DOI QR코드

DOI QR Code

Influence of the inclined edge notches on the shear-fracture behavior in edge-notched beam specimens

  • Haeri, Hadi (Department of Mining Engineering, Bafgh Branch, Islamic Azad University)
  • Received : 2015.06.10
  • Accepted : 2015.10.22
  • Published : 2015.10.25

Abstract

A coupled experimental and numerical study of shear fracture in the edge-notched beam specimens of quasi-brittle materials (concrete-like materials) are carried out using four point bending flexural tests. The crack initiation, propagation and breaking process of beam specimens are experimentally studied by producing the double inclined edge notches with different ligament angles in beams under four point bending. The effects of ligament angles on the shear fracturing path in the bridge areas of the double edge-notched beam specimens are studied. Moreover, the influence of the inclined edge notches on the shear-fracture behavior of double edge-notched beam specimens which represents a practical crack orientation is investigated. The same specimens are numerically simulated by an indirect boundary element method known as displacement discontinuity method. These numerical results are compared with the performed experimental results proving the accuracy and validity of the proposed study.

Keywords

Acknowledgement

Supported by : Iran's National Elites Foundation (INEF)

References

  1. Aliabadi, M.H. (1991), Rooke DP Numerical fracture mechanics, Computational Mechanics Publications, Southampton, U.K.
  2. Ameen, M., Raghu Prasad, B.K. and Gopalakrishnan, A.R. (2011), "Modeling of concrete cracking-A hybrid technique of using displacement discontinuity element method and direct boundary element method", Eng. Anal. Bound. Elem., 35, 1054-1059. https://doi.org/10.1016/j.enganabound.2011.03.009
  3. Ayatollahi, M.R. and Sistaninia, M. (2011), "Mode II fracture study of rocks using Brazilian disk specimens", Int. J. Rock Mech. Min. Sci., 48, 819-826. https://doi.org/10.1016/j.ijrmms.2011.04.017
  4. Barr, B. (1987), "The fracture characteristics of FRC materials in shear, fiber reinforced concrete: properties and applications", SP-105, Editado por S. P. Shah y B. Batson, American Concrete Institute.
  5. Bazant, Z.P. and Oh, B.H. (1983), "Crack band theory for fracture of concrete", Mater. Struct., 16, 155-77.
  6. Bowie, O.L. (1973), Solution of Plane Crack Problems by Mapping Technique, In Methods of Analysis and Solution of Crack Problems, Ed. G.C. Sih, Lehigh University, Bethlehem, Pennsylvania.
  7. Broek, D. (1989), The Practical Use of Fracture Mechanics, 4th Edition, Kluwer Academic Publishers, Netherland.
  8. Cheng-zhi, P. and Ping, C. (2012), "Breakage characteristics and its influencing factors of rock-like material with multi-fissures under uniaxial compression", Trans. Nonferrous Met. Soc. China, 22, 185-191. https://doi.org/10.1016/S1003-6326(11)61159-X
  9. Chuang, T. and Mai, Y. (1998), "Flexural behavior of strain-softening solids", Int. J. Solid. Struct., 25, 1427-1443.
