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On characteristic lengths used in notch fracture mechanics

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Abstract

In this paper, four kinds of characteristic length parameters used in a local notch fracture criterion are presented: (1) a characteristic length \({\uprho }_{\mathrm{c}}\) generally connecting to the notch radius, (2) a characteristic distance \(\hbox {X}_{\mathrm{c}}\) considered as intrinsic to material and connected to the microstructure, (3) a critical distance \(\hbox {d}_{0}\) considered as intrinsic to material and connected to the fracture process zone, (4) an effective distance \(\hbox {X}_{\mathrm{ef}}\) considered as a characteristic of the stress distribution. Each approach is discussed. The paper ends with the author’s opinion about the different methods.

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References

  • Akourri O, Elayachi I, Pluvinage G, Elayachi I, Bensalah MO, Lebienvenu M, Dlouhy I (2005) To joint effect of temperature and notch root radius on fracture toughness. Eng Mech 12(1):11–22

    Google Scholar 

  • Betegon C, Hancock JW (1991) Two parameter characteristics of elastic-plastic crack-tip fields. J Appl Mech 58:104–101

    Article  Google Scholar 

  • Clausmeyer H, Kussmaul K, Roos E (1991) Influence of stress state on the failure behaviour of cracked components made of steel. ASME Appl Mech Rev 44(2):77–92

    Article  Google Scholar 

  • Creager M, Paris PC (1967) Elastic field equations for blunt cracks with reference to stress corrosion cracking. Int J Fract 3:247–252

    Article  Google Scholar 

  • Dowling AR, Towley CHA (1975) The effect of defect on structural failures: a two-criteria approach. Int J Press Vessel Pip 3(2):77–107

    Article  Google Scholar 

  • Filippi S, Lazzarin P, Tovo R (2002) Developments of some explicit formulas useful to describe elastic stress fields ahead of notches in plates. Int J Solid Struct 39:4543–4565

    Article  Google Scholar 

  • Gogotsi GA (2003) Fracture toughness of ceramics and ceramic composites. Ceram Int 29(7):777–784

    Article  Google Scholar 

  • Gómez FJ, Elices MA (2004) Fracture criterion for blunted V-notched samples. Int J Fract 127:239–264

    Article  Google Scholar 

  • Gómez FJ, Elices MA (2004) Fracture criterion for blunted V-notched samples. Int J Fract 127:239–264

    Article  Google Scholar 

  • Guillemot LF (1965) Brittle fracture on welded materials. Second Commonwealth Welding Conference London, pp 353–382, C7

  • Irwin GR (1948) Analysis of stresses and strains near the end of a crack traversing a plate. Trans J Appl Mech 24:361–364

    Google Scholar 

  • Kaechele LE, Tetelman AS (1969) A statistical investigation of microcrack  formation. Acta Metall 17:463–475

    Google Scholar 

  • Kim JH, Kim DH, Moon SI (2004) Evaluation of static and dynamic fracture toughness using apparent fracture toughness of notched specimen. Mater Sci Eng A 11:387–389

    Google Scholar 

  • Lazzarin L, Tovo R (1996) A unified approach to the evaluation of linear elastic stress fields in the neighborhood of cracks and notches cracks and notches. Int J Fract 78:3–19

    Article  Google Scholar 

  • Lazzarin P, Berto F (2005) Some expressions for the strain energy in a finite volume surrounding the root of blunt V-notches. Int J Fract 135:161–85

    Article  Google Scholar 

  • Leguillon D (2001) A criterion for crack nucleation at a notch in homogeneous materials. C R Acad Sci Paris Ser IIb 329:97–102

    Google Scholar 

  • Livieri P (2008) Use of J-integral to predict static failures in sharp V-notches and rounded U-notches. Eng Fract Mech 75:1779–1793

    Article  Google Scholar 

  • Mehran S, Rouhi B, Ramzani B, Barati E (2012) Fracture analysis of functionally graded materials with U- and V-notches under mode I loading using the averaged strain-energy density criterion. Fatigue Fract Eng Mater Struct 35(7):614–627

