Size effects on parameters of cohesive zone model in mode I fracture of limestone
Source abstract
Abstract
A method was proposed to determine the cohesive zone model parameters by taking the size effects into account. It has been shown in the past that among the cohesive zone model parameters, the fracture energy in rocks can be considerably dependent on the specimen size. To incorporate the size effects in the fracture energy of rocks, the Bazant’s size effect law was modified based on the concept of the fracture process zone. For this purpose, the fracture process zone length was considered as a function of the specimen size. The proposed approach was employed for determining the cohesive zone model parameters of limestone. Then, the load–displacement curves predicted by the proposed model were compared with the experimental results reported for limestone. It was found that the proposed approach was able to predict the variation of the fracture energy with respect to the specimen size successfully.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Rock Mechanics and Modeling · Numerical methods in engineering · Geophysical Methods and Applications
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
School of Mechanical Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran
Fatigue and Fracture Lab., Center of Excellence in Experimental Solid Mechanics and Dynamics, School of Mechanical Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran
References (36)
Show source-provided references
1. Abdalla HM and Karihaloo BL (2003) Determination of size-independent specific fracture energy of concrete from three-point bend and wedge splitting tests. Magazine of Concrete Research 55(2): 133–141.10.1680/macr.55.2.133.37563 ↗
2. Abdalla HM and Karihaloo BL (2004) A method for constructing the bilinear tension softening diagram of concrete corresponding to its true fracture energy. Magazine of Concrete Research 56(10): 597–604.10.1680/macr.56.10.597.53679 ↗
3. Awaji H and Sato S (1978) Combined mode fracture toughness measurement by the disc test. Journal of Engineering Materials and Technology 100: 175–182.10.1115/1.3443468 ↗
4. Ayatollahi MR and Akbardoost J (2012) Size effects on fracture toughness of quasi-brittle materials – A new approach. Engineering Fracture Mechanics 92: 89–100.10.1016/j.engfracmech.2012.06.005 ↗
5. Ayatollahi MR and Aliha MRM (2011) Fracture analysis of some ceramics under mixed mode loading. Journal of the American Ceramic Society 94(2): 561–569.10.1111/j.1551-2916.2010.04076.x ↗
6. Barenblatt GI (1962) Mathematical theory of equilibrium cracks in brittle fracture. Advances in Applied Mechanics 7: 55–129.10.1016/S0065-2156(08)70121-2 ↗
7. Bazant ZP (1982) Crack band model for fracture of geomaterials. In: 4th international conference of numerical methods in geomechanics (ed Z Eisenstein), Edmonton, Alberta, Canada, pp.1137–1152.
8. Bazant ZP (1984) Size effect in blunt fracture: Concrete, rock, metal. Journal of Engineering Mechanics 110(4): 518–535.10.1061/(ASCE)0733-9399(1984)110:4(518) ↗
9. Bazant ZP and Kazemi MT (1990) Size effect in fracture of ceramics and its use to determine fracture energy and effective process zone length. Journal of the American Ceramic Society 73(7): 1841–1853.10.1111/j.1151-2916.1990.tb05233.x ↗
10. Bazant ZP and Planas J (1998) Fracture and Size Effect in Concrete and Other Quasibrittle Materials . London, UK: CRC Press in LLC, Taylor & Francis Group.
