Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Averaged strain energy density to assess mixed mode I/III fracture of U-notched GPPS samples

  • Saboori, Behnam (Fatigue and Fracture Research Laboratory, Center of Excellence in Experimental Solid Mechanics and Dynamics, School of Mechanical Engineering, Iran University of Science and Technology) ;
  • Torabi, A.R. (Fracture Research Laboratory, Faculty of New Sciences and Technologies, University of Tehran) ;
  • Berto, F. (Department of Mechanical and Industrial Engineering, Norwegian University of Science and Technology (NTNU)) ;
  • Razavi, S.M.J. (Department of Mechanical and Industrial Engineering, Norwegian University of Science and Technology (NTNU))
  • Received : 2017.10.03
  • Accepted : 2018.01.10
  • Published : 2018.03.25
⟨ Previous Next ⟩

Abstract

In the present contribution, fracture resistance of U-notched GPPS members under mixed mode I/III loading conditions is assessed by using the Averaged Strain Energy Density (ASED) criterion. This criterion has been founded based on the ASED parameter averaged over a well-defined control volume embracing the notch edge. The validation of the theoretical criterion predictions is evaluated through comparing with the results of a series of mixed mode I/III fracture tests conducted on rectangular-shaped GPPS specimens weakened by a single edge U-notch. A recently developed apparatus for mixed mode I/III fracture experiments is employed for measuring the fracture loads of the specimens. The test samples are fabricated with different notch tip radii with the aim of evaluating the influence of this major feature of the U-notched components on the mixed mode I/III fracture behavior. It is shown that the onset of brittle fracture in U-notched GPPS specimens under various combinations of tension and out-of-plane shear can well be predicted by means of the ASED criterion.

Keywords

References

  1. Ayatollahi, M.R., Rashidi Moghaddam, M., Razavi, S.M.J. and Berto, F. (2016), "Geometry effects on fracture trajectory of PMMA samples under pure mode-I loading", Eng. Fract. Mech., 163, 449-461. https://doi.org/10.1016/j.engfracmech.2016.05.014
  2. Ayatollahi, M.R., Razavi, S.M.J., Rashidi Moghaddam, M. and Berto, F. (2015), "Mode I fracture analysis of polymethylmetacrylate using modified energy-based models", Phys. Mesomech., 18(4), 326-336. https://doi.org/10.1134/S1029959915040050
  3. Ayatollahi, M.R. and Torabi, A.R. (2010a), "Brittle fracture in rounded-tip V-shaped notches", Mater. Des., 31(1), 60-67. https://doi.org/10.1016/j.matdes.2009.07.017
  4. Ayatollahi, M.R. and Torabi, A.R. (2010b), "Tensile fracture in notched polycrystalline graphite specimens", Carb., 48(8), 2255-2265. https://doi.org/10.1016/j.carbon.2010.02.041
  5. Barati, E. and Alizadeh, Y. (2011), "A numerical method for evaluation of J-integral in plates made of functionally graded materials with sharp and blunt V-notches", Fatig. Fract. Eng. Mater. Struct., 34(12), 1041-1052. https://doi.org/10.1111/j.1460-2695.2011.01593.x
  6. Becker, T.H., Mostafavi, M., Tait, R.B. and Marrow, T.J. (2012), "An approach to calculate the J-integral by digital image correlation displacement field measurement", Fatig. Fract. Eng. Mater. Struct., 35(10), 971-984. https://doi.org/10.1111/j.1460-2695.2012.01685.x
  7. Berto, F., Ayatollahi, M. and Campagnolo, A. (2017), "Fracture tests under mixed mode I + III loading: An assessment based on the local energy", J. Dam. Mech., 26(6), 881-894. https://doi.org/10.1177/1056789516628318
  8. Berto, F. and Ayatollahi, M.R. (2011), "Fracture assessment of Brazilian disc specimens weakened by blunt V-notches under mixed mode loading by means of local energy", Mater. Des., 32(5), 2858-2869. https://doi.org/10.1016/j.matdes.2010.12.034
  9. Berto, F. and Barati, E. (2011), "Fracture assessment of U-notches under three point bending by means of local energy density", Mater. Des., 32(2), 822-830. https://doi.org/10.1016/j.matdes.2010.07.017
  10. Berto, F., Campagnolo, A. and Ayatollahi, M.R. (2015), "Brittle Fracture of rounded V-notches in isostatic graphite under static multiaxial loading", Phys. Mesomech., 18(4), 283-297. https://doi.org/10.1134/S1029959915040025
  11. Berto, F., Cendon, D.A., Lazzarin, P. and Elices, M. (2013), "Fracture behaviour of notched round bars made of PMMA subjected to torsion at $-60^{\circ}C$", Eng. Fract. Mech., 102, 271-287. https://doi.org/10.1016/j.engfracmech.2013.02.011
  12. Berto, F., Elices, M., Lazzarin, P. and Zappalorto, M. (2012), "Fracture behaviour of notched round bars made of PMMA subjected to torsion at room temperature", Eng. Fract. Mech., 90, 143-160. https://doi.org/10.1016/j.engfracmech.2012.05.001
  13. Berto, F., Gallo, P. and Lazzarin, P. (2014), "High temperature fatigue tests of un-notched and notched specimens made of 40CrMoV13.9 steel", Mater. Des., 63(Supplement C), 609-619. https://doi.org/10.1016/j.matdes.2014.06.048
  14. Berto, F., Lazzarin, P. and Ayatollahi, M.R. (2012), "Brittle fracture of sharp and blunt V-notches in isostatic graphite under torsion loading", Carb., 49(5), 1942-1952.
