Structural Engineering and Mechanics

  • 제50권6호
  • /
  • Pages.723-740
  • /
  • 2014
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Mixed mode fracture assessment of U-notched graphite Brazilian disk specimens by means of the local energy

  • Torabi, A.R. (Fracture Research Laboratory, Faculty of New Science and Technologies, University of Tehran) ;
  • Berto, F. (Department of Management and Engineering, University of Padova)
  • 투고 : 2014.01.14
  • 심사 : 2014.03.05
  • 발행 : 2014.06.25
⟨ 이전 논문 다음 논문 ⟩

초록

A fracture criterion based on the strain energy density (SED) over a control volume, which embraces the notch edge, is employed in the present paper to assess the fracture loads of some U-notched Brazilian disk (UNBD) specimens. The specimens are made of commercial graphite and have been tested under pure mode I, pure mode II and mixed mode I/II loading. The results show that the SED criterion allows to successfully assess the fracture loads of graphite specimens for different notch tip radii and various mode mixity conditions with discrepancies that fall inside the scatter band of ${\pm}20%$.

키워드

참고문헌

  1. Aliha, M.R.M., Heidari-Rarani, M., Shokrieh, M.M. and Ayatollahi, M.R. (2012), "Experimental determination of tensile strength and $K_{Ic}$ of polymer concretes using semi-circular bend (SCB) specimens", Struct. Eng. Mech., 43(6), 823-833. https://doi.org/10.12989/sem.2012.43.6.823
  2. Ayatollahi, M.R. and Aliha, M.R.M. (2008), "Mixed mode fracture analysis of polycrystalline graphite-A modified MTS criterion", Carbon, 46, 1302-1308. https://doi.org/10.1016/j.carbon.2008.05.008
  3. Ayatollahi, M.R. and Aliha, M.R.M. (2005), "Cracked Brazilian disc specimen subjected to mode II deformation", Eng. Fract. Mech., 72, 493-503. https://doi.org/10.1016/j.engfracmech.2004.05.002
  4. Ayatollahi, M.R. and Aliha, M.R.M. (2006), "On determination of mode II fracture toughness using semicircular bend specimen", Int. J. Solids Struct., 43, 5217-5227. https://doi.org/10.1016/j.ijsolstr.2005.07.049
  5. Ayatollahi, M.R. and Aliha, M.R.M. (2011), "On the use of anti-symmetric four-point bend specimen for mode II fracture experiments", Fat. Fract. Eng. Mater. Struct., 34, 898-907. https://doi.org/10.1111/j.1460-2695.2011.01583.x
  6. Ayatollahi, M.R., Aliha, M.R.M. and Saghafi, H. (2011b), "An improved semi-circular bend specimen for investigating mixed mode brittle fracture", Eng. Fract. Mech., 78, 110-123. https://doi.org/10.1016/j.engfracmech.2010.10.001
  7. Ayatollahi, M.R., Berto, F. and Lazzarin, P. (2011a), "Mixed mode brittle fracture of sharp and blunt Vnotches in polycrystalline graphite", Carbon, 49, 2465-2474. https://doi.org/10.1016/j.carbon.2011.02.015
  8. Ayatollahi, M.R. and Pirmohammad, S. (2013), "Temperature effects on brittle fracture in cracked asphalt concretes", Struct. Eng. Mech., 45(1), 19-32. https://doi.org/10.12989/sem.2013.45.1.019
  9. Ayatollahi, M.R. and Torabi, A.R. (2011), "Failure assessment of notched polycrystalline graphite under tensile-shear loading", Mater. Sci. Eng. A, 528, 5685-5695. https://doi.org/10.1016/j.msea.2011.04.066
  10. Ayatollahi, M.R. and Torabi, A.R. (2010a), "Tensile fracture in notched polycrystalline graphite specimens", Carbon, 48, 2255-2265. https://doi.org/10.1016/j.carbon.2010.02.041
  11. Ayatollahi, M.R. and Torabi, A.R. (2010b), "Determination of mode II fracture toughness for U-shaped notches using Brazilian disc specimen", Int. J. Solids Struct., 47, 454-465. https://doi.org/10.1016/j.ijsolstr.2009.10.012
  12. Bazaj, D.K. and Cox, E.E. (1969), "Stress concentration factors and notch sensitivity of graphite", Carbon, 7(6), 689-697. https://doi.org/10.1016/0008-6223(69)90524-7
  13. Berto, F., Lazzarin, P. and Radaj, D. (2008), "Fictitious notch rounding concept applied to sharp V-notches: Evaluation of the microstructural support factor. Part I: Basic stress equations", Eng. Fract. Mech., 75, 3060-3072. https://doi.org/10.1016/j.engfracmech.2007.12.011