    Article  Google Scholar 

  • Meliani Hadj M, Matvienko Y, Pluvinage G (2011) Two-parameter fracture criterion (K rho, c-Tef, c) based on notch fracture mechanics. Int J Fract 167(2):173–182

    Article  Google Scholar 

  • Minor HE, Kifani A, Louah M, Azari Z, Pluvinage G (2003) Struct Safety 25

  • Neuber H (1937) Kerbspannungslehre. Springer, Berlin

    Book  Google Scholar 

  • Novozhilov VV (1969) On necessary and sufficient criterion of brittle strength. Appl Math Mech (PMM) 33:212–222

    Google Scholar 

  • O’Dowd NP, Shih CF (1991) Family of crack tip fields characterized by a triaxiality parameter. J Mech Phys Solids 39(8):989–1015

    Article  Google Scholar 

  • Osborne DE, Embury JD (1973) The influence of warm rolling on the fracture toughness of bainitic steel. Metall Trans 4:2051–2061

    Article  Google Scholar 

  • Peterson RE (1959) Notch sensitivity. In: Sines G, Waisman JL (eds) Metal fatigue. MacGraw Hill, New York

    Google Scholar 

  • Pluvinage G, Azari Z, Kadi N, Dlouhy I, Kozak V (1999) Effect of ferritic microstructure on local damage zone distance associated with fracture near notch. Theor Appl Fract Mech 31:149–156

    Article  Google Scholar 

  • Pluvinage G (2001) Notch effects in fatigue and fracture. Kluwer, Dordrecht

    Book  Google Scholar 

  • Pluvinage G (2003) Fracture and fatigue emanating from stress concentrators. Kluwer, Dordrecht

    Google Scholar 

  • Pluvinage G, Montariol F (1971) Influence de la taille de grain sur les courbes COD-Température d’essai d’un acier doux. Revue Metallurgie 68(4):73–81

    Google Scholar 

  • Ritchie RO, Knott JF, Rice JR (1973) On the relationship between critical tensile stress and fracture toughness in mild steel. J Mech Phys Solids 21:359–410

    Article  Google Scholar 

  • Saghafi H, Ayatollahi MR, Sistaninia M (2010) A modified MTS criterion (MMTS) for mixed-mode fracture toughness assessment of brittle materials. Mater Sci Eng A 527(21–22):5624–5630

    Article  Google Scholar 

  • Seweryn A (1994) Brittle fracture criterion for structures with sharp notches. Eng Fract Mech 47(4):673–681

    Article  Google Scholar 

  • Sih GC (1974) Strain energy density factor applied to mixed mode crack problems. Int J Fract 10(3):305-321

    Google Scholar 

  • Taylor D (2004) Predicting the fracture strength of ceramic materials using the theory of critical distances. Eng Fract Mech 71:2407–2416

    Article  Google Scholar 

  • Tovo R, Livieri P (2008) An implicit gradient application to fatigue of complex structures. Eng Fract Mech 75:1804–1814

    Google Scholar 

  • Vratnica M, Pluvinage G, Jodin P, Cvijovic Z, Rakin M, Burzic Z (2010) Influence of notch radius and microstructure on the fracture behaviour of Al–Zn–Mg–Cu alloys of different purity. Mater Des 31:1790–1798

    Google Scholar 

  • Whitney JM, Nuismer RJ (1974) Stress fracture criteria for laminated composites containing stress concentrations. J Comp Mater 8:253–265

    Google Scholar 

  • Williams ML (1957) On the stress distribution at the base of stationary crack. ASME J Appl Mech 24:109–1421

    Google Scholar 

  • Yang B, Ravi-Chandar K (1999) Evaluation of elastic T-stress by the stress difference method. Eng Fract Mech 64:589–605

    Article  Google Scholar 

  • Yosibash Z, Bussiba A, Gilad I (2004) Fracture criteria for brittle elastic materials. Int J Fract 125:307–333

    Article  Google Scholar 

Download references

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Pluvinage, G., Capelle, J. On characteristic lengths used in notch fracture mechanics. Int J Fract 187, 187–197 (2014). https://doi.org/10.1007/s10704-013-9924-2

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  • DOI: https://doi.org/10.1007/s10704-013-9924-2

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