Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Generalized fracture toughness for specimens with re-entrant corners: Experiments vs. theoretical predictions

  • Carpinteri, Alberto (Department of Structural Engineering and Geotechnics, Politecnico di Torino) ;
  • Cornetti, Pietro (Department of Structural Engineering and Geotechnics, Politecnico di Torino) ;
  • Pugno, Nicola (Department of Structural Engineering and Geotechnics, Politecnico di Torino) ;
  • Sapora, Alberto (Department of Structural Engineering and Geotechnics, Politecnico di Torino) ;
  • Taylor, David (Department of Mechanical and Manufacturing Engineering, Trinity College)
  • Received : 2008.12.11
  • Accepted : 2009.06.14
  • Published : 2009.07.30
⟨ Previous Next ⟩

Abstract

In this paper the results of a series of experimental tests upon three-point bending specimens made of polystyrene and containing re-entrant corners are firstly described. Tests involved different notch angles, different notch depths and finally different sizes of the samples. All the specimens broke at the defect, as expected because of the material brittleness and, hence, the generalized stress intensity factor was expected to be the governing failure parameter. Recorded failure loads are then compared with the predictions provided by a fracture criterion recently introduced in the framework of Finite Fracture Mechanics: fracture is assumed to propagate by finite steps, whose length is determined by the contemporaneous fulfilment of energy balance and stress requirements. This fracture criterion allows us to achieve the expression of the generalized fracture toughness as a function of the tensile strength, the fracture toughness and the notch opening angle. Comparison between theoretical predictions and experimental data turns out to be more than satisfactory.

Keywords

References

  1. Carpinteri, A. (1981), "Static and energetic fracture parameters for rocks and concretes", Mater. Struct., 14, 151-162 https://doi.org/10.1007/BF02473919
  2. Carpinteri, A. (1987), "Stress-singularity and generalized fracture toughness at the vertex of re-entrant corners", Eng. Fract. Mech., 26, 143-155 https://doi.org/10.1016/0013-7944(87)90086-5
  3. Carpinteri, A. and Pugno, N. (2005), "Fracture instability and limit strength conditions in structures with reentrant corners", Eng. Fract. Mech., 72, 1254-1267 https://doi.org/10.1016/j.engfracmech.2004.09.008
  4. Carpinteri, A., Cornetti, P., Barpi, F. and Valente, S. (2003), "Cohesive crack model description of ductile to brittle size-scale transition: Dimensional analysis vs. renormalization group theory", Eng. Fract. Mech., 70, 1809-1839 https://doi.org/10.1016/S0013-7944(03)00126-7
  5. 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, 1736-1752 https://doi.org/10.1016/j.engfracmech.2007.04.010
  6. Cornetti, P., Pugno, N., Carpinteri, A. and Taylor, D. (2006), "Finite fracture mechanics: A coupled stress and energy failure criterion", Eng. Fract. Mech., 73, 2021-2033 https://doi.org/10.1016/j.engfracmech.2006.03.010
  7. Dunn, M.L., Suwito, W. and Cunningham, S. (1997), “Fracture initiation at sharp notches: Correlation using critical stress intensities”, Int. J. Solids Struct., 34, 3873-3883 https://doi.org/10.1016/S0020-7683(96)00236-3
  8. Lazzarin, P. and Zambardi, R. (2001), "A finite-volume-energy based approach to predict the static and fatigue behaviour of components with sharp v-shaped notches", Int. J. Fract., 112, 275-298 https://doi.org/10.1023/A:1013595930617
  9. Leguillon, D. (2002), "Strength or toughness? A criterion for crack onset at a notch", Eur. J. Mech. A/Solids, 21,61-72 https://doi.org/10.1016/S0997-7538(01)01184-6
  10. Neuber, H. (1958), Theory of Notch Stresses, Springer, Berlin
  11. Novozhilov, V. (1969), "On a necessary and sufficient condition for brittle strength", Prik. Mat. Mek., 33, 212-222
  12. Pugno, N. and Ruoff, N. (2004), "Quantized fracture mechanics", Philos. Mag. A, 84, 2829-2845 https://doi.org/10.1080/14786430412331280382
  13. Seweryn, A. (1994), "Brittle fracture criterion for structures with sharp notches", Eng. Fract. Mech., 47, 673-681 https://doi.org/10.1016/0013-7944(94)90158-9
  14. Sih, G.C. (1991), "Mechanics of fracture initiation and propagation: Surface and volume energy density applied as failure criterion", Engineering Applications of Fracture Mechanics, Kluwer Academic Publisher: Dordrecht
  15. Sinclair, G.B., Okajima, M. and Griffin, J.H. (1984), "Path independent integrals for computing stress intensity factors at sharp notches in elastic plates", Int. J. Numer. Meth. Eng., 20, 999-1008 https://doi.org/10.1002/nme.1620200603
  16. Tada, H., Paris, P.C. and Irwin, G.R. (1985), The Stress Analysis of Cracks, Handbook, Second edition, Paris Productions Incorporated, St Louis, Missouri, USA
  17. Taylor, D. (1999), "Geometrical effects in fatigue: a unifying theoretical model", Int. J. Fatig., 21, 413-420 https://doi.org/10.1016/S0142-1123(99)00007-9
  18. Taylor, D. (2004), "Predicting the fracture strength of ceramic materials using the theory of critical distances", Eng. Fract. Mech., 71, 2407-2416 https://doi.org/10.1016/j.engfracmech.2004.01.002
  19. Taylor, D., Cornetti, P. and Pugno, N. (2005), "The fracture mechanics of finite crack extension", Eng. Fract.Mech., 72, 1021-1038 https://doi.org/10.1016/j.engfracmech.2004.07.001