  14. Berto, F., Lazzarin, P. and Radaj, D. (2009), "Fictitious notch rounding concept applied to sharp V-notches: evaluation of the microstructural support factor for different failure hypotheses. Part II: Microstructural support analysis", Eng. Fract. Mech., 76, 1151-1175. https://doi.org/10.1016/j.engfracmech.2008.01.015
  15. Berto, F. and Lazzarin, P. (2009), "A Review of the volume-based strain energy density approach applied to V-notches and welded structures", Theor. Appl. Fract. Mech., 52, 183-194. https://doi.org/10.1016/j.tafmec.2009.10.001
  16. Berto, F. and Lazzarin, P. (2010), "Fictitious notch rounding approach of pointed V-notches under inplane shear", Theor. Appl. Fract. Mech., 53, 127-135 https://doi.org/10.1016/j.tafmec.2010.03.003
  17. Berto, F. and Zappalorto, M. (2011), "Fictitious notch rounding concept applied to V-notches with end holes under mode 1 loading", Int. J. Fract., 171, 91-98. https://doi.org/10.1007/s10704-011-9626-6
  18. Berto, F. (2012), "Fictitious notch rounding concept applied to V-notches with end holes under mode 3 loading", Int. J. Fatigue, 38, 188-193. https://doi.org/10.1016/j.ijfatigue.2011.12.008
  19. Berto, F. and Zappalorto, M. (2012), "The fictitious notch rounding approach applied to V-notches with root holes subjected to mode 1 loading", J. Strain. Anal., 47(3), 176-186. https://doi.org/10.1177/0309324712437106
  20. Berto, F., Lazzarin, P. and Ayatollahi, M.R. (2012a), "Brittle fracture of sharp and blunt V-notches in isostatic graphite under torsion loading", Carbon, 50, 1942-1952. https://doi.org/10.1016/j.carbon.2011.12.045
  21. Berto, F., Lazzarin, P. and Marangon, C. (2012b), "Brittle fracture of U-notched graphite plates under mixed mode loading", Mater. Des., 41, 421-432. https://doi.org/10.1016/j.matdes.2012.05.022
  22. Berto, F., Lazzarin, P. and Ayatollahi, M.R. (2013), "Brittle fracture of sharp and blunt V-notches in isostatic graphite under pure compression loading", Carbon, 63, 101-116. https://doi.org/10.1016/j.carbon.2013.06.045
  23. Berto, F. and Lazzarin, P. (2014), "Recent developments in brittle and quasi-brittle failure assessment of engineering materials by means of local approaches", Mater. Sci. Eng. R, 75, 1-48. https://doi.org/10.1016/j.mser.2013.11.001
  24. Berto, F., Lazzarin, P. and Gallo, P. (2013), "High-temperature fatigue strength of a copper cobalt-beryllium alloy", J. Strain Anal. Eng. Des., DOI: 10.1177/0309324713511804.
  25. Berto, F., Lazzarin, P., Harding, S. and Kotousov, A. (2012c), "Out-of-plane singular stress fields in Vnotched plates and welded lap joints induced by in-plane shear load conditions", Fat. Fract. Eng. Mater. Struct., 34, 291-304.
  26. Berto, F., Lazzarin, P., Kotousov, A. and Pook, L. (2012c), "Induced out-of-plane mode at the tip of blunt lateral notches and holes under in-plane shear loading", Fat. Fract. Eng. Mater. Struct., 35, 538-555. https://doi.org/10.1111/j.1460-2695.2011.01647.x
  27. Brighenti, R. (2008), "A new discontinuous FE formulation for crack path prediction in brittle solids", Int. J. Solids Struct., 45, 6501-6517. https://doi.org/10.1016/j.ijsolstr.2008.08.008
  28. Brighenti, R. and Carpinteri, A. (2013a), "Surface cracks in fatigued structural components: A review", Fat. Fract. Eng. Mater. Struct., 36(12), 1209-1222. https://doi.org/10.1111/ffe.12100
  29. Bruno, A. and Latella, T.L. (2006), "The initiation and propagation of thermal shock cracks in graphite", Carbon, 44, 3043-3048. https://doi.org/10.1016/j.carbon.2006.05.011
  30. Carpinteri, A., Brighenti, R. and Vantadori, S. (2010a), "Influence of the cold-drawing process on fatigue crack growth of a V-notched round bar", Int. J. Fatigue, 32, 1136-1145. https://doi.org/10.1016/j.ijfatigue.2009.12.014
  31. Carpinteri, A., Ronchei, C. and Vantadori, S. (2013), "Stress intensity factors and fatigue growth of surface cracks in notched shells and round bars: Two decades of research work", Fat. Fract. Eng. Mater. Struct., 36(11), 1164-1177. https://doi.org/10.1111/ffe.12092