  10. Crouch, S.L. (1957a), "Analysis of stresses and displacements around underground excavations: an application of the Displacement Discontinuity Method", University of Minnesota Geomechanics Report, Minneapolis, Minnesota.
  11. Crouch, S.L. and Starfield, A. (1983), Boundary Element Methods in Solid Mechanics, Allen and Unwin, London.
  12. Dai, F., Xia, K., Zheng, H. and Wang, Y.X. (2011), "Determination of dynamic rock mode-I fracture parameters using cracked chevron notched semi-circular bend specimen", Eng. Fract. Mech., 78, 2633-2644. https://doi.org/10.1016/j.engfracmech.2011.06.022
  13. Erdogan, F. and Sih, G.C. (1963), "On the crack extension in plates under loading and transverse shear", J. Fluid. Eng., 85, 519-527.
  14. Ghazvinian, A., Sarfarazi, V., Schubert, W. and Blumel, M. (2011), "A study of the failure mechanism of planar non-persistent open joints using $PFC^{2D}$", Rock Mech. Rock Eng., 45, 677-693.
  15. Haeri, H., Shahriar K., Marji, M.F. and Moarefvand, P. (2014a), "Experimental and numerical study of crack propagation and coalescence in pre-cracked rock-like disks", Int. J. Rock Mech. Min. Sci., 67c, 20-28.
  16. Haeri, H., Khaloo, A. and Marji, M.F. (2014b), "Fracture analyses of different pre-holed concrete specimens under compression", Acta Mechanica Sinica, DOI:10.1007/s10409-015-0436-3.
  17. Haeri, H. (2015), Coupled Experimental-Numerical Fracture Mechanics, Lambert Academic Press, Germany.
  18. Haeri, H., Shahriar, K., Marji, M.F. and Moarefvand, P. (2015a), "On the crack propagation analysis of rock like Brazilian disc specimens containing cracks under compressive line loading", Latin Am. J. Solid. Struct., 11(8), 1400-1416. https://doi.org/10.1590/S1679-78252014000800007
  19. Haeri, H., Shahriar K., Marji, M.F. and Moarefvand, P. (2015b), "On the HDD analysis of micro cracks initiation, propagation and coalescence in brittle substances", Arab. J. Geoscie., 8, 2841-2852. https://doi.org/10.1007/s12517-014-1290-5
  20. Hillerborg, A. (1980), "Analysis of fracture by means of the fictitious crack model, particularly for fiber reinforced concrete", Int. J. Cement Compos., 2, 177-190.
  21. Hussian, M.A., Pu, E.L. and Underwood, J.H. (1974) "Strain energy release rate for a crack under combined mode I and mode II. In: Fracture analysis", ASTM STP 560. American Society for Testing and Materials, 2-28.
  22. Irwin, G.R. (1957), "Analysis of stress and strains near the end of a crack", J. Appl. Mech., 24, 361.
  23. Janeiro, R.P. and Einstein, H.H. (2010), "Experimental study of the cracking behavior of specimens containing inclusions (under uniaxial compression)", Int. J. Fract., 164, 83-102. https://doi.org/10.1007/s10704-010-9457-x
  24. Jenq, Y.S. and Shah, S.P. (1985), "Two parameter fracture model for concrete", J. Eng. Mech., 111, 1227-1241. https://doi.org/10.1061/(ASCE)0733-9399(1985)111:10(1227)
  25. Jiang, Z., Wan, S., Zhong, Z., Li, M. and Shen, K. (2014), "Determination of mode-I fracture toughness and non-uniformity for GFRP double cantilever beam specimens with an adhesive layer", Eng. Fract. Mech., 128, 139-156. https://doi.org/10.1016/j.engfracmech.2014.07.011
