Analysis of brittle fracture due to compressive loading using center-cracked Brazilian disk

Abstract

The center-cracked Brazilian disk subjected to diametral compressive stress uniformly distributed along parts of its cylindrical surface is used to investigate combined mode fracture of brittle material. A fracture analysis is made of this specimen configuration. Explicit formulae for mode I and mode II stress intensity factor calculation are derived based on boundary integral equation method and related numerical solution given by Atkinson. The proposed formulae are valid in wide range of crack length a/R. This configuration can avoid splitting along load line usually occuring in Brazilian test and permit one to achieve easily pure mode II crack growth (crack coplanar extension) and any combination of K_I and K_II by a simple alignment of crack orientation with respect to load line. SIF values from the present calculation and finite element solution are also given for comparison.

Keywords

brittle fracture / stress intensity factor / Brazilian disk / compression

References

[1] SchmidtR A. Fracture toughness testing of limestone. Exp Mech, 1976, 16: 161-167

[2] LaiM O, LeeK H. K_IC determination using a chevron notched compact tension specimen. Engng Fract Mech, 1992, 41(3): 453-456

[3] IngraffeaA R, GunsallusK L, BeechJ F, et al., et al.UnderwookJ H, et al., et al.A short rod bassed system for fracture toughness testing of rock, 1985, Philadelphia, PA, ASIM

[4] Ouchterlony F. Compliance calibration of a round fracture toughness bend specimen with chevron edge notch. SveDeVo Report D S, 1984, 8

[5] SunZongqi, QuchterlonyF. Fracture toughness of stripa granite cores. Int J Roch Mech Min Sci & Geomech Abstr, 1986, 23(6): 399-409

[6] Cotterell B. Notes on the paths and stability of crack. Int J Fract, 1996 (2):526–533

[7] HoriiH, Nemat-NasserS. Compression-induced micro-crack growth in brittle solids: axial splitting and shear failure. J Geophys Res, 1985, 90: 3105-3125

[8] Nemat-NasserS, HoriiH. Compression-induced nonplanar crack extension with application to splitting, exfoliation, and rockburst. J Geophys Res, 1982, 87: 6805-6821

[9] BandP, ReuschleT, CharlezP. An improved wing crack model for the deformation and failure of rock in compression. Int J Rock Mech Min Sci & Geomech Abstr, 1996, 33(5): 539-542

[10] MelinS. When does a crack grow under mode II conditions?. Int J of Fract, 1986, 30(2): 103-114

[11] Banks-SillsL, ArcanM. An edge-cracked mode II fracture specimen. Exp Mech, 1983, 23: 257-261

[12] YaremaS Ya, KrestinG SSoviet Materials Science, 1966, 2: 7-10

[13] LibatskiiL L, KovchikS ESoviet Materials Science, 1967, 3: 334-339

[14] AwajiH, SatoS. Combined mode fracture toughness measurement by the disk test. J Engng Mater & Technology, 1978, 100: 175-182

[15] AtkinsonC, SmelserR E, SanchezJ. Combined mode fracture via the cracked Brazilian disk test. Int J of Fract, 1982, 18(4): 279-291

[16] ShettyD K, RosenfieldA R, DuckworthW H. Mixed-mode fracture in biaxial stress state. Application of diametral-compression (Brazilian Disk) test. Engng Fract Mech, 1987, 26(6): 825-840

[17] LiuC, HuangY, LovatoM L, et al.. Measurement of the fracture toughness of a fiber-reinforced composite using the Brazilian disk geometry. Int J of Fract, 1997, 87: 241-263

[18] Crouch S L, Starfield A M. Boundary element method in solid mechanics. Geoge Allen and Unwin, 1983