  32. Carpinteri, A., Spagnoli, A. and Vantadori, S. (2010b), "A multifractal analysis of fatigue crack growth and its application to concrete", Eng. Fract. Mech., 77(6), 974-984. https://doi.org/10.1016/j.engfracmech.2010.01.019
  33. Etter, T., Kuebler, J., Frey, T., Schulz, P., Loffler, J.F. and Uggowitzer, P.J. (2004), "Strength and fracture toughness of interpenetrating graphite/aluminum composites produced by the indirect squeeze casting process", Mater. Sci. Eng. A, 386, 61-67. https://doi.org/10.1016/j.msea.2004.06.066
  34. Glinka, G. (1985), "Energy density approach to calculation of inelastic strain stress near notches and cracks", Eng. Fract. Mech., 22(3), 485-508. https://doi.org/10.1016/0013-7944(85)90148-1
  35. Glinka, G., Shen, G. and Plumtree, A. (1995), "Multiaxial fatigue strain energy density parameter related to the critical fracture plane", Fat. Fract. Eng. Mater. Struct., 18(1), 37-46. https://doi.org/10.1111/j.1460-2695.1995.tb00140.x
  36. Gomez, F.J., Elices, M., Berto, F. and Lazzarin, P. (2007), "Local strain energy to assess the static failure of U-notches in plates under mixed mode loading", Int. J. Fract., 145, 29-45. https://doi.org/10.1007/s10704-007-9104-3
  37. Harding, S., Kotousov, A., Lazzarin, P. and Berto, F. (2010), "Transverse singular effects in V-shaped notches stressed in mode II", Int. J. Fract., 164, 1-14. https://doi.org/10.1007/s10704-010-9449-x
  38. Jae, H.K., Young, S.L., Duck, H.K., No, S.P., Jeong, S.J., Kim, O. and Moon, S.I. (2004), "Evaluation of thermal shock strengths for graphite materials using a laser irradiation method", Mater. Sci. Eng. A, 387-389, 385-389. https://doi.org/10.1016/j.msea.2004.01.136
  39. Kawakami, H. (1985), "Notch sensitivity of graphite materials for VHTR", J. Atom. Energy Soc. Jap., 27(4), 357-364. https://doi.org/10.3327/jaesj.27.357
  40. Kotousov, A., Lazzarin, P., Berto, F. and Harding, S. (2010), "Effect of the thickness on elastic deformation and quasi-brittle fracture of plate components", Eng. Fract. Mech., 77, 1665-1681. https://doi.org/10.1016/j.engfracmech.2010.04.008
  41. Lazzarin, P., Berto, F. and Ayatollahi, M.R. (2013), "Brittle failure of inclined key-hole notches in isostatic graphite under in-plane mixed mode loading", Fat. Fract. Eng. Mater. Struct., 36(9), 942-955. https://doi.org/10.1111/ffe.12057
  42. Lazzarin, P. and Zambardi, R. (2001), "A finite-volume-energy based approach to predict the static and fatigue behavior of components with sharp V-shaped notches", Int. J. Fract., 112, 275-298. https://doi.org/10.1023/A:1013595930617
  43. Lazzarin, P. and Berto, F. (2005), "Some expressions for the strain energy in a finite volume surrounding the root of blunt V-notches", Int. J. Fract., 135, 161-185. https://doi.org/10.1007/s10704-005-3943-6
  44. Lazzarin, P., Berto, F., Elices, M. and Gomez, F.J. (2009), "Brittle failures from U- and V-notches in mode I and mixed, I + II, mode: A synthesis based on the strain energy density averaged on finite-size volumes", Fat. Fract. Eng. Mater. Struct., 32(8), 671-684. https://doi.org/10.1111/j.1460-2695.2009.01373.x
  45. Lazzarin, P., Berto, F., Gomez, F.J. and Zappalorto, M. (2008), "Some advantages derived from the use of the strain energy density over a control volume in fatigue strength assessments of welded joints", Int. J. Fatigue, 30, 1345-1357. https://doi.org/10.1016/j.ijfatigue.2007.10.012
  46. Lazzarin, P., Berto, F. and Zappalorto, M. (2010), "Rapid calculations of notch stress intensity factors based on averaged strain energy density from coarse meshes: Theoretical bases and applications", Int. J. Fatigue, 32, 1559-1567. https://doi.org/10.1016/j.ijfatigue.2010.02.017
  47. Lomakin, E.V., Zobnin, A.I. and Berezin, A.V. (1975), "Finding the fracture toughness characteristics of graphite materials in plane strain", Strength Mater., 7(4), 484-487. https://doi.org/10.1007/BF01522870
  48. Mostafavi, M. and Marrow, T.J. (2012), "Quantitative in situ study of short crack propagation in polygranular graphite by digital image correlation", Fat. Fract. Eng. Mater. Struct., 35, 695-707. https://doi.org/10.1111/j.1460-2695.2012.01648.x