  26. Kaplan, M.F. (1961), "Crack propagation and the fracture of concrete", ACI J., 58, 591-610.
  27. Lancaster, I.M., Khalid, H.A. and Kougioumtzoglou, I.A. (2013), "Extended FEM modelling of crack propagation using the semi-circular bending test", Constr. Build. Mater., 48, 270-277. https://doi.org/10.1016/j.conbuildmat.2013.06.046
  28. Leonel, E.D., Chateauneuf, A. and Venturini, W.S. (2012), "Probabilistic crack growth analyses using a boundary element model: Applications in linear elastic fracture and fatigue problems", Eng. Anal. Bound. Elem., 36, 944-959. https://doi.org/10.1016/j.enganabound.2011.12.016
  29. Lei, J., Wang, Y.S., Huang, Y., Yang, Q. and Zhang, C. (2012), "Dynamic crack propagation in matrix involving inclusions by a time-domain BEM", Eng. Anal. Bound. Elem., 36, 651-57. https://doi.org/10.1016/j.enganabound.2011.12.005
  30. Liu, H. (2003), "Numerical modelling of the rock fracture process under mechanical loading", Thesis, LULEA university of technology, Sweden.
  31. Noel, M. and Soudki, K. (2014), "Estimation of the crack width and deformation of FRP-reinforced concrete flexural members with and without transverse shear reinforcement", Eng. Struct., 59, 393-398. https://doi.org/10.1016/j.engstruct.2013.11.005
  32. Oliveira, H.L. and Leonel, E.D. (2014), "An alternative BEM formulation, based on dipoles of stresses and tangent operator technique, applied to cohesive crack growth modeling", Eng. Anal. Bound. Elem., 41, 74-82. https://doi.org/10.1016/j.enganabound.2014.01.002
  33. Ozcebe, G. (2011), "Minimum flexural reinforcement for T-beams made of higher strength concrete", Can. J. Civil Eng., 26, 525-534.
  34. Ruiz, G. and Carmona, R.J. (2006a), "Experimental study on the influence of the shape of the cross-section and the rebar arrangement on the fracture of LRC beams", Mater. Struct., 39, 343-352.
  35. Ruiz, G., Carmona J.R. and Cendon, D.A. (2006b), "Propagation of a cohesive crack through adherent reinforcement layers", Comput. Meth. Appl. Mech. Eng., 195, 7237-7248. https://doi.org/10.1016/j.cma.2005.01.029
  36. Sanford, R.J. (2003), Principles of Fracture Mechanics, Pearson Education, hIC., Upper Saddle River, New Jersey.
  37. Sarfarazi, V., Ghazvinian, A., Schubert, W., Blumel, M. and Nejati, H.R. (2014), "Numerical Simulation of the Process of Fracture of Echelon Rock Joints", Rock. Mech. Rock. Eng., 47, 1355-1371. https://doi.org/10.1007/s00603-013-0450-3
  38. Savilahti, T., Nordlund, E. and Stephansson, O. (1990), "Shear box testing and modeling of joint bridge", Proceedings of international symposium on shear box testing and modeling of joint bridge Rock Joints, Norway.
  39. Shah, S., Swartz, S.Y. and Ouyang, C. (1995), Fracture Mechanics of concrete: Applications of Fracture Mechanics to Concrete, Rock, and Other Quasi-Brittle Materials, John Wiley & Sons, New York.
  40. Shou, K.J. (2000a), "A novel superposition scheme to obtain fundamental boundary element solutions in multi-layered elastic media", Int. J. Numer. Anal. Meth. Geomech., 24(10), 795-814. https://doi.org/10.1002/1096-9853(20000825)24:10<795::AID-NAG99>3.0.CO;2-L
