Mechanism of fracture in macro- and micro-scales in hollow centre cracked disc specimen

Abstract

The hollow centre cracked disc (HCCD) specimen is one of the suggested alternative methods for determining the fracture toughness of rock. This work aims to investigate the fracture mechanism in HCCD in macro- and micro-scales using numerical methods, extended finite element method (X-FEM) and particle flow code (PFC) modeling, respectively. In the X-FEM, heaviside and near-tip enrichment functions are employed to consider the presence of the crack in the model. In PFC modeling the movement and interaction of stressed assemblies of rigid spherical particles are modeled using the distinct element method (DEM). A numerical code called MEX-FEM based on XFEM has been developed to simulate the problems involving crack. The models of pure modes I and II in macro-scale are simulated in micro-scale. The results show that dimensionless stress intensity factors (Y_I, Y_II) for pure modes I and II increase by increasing the crack length ratio. The angle at which the pure mode II occurs decreases by increasing the crack length ratio. In mixed mode I-II, The value of Y_I decreases by increasing the crack angle, while the value of Y_II increases to a given crack angle and then it decreases. Moreover, the fracture in micro-scale, unlike the macro-scale, includes a combination of different modes of fracturing.

Keywords

hollow centre cracked disc (HCCD) / extended finite element method (X-FEM) / particle flow code (PFC) / crack / stress intensity factor

References

[1] KeC C, ChenC S, TuC H. Determination of fracture toughness of anisotropic rocks by boundary element method [J]. Rock Mechanics and Rock Engineering, 2008, 41: 509-538

[2] IsakssonP, StÅHleP. Mode II crack paths under compression in brittle solids — a theory and experimental comparison [J]. International Journal of Solids and Structures, 2002, 39: 2281-2297

[3] OuchterlonyF. Suggested methods for determining the fracture toughness of rock [J]. International Journal of Rock Mechanics and Mining Sciences, 1988, 25: 71-96

[4] FowellR J. Suggested method for determining mode I fracture toughness using cracked chevron notched Brazilian disc (CCNBD) specimens [J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1995, 32: 57-64

[5] WangQ, JiaX, KouS, ZhangZ, LindqvistP A. More accurate stress intensity factor derived by finite element analysis for the ISRM suggested rock fracture toughness specimen—CCNBD [J]. International Journal of Rock Mechanics and Mining Sciences, 2003, 40: 233-241

[6] ChongK, KuruppuM. New specimen for fracture toughness determination for rock and other materials [J]. International Journal of Fracture, 1984, 26: R59-R62

[7] AwajiH, SatoS. Combined mode fracture toughness measurement by the disk test [J]. Journal of Engineering Materials and Technology, 1978, 100: 175-182

[8] WangQ, JiaX, KouS, ZhangZ, LindqvistP A. The flattened Brazilian disc specimen used for testing elastic modulus, tensile strength and fracture toughness of brittle rocks: analytical and numerical results [J]. International Journal of Rock Mechanics and Mining Sciences, 2004, 41: 245-253

[9] ChenF, SunZ, XuJ. Mode I fracture analysis of the double edge cracked Brazilian disk using a weight function method [J]. International Journal of Rock Mechanics and Mining Sciences, 2001, 38: 475-479

[10] ShiryaevA, KotkisA. Methods for determining fracture toughness of brittle porous materials [J]. INDUST LAB, 1983, 48: 917-918

[11] AmrollahiH, BaghbananA, HashemolhosseiniH. Measuring fracture toughness of crystalline marbles under modes I and II and mixed mode I-II loading conditions using CCNBD and HCCD specimens [J]. International Journal of Rock Mechanics and Mining Sciences, 2011, 48: 1123-1134

[12] WongR H, ChauK, WangP. Microcracking and grain size effect in Yuen Long marbles [J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1996, 33: 479-485