  49. Mostafavi, M., McDonald, S.A., C etinela, H., Mummery, P.M. and Marrow, T.J. (2013), "Flexural strength and defect behaviour of polygranular graphite under different states of stress", Carbon, 59, 325-336. https://doi.org/10.1016/j.carbon.2013.03.025
  50. Nakhodchi, S., Smith, D.J. and Flewitt, P.E.J. (2013), "The formation of fracture process zones in polygranular graphite as a precursor to fracture", J. Mater. Sci., 48, 720-732. https://doi.org/10.1007/s10853-012-6785-4
  51. Neuber, H. (1958), Theory of notch stresses, Kerbspannungslehre, Springer-Verlag, Berlin, Germany.
  52. Radaj, D., Berto, F. and Lazzarin, P. (2009a), "Local fatigue strength parameters for welded joints based on strain energy density with inclusion of small-size notches", Eng. Fract. Mech., 76, 1109-1130. https://doi.org/10.1016/j.engfracmech.2009.01.009
  53. Radaj, D., Lazzarin, P. and Berto, F. (2009b), "Fatigue assessment of welded joints under slit-parallel loading based on strain energy density or notch rounding", Int. J. Fatigue, 31, 1490-1504. https://doi.org/10.1016/j.ijfatigue.2009.05.005
  54. Radaj, D., Lazzarin, P. and Berto, F. (2013), "Generalised Neuber concept of fictitious notch rounding", Int. J. Fatigue, 51, 105-115. https://doi.org/10.1016/j.ijfatigue.2013.01.005
  55. Sato, S., Kawamata, K., Awaji, H., Osawa, M. and Manaka, M. (1981), "Thermal shock resistance and fracture toughness during the graphitization process", Carbon, 19, 111-118. https://doi.org/10.1016/0008-6223(81)90116-0
  56. Shi, L., Haiyan, L., Zhenmin, Z., Fok, A.S.L., Marsden, B.J., Hodgkins, A., Mummery, P.M. and Marrow, J. (2008), "Analysis of crack propagation in nuclear graphite using three-point bending of sandwiched specimens", J. Nucl. Mater., 372, 141-151. https://doi.org/10.1016/j.jnucmat.2007.02.012
  57. 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
  58. Smith, D.J., Ayatollahi, M.R. and Pavier, M.J. (2001), "The role of T-stress in brittle fracture for linear elastic materials under mixed mode loading", Fat. Fract. Eng. Mater. Struct., 24(2), 137-150. https://doi.org/10.1046/j.1460-2695.2001.00377.x
  59. Torabi, A.R. (2013a), "Fracture assessment of U-notched graphite plates under tension", Int. J. Fract., 181, 285-292. https://doi.org/10.1007/s10704-012-9799-7
  60. Torabi, A.R. (2013b), "Sudden fracture from U-notches in fine-grained isostatic graphite under mixed mode I/II loading", Int. J. Fract., 181, 309-316. https://doi.org/10.1007/s10704-013-9832-5
  61. Torabi, A.R., Fakoor, M. and Pirhadi, E. (2013a), "Tensile fracture in coarse-grained polycrystalline graphite weakened by a U-shaped notch", Eng. Fract. Mech., 111, 77-85. https://doi.org/10.1016/j.engfracmech.2013.08.015
  62. Torabi, A.R., Fakoor, M. and Darbani, M.A. (2013b), "Pure shear fracture study in a brittle graphite material containing a U-notch", Int. J. Damage Mech., DOI: 10.1177/1056789513514071.
  63. Torabi, A.R., Fakoor, M. and Pirhadi, E. (2013c), "Fracture analysis of U-notched disc-type graphite specimens under mixed mode loading", Int. J. Solids Struct., 51(6), 1287-1298.
  64. Torabi, A.R. and Jafarinezhad, M.R., (2012), "Comprehensive data for rapid calculation of notch stress intensity factors in U-notched Brazilian disc specimen under tensile-shear loading", Mater. Sci. Eng. A, 541, 135-142. https://doi.org/10.1016/j.msea.2012.02.014
  65. Torabi, A.R. and Berto, F. (2013), "Strain energy density to assess mode II fracture in U-notched disk-type graphite plates", Int. J. Damage Mech., DOI: 10.1177/1056789513519349.
  66. Yamauchi, Y., Nakano, M., Kishida, K. and Okabe, T. (2001), "Measurement of mixed-mode fracture toughness for brittle materials using edge-notched half-disk specimen", Zairyo/J. Soc. Mater. Sci. Jap., 50, 224-229.
  67. Yosibash, Z., Bussiba, A. and Gilad, I. (2004), "Failure criteria for brittle elastic materials", Int. J. Fract., 125, 307-333. https://doi.org/10.1023/B:FRAC.0000022244.31825.3b