  15. Campagnolo, A., Berto, F. and Leguillon, D. (2016), "Fracture assessment of sharp V-notched components under Mode II loading: A comparison among some recent criteria", Theoret. Appl. Fract. Mech., 85(Part B), 217-226. https://doi.org/10.1016/j.tafmec.2016.02.001
  16. Campagnolo, A., Meneghetti, G. and Berto, F. (2016), "Rapid finite element evaluation of the averaged strain energy density of mixed-mode (I + II) crack tip fields including the T-stress contribution", Fatig. Fract. Eng. Mater. Struct., 39(8), 982-998. https://doi.org/10.1111/ffe.12439
  17. Carpinteri, A., Cornetti, P., Pugno, N., Sapora, A. and Taylor, D. (2008), "A finite fracture mechanics approach to structures with sharp V-notches", Eng. Fract. Mech., 75(7), 1736-1752. https://doi.org/10.1016/j.engfracmech.2007.04.010
  18. Cendon, D.A., Torabi, A.R. and Elices, M. (2015), "Fracture assessment of graphite V-notched and U-notched specimens by using the cohesive crack model", Fatig. Fract. Eng. Mater. Struct., 38(5), 563-573. https://doi.org/10.1111/ffe.12264
  19. Ferro, P., Lazzarin, P. and Berto, F. (2012), "Fatigue properties of ductile cast iron containing chunky graphite", Mater. Sci. Eng.: A, 554, 122-128. https://doi.org/10.1016/j.msea.2012.06.024
  20. Gomez, F.J. and Elices, M. (2003), "A fracture criterion for sharp V-notched samples", J. Fract., 123(3-4), 163-175. https://doi.org/10.1023/B:FRAC.0000007374.80996.a2
  21. 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", J. Fract., 145(1), 29-45. https://doi.org/10.1007/s10704-007-9104-3
  22. Gomez, F.J., Elices, M., Berto, F. and Lazzarin, P. (2008), "A generalised notch stress intensity factor for U-notched components loaded under mixed mode", Eng. Fract. Mech. 75(16), 4819-4833. https://doi.org/10.1016/j.engfracmech.2008.07.001
  23. Gomez, F.J., Elices, M., Berto, F. and Lazzarin, P. (2009), "Fracture of V-notched specimens under mixed mode (I + II) loading in brittle materials", J. Fract., 159(2), 121-135. https://doi.org/10.1007/s10704-009-9387-7
  24. Gomez, F.J., Elices, M. and Valiente, A. (2000), "Cracking in PMMA containing U-shaped notches", Fatig. Fract. Eng. Mater. Struct., 23(9), 795-803. https://doi.org/10.1046/j.1460-2695.2000.00264.x
  25. Lazzarin, P. and Berto, F. (2005), "Some expressions for the strain energy in a finite volume surrounding the root of blunt Vnotches", J. Fract., 135(1), 161-185. https://doi.org/10.1007/s10704-005-3943-6
  26. 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", J. Fatig., 30(8), 1345-1357. https://doi.org/10.1016/j.ijfatigue.2007.10.012
  27. Lazzarin, P., Berto, F. and Radaj, D. (2009), "Fatigue-relevant stress field parameters of welded lap joints: Pointed slit tip compared with keyhole notch", Fatig. Fract. Eng. Mater. Struct., 32(9), 713-735. https://doi.org/10.1111/j.1460-2695.2009.01379.x
  28. 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", J. Fatig., 32(10), 1559-1567. https://doi.org/10.1016/j.ijfatigue.2010.02.017
  29. Lazzarin, P., Sonsino, C.M. and Zambardi, R. (2004), "A notch stress intensity approach to assess the multiaxial fatigue strength of welded tube-to-flange joints subjected to combined loadings", Fatig. Fract. Eng. Mater. Struct., 27(2), 127-140. https://doi.org/10.1111/j.1460-2695.2004.00733.x
  30. 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", J. Fract., 112(3), 275-298. https://doi.org/10.1023/A:1013595930617
  31. Leguillon, D. (2002), "Strength or toughness? A criterion for crack onset at a notch", Eur. J. Mech.-A/Sol., 21(1), 61-72.
