetime probability distributions of quasibrittle structures based on atomistic fracture mechanics. Proc. Natl. Acad. Sci. U.S.A. 2009, 106(28):11484-11489. PNASA6, 0027-8424, 10.1073/pnas.0904797106
14. Bažant Z.P. Li Z. Zero-brittleness size-effect method for one-size fracture test of concrete. J. Eng. Mech. 1996, 122(5):458-468. JENMDT, 0733-9399, 10.1061/(ASCE)0733-9399(1996)122:5(458)
15. Bažant Z.P. Novák D. Probabilistic nonlocal theory for quasibrittle fracture initiation and size effect. I. Theory. J. Eng. Mech. 2000a, 126(2):166-174. JENMDT, 0733-9399, 10.1061/(ASCE)0733-9399(2000)126:2(166)
16. Bažant Z.P. Novák D. Probabilistic nonlocal theory for quasibrittle fracture initiation and size effect. II. Application. J. Eng. Mech. 2000b, 126(2):175-185. JENMDT, 0733-9399, 10.1061/(ASCE)0733-9399(2000)126:2(175)
17. Bažant Z.P. Pang S.-.D. Mechanics based statistics of failure risk of quasibrittle structures and size effect on safety factors. Proc. Natl. Acad. Sci. U.S.A. 2006, 103(25):9434-9439. PNASA6, 0027-8424, 10.1073/pnas.0602684103
18. Bažant Z.P. Pang S.-.D. Activation energy based extreme value statistics and size effect in brittle and quasibrittle fracture.'. J. Mech. Phys. Solids 2007, 55:91-134. JMPSA8, 0022-5096, 10.1016/j.jmps.2006.05.007
19. Bažant Z.P. Pfeiffer P.A. Determination of fracture energy from size effect and brittleness number. ACI Mater. J. 1987, 84:463-480. AMAJEF, 0889-325X
20. Bažant Z.P. Planas J. Fracture and size effect in concrete and other quasibrittle materials 1998, and ., CRC, Boca Raton, Fla.
21. Bažant Z.P. Vořechovský M. Novák D. Asymptotic prediction of energetic-statistical size effect from deterministic finite element solutions. J. Eng. Mech. 2007, 133:153-162. JENMDT, 0733-9399, 10.1061/(ASCE)0733-9399(2007)133:2(153)
22. Bažant Z.P. Xi Y. Statistical size effect in quasi-brittle structures: II. Nonlocal theory. J. Eng. Mech. 1991, 117(7):2623-2640. JENMDT, 0733-9399, 10.1061/(ASCE)0733-9399(1991)117:11(2623)
23. Bažant Z.P. Yu Q. Size effect in concrete specimens and structures: New problems and progress. Proc., FraMCoS-5, 5th Int. Conf. on Fracture Mech. of Concrete and Concr. Structures 2004, 1:153-162. V. C. Li, K. Y. Leung, K. J. Willam, S. L. Billingtoneds., IA-FraMCos, Evanston, Ill
24. Bažant Z.P. Yu Q. Universal size effect law and effect of crack depth on quasi-brittle structure strength. J. Eng. Mech. 2009, 135(2):78-84. JENMDT, 0733-9399, 10.1061/(ASCE)0733-9399(2009)135:2(78)
25. Bažant Z.P. Yu Q. Zi G. Choice of standard fracture test for concrete and its statistical evaluation. Int. J. Fract. 2002, 118:303-337. IJFRAP, 0376-9429, 10.1023/A:1023399125413
26. Cedolin L. Cusatis G. Identification of concrete fracture parameters through size-effect experiments. Cem. Concr. Res. 2008, 30:788-797. CCNRAI, 0008-8846, 10.1016/j.cemconcomp.2008.05.007
27. Cusatis G. Cedolin L. Two-scale analysis of concrete fracturing behavior. Eng. Fract. Mech. 2007, 74:3-17. EFMEAH, 0013-7944, 10.1016/j.engfracmech.2006.01.021
28. Cusatis G. Schauffert E.A. Cohesive crack analysis of size effect. Eng. Fract. Mech. 2009, 76:2163-2173. EFMEAH, 0013-7944
29. Duan K. Hu X. Specimen boundary induced size effect on quasi-brittle fracture. Strength, Fracture, and Complexity 2004, 2(2):47-68