  41. Shen, B. and Stephansson, O. (1994), "Modification of the G-criterion for crack propagation subjected to compression", Eng. Fract. Mech., 47, 177-189. https://doi.org/10.1016/0013-7944(94)90219-4
  42. Sih, G.C. (1974), "Strain-energy-density factor applied to mixed mode crack problems", Int. J. Fract., 10, 305-321. https://doi.org/10.1007/BF00035493
  43. Tang, C.A., Lin, P., Wong, R.H.C. and Chau, K.T. (2001), "Analysis of crack coalescence in rock-like materials containing three flaws- Part II: Numerical approach", Int. J. Rock Mech. Min. Sci., 38, 925-939. https://doi.org/10.1016/S1365-1609(01)00065-X
  44. Tavara, L., Mantic, V., Graciani, E. and Paris, F. (2011), "BEM analysis of crack onset and propagation along fiber-matrix interface under transverse tension using a linear elastic-brittle interface model", Eng. Anal. Bound. Elem., 35, 207-222. https://doi.org/10.1016/j.enganabound.2010.08.006
  45. Wang, Q.Z., Feng, F., Ni, M. and Gou, X.P. (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", Eng. Fract. Mech., 78, 2455-2469. https://doi.org/10.1016/j.engfracmech.2011.06.004
  46. Wang, Q.Z., Gou, X.P. and Fan, H. (2012), "The minimum dimensionless stress intensity factor and its upper bound for CCNBD fracture toughness specimen analyzed with straight through crack assumption", Eng. Fract. Mech., 82, 1-8. https://doi.org/10.1016/j.engfracmech.2011.11.001
  47. Wang, T., Dai, J.G. and Zheng, J.J. (2015), "Multi-angle truss model for predicting the shear deformation of RC beams with low span-effective depth ratios", Eng. Struct., 91, 85-95. https://doi.org/10.1016/j.engstruct.2015.02.035
  48. Whittaker, B.N., Singh, R.N. and Sun, G. (1992), Rock Fracture Mechanics, Principles, Design and Applications, Elsevier, Netherlands.
  49. Wong, R.H.C., Leung, W.L. and Wang, S.W. (2001), Shear strength study on rock-like models containing arrayed open joints, Eds. Elsworth, D., Tinucci, J.P., Heasley, K.A., Rock mechanics in the national interest. Swets & Zeitlinger Lisse, Leiden.
  50. Yang, Q., Dai, Y.H., Han, L.J. and Jin, Z.Q. (2009), "Experimental study on mechanical behavior of brittle marble samples containing different flaws under uniaxial compression", Eng. Fract. Mech., 76, 1833-1845S https://doi.org/10.1016/j.engfracmech.2009.04.005
  51. Yang, S.Q. (2011), "Crack coalescence behavior of brittle sandstone samples containing two coplanar fissures in the process of deformation breakage", Eng. Fract. Mech., 78, 3059-3081. https://doi.org/10.1016/j.engfracmech.2011.09.002
  52. Yoshihara, H. (2013), "Initiation and propagation fracture toughness of solid wood under the mixed Mode I/II condition examined by mixed-mode bending test", Eng. Fract. Mech., 104, 1-15. https://doi.org/10.1016/j.engfracmech.2013.03.023
  53. Zeng, G.,Yang, X., Yina, A. and Bai, F. (2014), "Simulation of damage evolution and crack propagation in three-point bending pre-cracked asphalt mixture beam", Constr. Build. Mater., 55, 323-332. https://doi.org/10.1016/j.conbuildmat.2014.01.058