피인용 문헌

  1. Brittle fracture analysis of blunt V-notches under compression vol.67-68, 2015, https://doi.org/10.1016/j.ijsolstr.2015.04.022
  2. Application of the equivalent material concept to ductile failure prediction of blunt V-notches encountering moderate-scale yielding vol.25, pp.6, 2016, https://doi.org/10.1177/1056789515625451
  3. A successful combination of the equivalent material concept and the averaged strain energy density criterion for predicting crack initiation from blunt V-notches in ductile aluminum plates under mixed mode loading vol.19, pp.4, 2016, https://doi.org/10.1134/S1029959916040056
  4. Local strain energy density to predict mode II brittle fracture in Brazilian disk specimens weakened by V-notches with end holes vol.69, 2015, https://doi.org/10.1016/j.matdes.2014.12.037
  5. Mixed mode I/II brittle fracture in V-notched Brazilian disk specimens under negative mode I conditions vol.19, pp.3, 2016, https://doi.org/10.1134/S1029959916030115
  6. Tensile fracture analysis of V-notches with end holes by means of the local energy vol.18, pp.3, 2015, https://doi.org/10.1134/S1029959915030030
  7. Mixed mode I/II crack initiation from U-notches in Al 7075-T6 thin plates by large-scale yielding regime vol.86, 2016, https://doi.org/10.1016/j.tafmec.2016.08.002
  8. Elastic-plastic fracture analysis of notched Al 7075-T6 plates by means of the local energy combined with the equivalent material concept vol.19, pp.2, 2016, https://doi.org/10.1134/S1029959916020144
  9. Brittle fracture assessment of engineering components in the presence of notches: a review vol.39, pp.3, 2016, https://doi.org/10.1111/ffe.12379
  10. Experimental and theoretical investigation of brittle fracture in key-hole notches under mixed mode I/II loading vol.226, pp.7, 2015, https://doi.org/10.1007/s00707-015-1323-5
  11. Tensile Fracture Analysis of Key-Hole Notches by Means of the Strain Energy Density vol.48, pp.2, 2016, https://doi.org/10.1007/s11223-016-9761-4
  12. Mode II Brittle Fracture Assessment of Key-Hole Notches by Means of the Local Energy vol.44, pp.3, 2016, https://doi.org/10.1520/JTE20140295
  13. Experimental verification of two stress-based criteria for mixed mode I/III brittle fracture assessment of U-notched components vol.182, 2017, https://doi.org/10.1016/j.engfracmech.2017.06.005
  14. Theoretical and experimental investigation of brittle fracture in V-notched PMMA specimens under compressive loading vol.135, 2015, https://doi.org/10.1016/j.engfracmech.2015.01.005
  15. Mode III Notch Fracture Toughness Assessment for Various Notch Features vol.21, pp.4, 2018, https://doi.org/10.1134/S1029959918040069
  16. Averaged strain energy density to assess mixed mode I/III fracture of U-notched GPPS samples vol.65, pp.6, 2014, https://doi.org/10.12989/sem.2018.65.6.699
  17. Investigation the fracture behavior of high-density polyethylene PE80 weakened by inclined U-notch with end hole vol.74, pp.5, 2014, https://doi.org/10.12989/sem.2020.74.5.601
  18. Out-of-plane ductile failure of notch: Evaluation of Equivalent Material Concept vol.75, pp.5, 2020, https://doi.org/10.12989/sem.2020.75.5.559
  19. Experimental and numerical analysis of mixed mode I/III fracture of sandstone using three-point bending specimens vol.76, pp.6, 2014, https://doi.org/10.12989/sem.2020.76.6.725