  32. Livieri, P. (2003), "A new path independent integral applied to notched components under mode I loadings", J. Fract., 123(3-4), 107-125. https://doi.org/10.1023/B:FRAC.0000007371.25227.aa
  33. Matvienko, Y.G. and Morozov, E.M. (2004), "Calculation of the energy J-integral for bodies with notches and cracks", J. Fract., 125(3-4), 249-261. https://doi.org/10.1023/B:FRAC.0000022241.23377.91
  34. Meneghetti, G., Campagnolo, A. and Berto, F. (2016), "Averaged strain energy density estimated rapidly from the singular peak stresses by FEM: Cracked bars under mixed-mode (I+ III) loading", Eng. Fract. Mech., 167, 20-33.
  35. Meneghetti, G., Campagnolo, A., Berto, F. and Atzori, B. (2015), "Averaged strain energy density evaluated rapidly from the singular peak stresses by FEM: Cracked components under mixed-mode (I+ II) loading", Theoret. Appl. Fract. Mech., 79, 113-124. https://doi.org/10.1016/j.tafmec.2015.08.001
  36. Priel, E., Yosibash, Z. and Leguillon, D. (2008), "Failure initiation at a blunt V-notch tip under mixed mode loading", J. Fract., 149(2), 143-173. https://doi.org/10.1007/s10704-008-9234-2
  37. Rashidi Moghaddam, M., Ayatollahi, M.R., Razavi, S.M.J. and Berto, F. (2017), "Mode II brittle fracture assessment using an energy based criterion", Phys. Mesomech., 20(2), 142-148. https://doi.org/10.1134/S1029959917020047
  38. Razavi, S., Aliha, M. and Berto, F. (2017), "Application of an average strain energy density criterion to obtain the mixed mode fracture load of granite rock tested with the cracked asymmetric four-point bend specimens", Theoret. Appl. Fract. Mech.
  39. Razavi, S., Ferro, P., Berto, F. and Torgersen, J. (2017), "Fatigue strength of blunt V-notched specimens produced by selective laser melting of Ti-6Al-4V", Theoret. Appl. Fract. Mech.
  40. Saboori, B., Ayatollahi, M.R., Torabi, A.R. and Berto, F. (2016), "Mixed mode I/III brittle fracture in round-tip V-notches", Theoret. Appl. Fract. Mech., 83, 135-151. https://doi.org/10.1016/j.tafmec.2015.12.002
  41. Saboori, B., Torabi, A.R., Ayatollahi, M.R. and Berto, F. (2017), "Experimental verification of two stress-based criteria for mixed mode I/III brittle fracture assessment of U-notched components", Eng. Fract. Mech., 182(Supplement C), 229-244. https://doi.org/10.1016/j.engfracmech.2017.06.005
  42. Safaei, S., Ayatollahi, M.R. and Saboori, B. (2017), "Fracture behavior of GPPS brittle polymer under mixed mode I/III loading", Theoret. Appl. Fract. Mech., 91(Supplement C), 103-115.