[13] HatzorY, PalchikV. The influence of grain size and porosity on crack initiation stress and critical flaw length in dolomites [J]. International Journal of Rock Mechanics and Mining Sciences, 1997, 34: 805-816

[14] PrikrylR. Some microstructural aspects of strength variation in rocks [J]. International Journal of Rock Mechanics and Mining Sciences, 2001, 38: 671-682

[15] HoaglandR G, HahnG T, RosenfieldA R. Influence of microstructure on fracture propagation in rock [J]. Rock Mechanics, 1973, 5: 77-106

[16] StanchitsS, BackersT, StephanssonO, DresenGComparison of acoustic emission events and micromechanics of granite under Mode I and Mode II loading [C]// EURO Conference on Rock Physics and Geomechanics–Micromechanics, 2003The NetherlandsFlow and Chemical Reactions Delft

[17] BackersT. Fracture toughness determination and micromechanics of rock under mode I and mode II loading [D]. Potsdam: Universitätsbibliothek, 2005

[18] KazeraniT, ZhaoJ. Micromechanical parameters in bonded particle method for modelling of brittle material failure [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2010, 34: 1877-1895

[19] NorouziS, BaghbananA, KhaniA. Investigation of grain size effects on micro/macro-mechanical properties of intact rock using voronoi element—discrete element method approach [J]. Particulate Science and Technology, 2013, 31: 507-514

[20] KulatilakeP, MalamaB, WangJ. Physical and particle flow modeling of jointed rock block behavior under uniaxial loading [J]. International Journal of Rock Mechanics and Mining Sciences, 2001, 38: 641-657

[21] ParkJ W, SongJ J. Numerical simulation of a direct shear test on a rock joint using a bonded-particle model [J]. International Journal of Rock Mechanics and Mining Sciences, 2009, 46: 1315-1328

[22] XiaM, ZhouK P. Particle simulation of the failure process of brittle rock under triaxial compression [J]. International Journal of Minerals, Metallurgy, and Materials, 2010, 17: 507-513

[23] BelytschkoT, BlackT. Elastic crack growth in finite elements with minimal remeshing [J]. International Journal for Numerical Methods in Engineering, 1999, 45: 601-620

[24] MoesN, DolbowJ, BelytschkoT. A finite element method for crack growth without remeshing [J]. International Journal for Numerical Methods in Engineering, 1999, 46: 131-150

[25] DolbowJ E. An extended finite element method with discontinuous enrichment for applied mechanics [D]. Evanston, Lllincis: Northwestern University, 1999

[26] RichardsonCL, HegemannJ, SifakisE, HellrungJ, TeranJ M. An XFEM method for modeling geometrically elaborate crack propagation in brittle materials [J]. International Journal for Numerical Methods in Engineering, 2011, 88: 1042-1065

[27] CundallP A, StrackO D. A discrete numerical model for granular assemblies [J]. Geotechnique, 1979, 29: 47-65

[28] ITASCA.. PFD3D-particle flow code in 3 dimensions, user’s guide, version 4.0 [M]. Itasca Consulting Group Inc, 2004

[29] FlemingM, ChuY, MoranB, BelytschkoT, LuY, GuL. Enriched element-free Galerkin methods for crack tip fields [J]. International Journal for Numerical Methods in Engineering, 1997, 40: 1483-1504

[30] MohammadiS. Extended finite element method: for fracture analysis of structures [M]. Malden: John Wiley & Sons, 2008

[31] BackersT, StephanssonO. ISRM suggested method for the determination of mode II fracture toughness [J]. Rock Mechanics and Rock Engineering, 2012, 45: 1011-1022

[32] ShenB, StephanssonO. Numerical analysis of mixed mode I and mode II fracture propagation [J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1993, 30: 861-867

[33] XiaZ C, HutchinsonJ W. Mode II fracture toughness of a brittle adhesive layer [J]. International Journal of Solids and Structures, 1994, 31: 1133-1148