Cited by

  1. Brittle Materials and Stress Concentrations: are they Able to withstand? vol.109, 2015, https://doi.org/10.1016/j.proeng.2015.06.236
  2. A Finite Fracture Mechanics approach to V-notched elements subjected to mixed-mode loading vol.97, 2013, https://doi.org/10.1016/j.engfracmech.2012.11.006
  3. Fracture Behavior Investigation of a Typical Sandstone Under Mixed-Mode I/II Loading Using the Notched Deep Beam Bending Method vol.50, pp.8, 2017, https://doi.org/10.1007/s00603-017-1227-x
  4. Computation of V-notch shape factors in four-point bend specimen for fracture tests on brittle materials vol.83, pp.3, 2013, https://doi.org/10.1007/s00419-012-0654-0
  5. V-notched elements under mode II loading conditions vol.49, pp.4, 2014, https://doi.org/10.12989/sem.2014.49.4.499
  6. Size effects on brittle fracture of Brazilian disk samples containing a circular hole vol.186, 2017, https://doi.org/10.1016/j.engfracmech.2017.11.008
  7. T-stress effects on crack kinking in Finite Fracture Mechanics vol.132, 2014, https://doi.org/10.1016/j.engfracmech.2014.10.011
  8. Characteristics of the process zone at sharp notch roots vol.48, pp.14-15, 2011, https://doi.org/10.1016/j.ijsolstr.2011.03.023
  9. Finite fracture mechanics predictions on the apparent fracture toughness of as-quenched Charpy V-type AISI 4340 steel specimens vol.40, pp.6, 2017, https://doi.org/10.1111/ffe.12555
  10. Brittle failures at rounded V-notches: a finite fracture mechanics approach vol.172, pp.1, 2011, https://doi.org/10.1007/s10704-011-9640-8
  11. On the most dangerous V-notch vol.47, pp.7-8, 2010, https://doi.org/10.1016/j.ijsolstr.2009.11.017
  12. Finite Fracture Mechanics: a deeper investigation on negative T-stress effects vol.197, pp.1, 2016, https://doi.org/10.1007/s10704-015-0059-5
  13. An improved Finite Fracture Mechanics approach to blunt V-notch brittle fracture mechanics: Experimental verification on ceramic, metallic, and plastic materials vol.78, 2015, https://doi.org/10.1016/j.tafmec.2015.04.004
  14. 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
  15. Sharp notch roots subject to in-plane and anti-plane loading: An alternative normalisation of the eigenfields & their application to example problems vol.86, 2016, https://doi.org/10.1016/j.tafmec.2016.08.005
  16. Influence of occlusal geometry on ceramic crown fracture; role of cusp angle and fissure radius vol.4, pp.7, 2011, https://doi.org/10.1016/j.jmbbm.2011.03.014
  17. Maximum mean principal stress criterion for three-dimensional brittle fracture vol.102-103, 2016, https://doi.org/10.1016/j.ijsolstr.2016.10.009
  18. Blunt V-Notch Brittle Fracture: An Improved Finite Fracture Mechanics Approach vol.1105, pp.1662-8985, 2015, https://doi.org/10.4028/www.scientific.net/AMR.1105.237
  19. Finite Fracture Mechanics Assessment in Moderate and Large Scale Yielding Regimes vol.9, pp.5, 2009, https://doi.org/10.3390/met9050602
  20. Comparison between two nonlocal criteria: A case study on pressurized holes vol.33, pp.None, 2009, https://doi.org/10.1016/j.prostr.2021.10.052