Cited by

  1. Experimental crack analyses of concrete-like CSCBD specimens using a higher order DDM vol.16, pp.6, 2015, https://doi.org/10.12989/cac.2015.16.6.881
  2. The deformable multilaminate for predicting the Elasto-Plastic behavior of rocks vol.18, pp.2, 2016, https://doi.org/10.12989/cac.2016.18.2.201
  3. Effect of tensile strength of rock on tensile fracture toughness using experimental test and PFC2D simulation vol.52, pp.4, 2016, https://doi.org/10.1134/S1062739116041046
  4. A review of experimental and numerical investigations about crack propagation vol.18, pp.2, 2016, https://doi.org/10.12989/cac.2016.18.2.235
  5. Numerical simulation of tensile failure of concrete using Particle Flow Code (PFC) vol.18, pp.1, 2016, https://doi.org/10.12989/cac.2016.18.1.039
  6. The effect of micro pore on the characteristics of crack tip plastic zone in concrete vol.17, pp.1, 2016, https://doi.org/10.12989/cac.2016.17.1.107
  7. Experimental and Numerical Investigation of the Center-Cracked Horseshoe Disk Method for Determining the Mode I Fracture Toughness of Rock-Like Material vol.51, pp.1, 2018, https://doi.org/10.1007/s00603-017-1310-3
  8. Suggesting a new testing device for determination of tensile strength of concrete vol.60, pp.6, 2016, https://doi.org/10.12989/sem.2016.60.6.939
  9. Experimental study of shear behavior of planar nonpersistent joint vol.17, pp.5, 2016, https://doi.org/10.12989/cac.2016.17.5.639
  10. The effect of non-persistent joints on sliding direction of rock slopes vol.17, pp.6, 2016, https://doi.org/10.12989/cac.2016.17.6.723
  11. Cracking Behaviors of Rock-Like Specimens Containing Two Sets of Preexisting Cross Flaws under Uniaxial Compression vol.47, pp.2, 2018, https://doi.org/10.1520/JTE20170358
  12. Numerical simulation of hydraulic fracturing in circular holes vol.18, pp.6, 2015, https://doi.org/10.12989/cac.2016.18.6.1135
  13. Effect of normal load on the crack propagation from pre-existing joints using Particle Flow Code (PFC) vol.19, pp.1, 2015, https://doi.org/10.12989/cac.2017.19.1.099
  14. Direct and indirect methods for determination of mode I fracture toughness using PFC2D vol.20, pp.1, 2015, https://doi.org/10.12989/cac.2017.20.1.039
  15. Experimental and numerical study of shear crack propagation in concrete specimens vol.20, pp.1, 2015, https://doi.org/10.12989/cac.2017.20.1.057
  16. The effect of compression load and rock bridge geometry on the shear mechanism of weak plane vol.13, pp.3, 2015, https://doi.org/10.12989/gae.2017.13.3.431
  17. Investigation of ratio of TBM disc spacing to penetration depth in rocks with different tensile strengths using PFC2D vol.20, pp.4, 2015, https://doi.org/10.12989/cac.2017.20.4.429
  18. A fracture mechanics simulation of the pre-holed concrete Brazilian discs vol.66, pp.3, 2015, https://doi.org/10.12989/sem.2018.66.3.343
  19. Investigation of the model scale and particle size effects on the point load index and tensile strength of concrete using particle flow code vol.66, pp.4, 2015, https://doi.org/10.12989/sem.2018.66.4.445
  20. Simulation of crack initiation and propagation in three point bending test using PFC2D vol.66, pp.4, 2015, https://doi.org/10.12989/sem.2018.66.4.453
  21. Experimental and numerical simulating of the crack separation on the tensile strength of concrete vol.66, pp.5, 2015, https://doi.org/10.12989/sem.2018.66.5.569
  22. Direct shear testing of brittle material samples with non-persistent cracks vol.15, pp.4, 2015, https://doi.org/10.12989/gae.2018.15.4.927
  23. Simulation of the tensile failure behaviour of transversally bedding layers using PFC2D vol.67, pp.5, 2015, https://doi.org/10.12989/sem.2018.67.5.493
  24. Investigation of the effects of particle size and model scale on the UCS and shear strength of concrete using PFC2D vol.67, pp.5, 2015, https://doi.org/10.12989/sem.2018.67.5.505
  25. The effect of ball size on the hollow center cracked disc (HCCD) in Brazilian test vol.22, pp.4, 2015, https://doi.org/10.12989/cac.2018.22.4.373
  26. The effect of ball size on the hollow center cracked disc (HCCD) in Brazilian test vol.22, pp.4, 2015, https://doi.org/10.12989/cac.2018.22.4.373
  27. PFC3D simulation of the effect of particle size on the single edge-notched rectangle bar in bending test vol.68, pp.4, 2015, https://doi.org/10.12989/sem.2018.68.4.497
  28. Numerical simulation of the effect of bedding layer geometrical properties on the punch shear test using PFC3D vol.68, pp.4, 2015, https://doi.org/10.12989/sem.2018.68.4.507
  29. Numerical simulation of the effect of bedding layer geometrical properties on the shear failure mechanism using PFC3D vol.22, pp.5, 2015, https://doi.org/10.12989/sss.2018.22.5.611
  30. Experimental investigating the properties of fiber reinforced concrete by combining different fibers vol.25, pp.6, 2020, https://doi.org/10.12989/cac.2020.25.6.509
  31. Numerical simulation and experimental investigation of the shear mechanical behaviors of non-persistent joint in new shear test condition vol.26, pp.3, 2020, https://doi.org/10.12989/cac.2020.26.3.239