11. Bažant ZP and Yu Q (2011) Effect testing of cohesive fracture parameters and nonuniqueness of work-of-fracture method. Journal of Engineering Mechanics 137(8): 580–588.10.1061/(ASCE)EM.1943-7889.0000254 ↗
12. Bazant ZP, Gettu R and Kazemi MT (1991a) Identification of nonlinear fracture properties from size effect tests and structural analysis based on geometry-dependent R-curves. International Journal of Rock Mechanics and Mining Sciences 28(1): 43–51.10.1016/0148-9062(91)93232-U ↗
13. Bazant ZP, Kazemi MT, Hasegawa T, et al. (1991b) Size effect in Brazilian split-cylinder tests: measurement and fracture analysis. ACI Material Journal 88(3): 325–332.10.14359/1987 ↗
14. Bazant ZP, Kim J-K and Pfeiffer PA (1986) Nonlinear Fracture Properties From Size Effect Tests. Journal of Structural Engineering (New York, NY) 112(2): 289–307.10.1061/(ASCE)0733-9445(1986)112:2(289) ↗
15. Cedolin L and Cusatis G (2008) Identification of concrete fracture parameters through size effect experiments. Cement and Concrete Composites 30(9): 788–797.10.1016/j.cemconcomp.2008.05.007 ↗
16. Dugdale DS (1960) Yielding of steel sheets containing slits. Journal of the Mechanics and Physics of Solids 8(2): 100–104.10.1016/0022-5096(60)90013-2 ↗
17. Guo XH and Gilbert RI (2000) Effect of specimen size on the fracture energy and softening function of concrete. Materials and Structures/Materiaux et Constructions 33(5): 309–316.10.1007/BF02479701 ↗
18. Hillerborg A, Modéer M and Petersson PE (1976) Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement and Concrete Research 6(6): 773–781.10.1016/0008-8846(76)90007-7 ↗
19. Hu X and Wittmann F (2000) Size effect on toughness induced by crack close to free surface. Engineering Fracture Mechanics 65(2–3): 209–221.10.1016/S0013-7944(99)00123-X ↗
20. Karihaloo BL (1999) Size effect in shallow and deep notched quasi-brittle structures. International Journal of Fracture 95(1–4): 379–390.10.1023/A:1018633208621 ↗
21. Karihaloo BL and Xiao QZ (2001) Higher order terms of the crack tip asymtotic field for a notched three-point bend beam. International Journal of Fracture 112(2): 111–128.10.1023/A:1013392324585 ↗
22. Karihaloo BL, Abdalla HM and Xiao QZ (2003) Size effect in concrete beams. Engineering Fracture Mechanics 70(7–8): 979–993.10.1016/S0013-7944(02)00161-3 ↗
23. Lens LN, Bittencourt E and d’Avila VMR (2009) Constitutive models for cohesive zones in mixed-mode fracture of plain concrete. Engineering Fracture Mechanics 76(14): 2281–2297.10.1016/j.engfracmech.2009.07.020 ↗
24. Morel S (2008) Size effect in quasibrittle fracture: derivation of the energetic Size Effect Law from equivalent LEFM and asymptotic analysis. International Journal of Fracture 154(1): 15–26.10.1007/s10704-008-9291-6 ↗
25. Omiya M and Kishimoto K (2010) Damage-based cohesive zone model for rate-depend interfacial fracture. International Journal of Damage Mechanics 19: 397–420.10.1177/1056789509103643 ↗
26. Planas J and Elices M (1992) Asymptotic analysis of a cohesive crack: 1. Theoretical background. International Journal of Fracture 55(2): 153–177.10.1007/BF00017275 ↗
27. Rocco C, Guinea G, Planas J, et al. (1999) Size effect and boundary conditions in the Brazilian Test: Theoretical analysis. Materials and Structures 32(6): 437–444.10.1007/BF02482715 ↗
28. Roesler J, Paulino GH, Park K, et al. (2007) Concrete fracture prediction using bilinear softening. Cement and Concrete Composites 29(4): 300–312.10.1016/j.cemconcomp.2006.12.002 ↗
29. Schmidt RA (1980) A microcrack model and its significance to hydraulic fracturing and fracture toughness testing. In: Proceedings of the 21st US Symposium on Rock Mechanics , Rolla, Missouri, USA, pp. 581–590.
30. Tang W, Lo Y and Cui H (2012) Size effect of waste compact disc shred on properties of concrete. Advanced Materials Research 346: 40–46.10.4028/www.scientific.net/AMR.346.40 ↗
31. Wang QZ, Feng F, Ni M, et al. (2011) Measurement of mode I and mode II rock dynamic fracture toughness with cracked straight through flattened Brazilian disc impacted by split Hopkinson pressure bar. Engineering Fracture Mechanics 78(12): 2455–2469.10.1016/j.engfracmech.2011.06.004 ↗
32. Wang QZ, Jia XM, Kou SQ, et al. (2004a) The flattened Brazilian disc specimen used for testing elastic modulus, tensile strength and fracture toughness of brittle rocks: analytical and numerical results. International Journal of Rock Mechanics and Mining Sciences 41(2): 245–253.10.1016/S1365-1609(03)00093-5 ↗
33. Wang QZ, Jia XM and Wu LZ (2004b) Wide-range stress intensity factors for the ISRM suggested method using CCNBD specimens for rock fracture toughness tests. International Journal of Rock Mechanics and Mining Sciences 41(4): 709–716.10.1016/j.ijrmms.2004.01.004 ↗
34. Williams ML (1957) On the stress distribution at the base of a stationary crack. Journal of Applied Mechanics 24: 109–114.10.1115/1.4011454 ↗
35. Wittmann FH and Hu X (1991) Fracture process zone in cementitious materials. International Journal of Fracture 51(1): 3–18.10.1007/BF00020849 ↗
36. Wittmann FH, Mihashi H and Nomura N (1990) Size effect on fracture energy of concrete. Engineering Fracture Mechanics 35(1–3): 107–115.10.1016/0013-7944(90)90188-M ↗