  43. Sapora, A., Cornetti, P. and Carpinteri, A. (2013), "A Finite Fracture Mechanics approach to V-notched elements subjected to mixed-mode loading", Eng. Fract. Mech., 97, 216-226. https://doi.org/10.1016/j.engfracmech.2012.11.006
  44. Sapora, A., Cornetti, P. and Carpinteri, A. (2014), "V-notched elements under mode II loading conditions", Struct. Eng. Mech., 49(4), 499-508. https://doi.org/10.12989/sem.2014.49.4.499
  45. Sapora, A. and Firrao, D. (2017), "Finite fracture mechanics predictions on the apparent fracture toughness of as-quenched charpy V-type AISI 4340 steel specimens", Fatig. Fract. Eng. Mater. Struct., 40(6), 949-958. https://doi.org/10.1111/ffe.12555
  46. Sih, G.C. (1974), "Strain-energy-density factor applied to mixed mode crack problems", J. Fract., 10(3), 305-321. https://doi.org/10.1007/BF00035493
  47. Torabi, A. (2014), "Closed-form expressions of mode I apparent notch fracture toughness for key-hole notches", J. Str. Analy. Eng. Des., 49(8), 583-591. https://doi.org/10.1177/0309324714541882
  48. Torabi, A. and Amininejad, S. (2015), "Brittle fracture in V-notches with end holes", J. Dam. Mech., 24(4), 529-545. https://doi.org/10.1177/1056789514538293
  49. Torabi, A. and Berto, F. (2013), "Fracture assessment of blunt V-notched graphite specimens by means of the strain energy density", Strengt. Mater., 45(6), 635-647. https://doi.org/10.1007/s11223-013-9500-z
  50. Torabi, A. and Berto, F. (2014a), "Mixed mode fracture assessment of U-notched graphite Brazilian disk specimens by means of the local energy", Struct. Eng. Mech., 50(6), 723-740. https://doi.org/10.12989/sem.2014.50.6.723
  51. Torabi, A. and Berto, F. (2014b), "Strain energy density to assess mode II fracture in U-notched disk-type graphite plates", J. Dam. Mech., 23(7), 917-930. https://doi.org/10.1177/1056789513519349
  52. Torabi, A., Berto, F. and Razavi, S. (2017a), "Ductile failure prediction of thin notched aluminum plates subjected to combined tension-shear loading", Theoret. Appl. Fract. Mech.
  53. Torabi, A., Berto, F. and Razavi, S. (2017b), "Tensile failure prediction of U-notched plates under moderate-scale and large-scale yielding regimes", Theoret. Appl. Fract. Mech.
  54. Torabi, A., Campagnolo, A. and Berto, F. (2014), "Mode II brittle fracture assessment of key-hole notches by means of the local energy", J. Test. Evaluat., 44(3), 1261-1270.
  55. Torabi, A., Campagnolo, A. and Berto, F. (2015a), "Experimental and theoretical investigation of brittle fracture in key-hole notches under mixed mode I/II loading", Acta Mech., 226(7), 2313-2322. https://doi.org/10.1007/s00707-015-1323-5
  56. Torabi, A., Campagnolo, A. and Berto, F. (2015b), "Local strain energy density to predict mode II brittle fracture in Brazilian disk specimens weakened by V-notches with end holes", Mater. Des., 69, 22-29. https://doi.org/10.1016/j.matdes.2014.12.037
  57. Torabi, A.R. (2013), "Sudden fracture from U-notches in fine-grained isostatic graphite under mixed mode I/II loading", J. Fract., 181(2), 309-316. https://doi.org/10.1007/s10704-013-9832-5
  58. Torabi, A.R. and Abedinasab, S.M. (2015), "Fracture study on key-hole notches under tension: Two brittle fracture criteria and notch fracture toughness measurement by the disk test", Experiment. Mech., 55(2), 393-401. https://doi.org/10.1007/s11340-014-9949-0
  59. Torabi, A.R. and Berto, F. (2014c), "Notch fracture toughness evaluation for a brittle graphite material", Mater. Perform. Characterizat., 3(3), 398-413.
  60. Torabi, A.R., Fakoor, M. and Pirhadi, E. (2013), "Tensile fracture in coarse-grained polycrystalline graphite weakened by a Ushaped notch", Eng. Fract. Mech., 111, 77-85. https://doi.org/10.1016/j.engfracmech.2013.08.015
  61. Yosibash, Z., Bussiba, A. and Gilad, I. (2004), "Failure criteria for brittle elastic materials", J. Fract., 125(3-4), 307-333. https://doi.org/10.1023/B:FRAC.0000022244.31825.3b
  62. Zappalorto, M., Lazzarin, P. and Yates, J. (2008), "Elastic stress distributions for hyperbolic and parabolic notches in round shafts under torsion and uniform antiplane shear loadings", J. Sol. Struct., 45(18), 4879-4901. https://doi.org/10.1016/j.ijsolstr.2008.04.020