30. Duan K. Hu X. Wittmann F. Scaling of quasi-brittle fracture: Boundary and size effect. Mech. Mater. 2006, 38:128-141. MSMSD3, 0167-6636, 10.1016/j.mechmat.2005.05.016
31. Freudenthal A.M. Statistical approach to brittle fracture. Fracture: An advanced treatises 1968, 2:591-619. H. Liebowitz, ed. Academic, New York
32. Hillerborg A. The theoretical basis of a method to determine the fracture energy GF of concrete. Mater. Struct. 1985, 18:291-296. MASTED, 1359-5997, 10.1007/BF02472919
33. Hillerborg A. Modéer M. Petersson P.E. Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cem. Concr. Res. 1976, 6:773-782. CCNRAI, 0008-8846, 10.1016/0008-8846(76)90007-7
34. Hu X. An asymptotic approach to size effect on fracture toughness and fracture energy of composites. Eng. Fract. Mech. 2002, 69:555-564. EFMEAH, 0013-7944, 10.1016/S0013-7944(01)00102-3
35. Hu X. Duan K. Size effect: Influence of proximity of fracture process zone to specimen boundary. Eng. Fract. Mech. 2007, 74:1093-1100. EFMEAH, 0013-7944, 10.1016/j.engfracmech.2006.12.009
36. Hu X. Duan K. Size effect and quasi-brittle fracture: The role of FPZ. Int. J. Fract. 2008, 154:3-14. IJFRAP, 0376-9429, 10.1007/s10704-008-9290-7
37. Hu X. Duan K. Mechanism behind the size effect phenomenon. J. Eng. Mech. 2010, 136(1):60-68. JENMDT, 0733-9399
38. Hu X. Wittmann F. Size effect on toughness induced by crack close to free surface. Eng. Fract. Mech. 2000, 65:209-221. EFMEAH, 0013-7944, 10.1016/S0013-7944(99)00123-X
39. Irwin G.R. Fracture. Handbuch der physik 1958, 6:551-590. S. Flügge,ed. Springer, Berlin
40. Karihaloo B.L. Abdalla H.M. Xiao Q.Z. Size effect in concrete beams. Eng. Fract. Mech. 2003, 70:979-993. EFMEAH, 0013-7944, 10.1016/S0013-7944(02)00161-3
41. Nakayama J. Direct measurement of fracture energies of brittle heterogeneou material. J. Am. Ceram. Soc. 1965, 48(11):583-587. JACTAW, 0002-7820, 10.1111/j.1151-2916.1965.tb14677
42. Petersson P.E. Crack growth and development of fracture zone in plain concrete and similar materials. 1981 . Rep. No.TVBM-1006, Div. of Building Materials, Lund Institute of Technology, Lund, Sweden.
43. Rice J.R. Mathematical analysis in the mechanics of fracture-An advanced treatise 1968, 2:191-308. H. Liebowitz, Academic, New York
44. Determination of the fracture energy of mortar and concrete by means of three-point bend tests on notched beams. Mater. Struct. 1985, 18:285-290. RILEM, MASTED, 1359-5997, 10.1007/BF02472917
45. Quasibrittle fracture scaling and size effect-Final report. Mater. Struct. 2004, 37(272):547-586. RILEM TC QFS, MASTED, 1359-5997, 10.1617/14109
46. Tang T. Bažant Z.P. Yang S. Zollinger D. Variable-notch one-size test method for fracture energy and process zone length. Eng. Fract. Mech. 1996, 55(3):383-404. EFMEAH, 0013-7944, 10.1016/0013-7944(96)00030-6
47. Tattersall H.G. Tappin G. The work of fracture and its measurement in metals, ceramics and other materials. J. of Materials Society 1966, 1(3):296-301. 10.1007/BF00550177
48. Weibull W. The phenomenon of rupture in solids. Proc., Royal Swedish Institute of Engineering Research 1939, 153:1-55 Ingenioersvetenskaps Akad. Handl., Stockholm
49. Weibull W. A statistical distribution function of wide applicability. ASME J. Appl. Mech. 1951, 18:293-297. JAMCAV, 0021-8936