Skip to main content
SpringerLink
Log in

Two Parameter Engineering Fracture Mechanics: Calculation of the Relevant Parameters and Investigation of Their Influence on the Surface Notch

  • Conference paper
  • First Online:
Integrity of Pipelines Transporting Hydrocarbons

Part of the book series: NATO Science for Peace and Security Series C: Environmental Security ((NAPSC,volume 1))

Abstract

In the present research, T-stress solutions are provided for a U-shaped notch in the case of four specimens: CT, DCB, SENT and Romain Tile (RT). The U-shaped notch is analyzed using the finite element method to determine the stress distribution ahead of the notch tip. In contrast to a crack, it was found that the T-stress is not constant and depends on distance from the notch-tip. To estimate the T-stress in the case of a notch, a novel method, namely, method of line, inspired from the volumetric method approach proposed by Pluvinage has been developed. Thus, the two-parameter approach was adopted for the notch two-parameter fracture mechanics in terms of the notch stress intensity factor Kρc and the effective (average) T-stress, Tef. Fracture toughness transferability curve (Kρc -Tef) of X52 pipe steels has been established.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. M.L. Williams, On the stress distribution at the base of stationary crack. ASME J. Appl. Mech. 24, 109–14 (1957)

    Google Scholar 

  2. J.R. Rice, Limitations to the-scale yielding approximation for crack-tip plasticity. J. Mech. Solids 22, 17–26 (1974)

    Article  Google Scholar 

  3. S.G. Larsson, A.J. Carlsson, Influence of non-singular stress terms and specimen geometry on small-scale yielding at crack tips in elastic-plastic materials. J. Mech. Phys. Solids 21, 263–278 (1973)

    Article  Google Scholar 

  4. P.S. Leevers, J.C. Radon, Inherent stress biaxiality in various fracture specimen geometries. Int. J. Fract. 19, 11–25 (1982)

    Article  Google Scholar 

  5. D.E. Richardson, A new biaxial stress fracture criterion, Ph.D. dissertation, Clemson University, 1991

    Google Scholar 

  6. Y.J. Chao, X. Zhang, Constraint effect in brittle fracture. 27th National Symposium on Fatigue and fracture, ASTM STP 1296, ed. by R.S. Piascik, J.C. Newman, Jr., D.E. Dowling, American Society for Testing and Materials, Philadelphia, 1997, pp. 41–60

    Google Scholar 

  7. Y.J. Chao, S. Liu, B.J. Broviak, Variation of fracture toughness with constraint of PMMA specimens. Proc. ASME-PVP Conf. 393, 113–120 (1999)

    Google Scholar 

  8. Y.J. Chao, S. Liu, B.J. Broviak, Brittle fracture: variation of fracture toughness with constraint and crack curving under mode I conditions. Exp. Mech. 41(3), 232–241 (2001)

    Article  CAS  Google Scholar 

  9. D.J. Smith, M.R. Ayatollahi, M.J. Pavier, The role of T-stress in brittle fracture for linear elastic materials under mixed mode loading. Fatigue Eng. Mater. Struct. 24(2), 137–150 (2001)

    Article  Google Scholar 

  10. M.R. Ayatollahi, M.J. Pavier, D.J. Smith, Mode I cracks subjected to large T-stresses. Int. J. Fracture 117(2), 159–174 (2002)

    Article  Google Scholar 

  11. ASTM E399, Standard test methods for plane-strain fracture toughness of metallic materials, Annual Book of ASTM Standards, (1997) Vol. 03.01.

    Google Scholar 

  12. J.R. Willis, Asymptotic analysis in fracture: an update. Int. J. Fracture 100, 85–103 (1999)

    Article  Google Scholar 

  13. M.G. Dawes, H.G. Pisarski, O.L. Towers, S. Williams, Fracture mechanics measurements of toughness in welded joints, in Fracture Toughness Testing: Methods, Interpretation, and Application (The Welding Institute, Cambridge, 1982), pp. 165–178

    Google Scholar 

  14. J.D.S. Sumpter, An experimental investigation of the T stress approach, in Constraint effects Fracture, ASTM STP 1171, ed. by E.M. Hackett, K.-H. Schwalbe, R.H. Dodds (American Society for Testing and Materials, Philadelphia, 1993), pp. 492–502

    Chapter  Google Scholar 

  15. M.T. Kirk, R.H. Dodds, J and CTOD estimation equations for shallow cracks in single edge notch bend specimens. Shallow crack fracture mechanics, toughness tests and applications. TWI (1992).

    Google Scholar 

  16. M.T. Kirk, The second ASTM/ESIS symposium on constraint effects in fracture; an overview. Int. J. Pres. Vessels Piping 64, 259–275 (1995)

    Article  Google Scholar 

  17. T. Nakamura, D.M. Parks, Determination of elastic T-stress along three-dimensional crack fronts using an interaction integral. Int. J. Solids Struct. 29, 1597–1611 (1991)

    Google Scholar 

  18. B.A. Bilby, G.E. Cardew, M.R. Goldthorpe, I.C.A. Howard, Finite element investigation of the effect of specimen geometry on the fields of stress and strain at the tips of stationary cracks, in Size Effects in Fracture (Mechanical Engineering Publications Limited, London, 1986), pp. 37–46

    Google Scholar 

  19. C. Betegon, J.W. Hancock, Two-parameter characterization of elastic plastic crack tip fields. ASME J. Appl. Mech. 58, 104–110 (1991)

    Article  Google Scholar 

  20. Z.Z. Du, J.W. Hancock, The effect of non-singular stresses on crack tip constraint. J. Mech. Phys. Solids 39, 555–67 (1991)

    Article  Google Scholar 

  21. B. Cotterell, Notes on the paths and stability of cracks. Int. J. Fracture Mech. 2, 526–533 (1966)

    Google Scholar 

  22. B. Cotterell, On fracture path stability in the compact tension test. Int. J. Fracture Mech. 6, 189–192 (1970)

    Google Scholar 

  23. S. Melin, Why do cracks avoid each other? Int. J. Fracture 23, 37–45 (1983)

    Article  Google Scholar 

  24. M. Marder, Instability of crack in a heatep strip. Phys. Rev. E. 49(1), 49–53 (1994)

    Article  Google Scholar 

  25. A. Yuse, M. Sano, Transition between crack patterns in quenched glass plates. Nature 362, 329 (1993). London

    Article  Google Scholar 

  26. B. Cotterell, J.R. Rice, Slightly curved or kinked cracks. Int. J. Fracture 16, 155–169 (1980)

    Article  Google Scholar 

  27. A.S. Selvarathinam, J.G. Goree, T-stress based fracture model for cracks in isotropic materials. Eng. Fract. Mech. 60, 543–561 (1998)

    Article  Google Scholar 

  28. M. Ramulu, A.S. Kobayashi, Dynamic crack curving: a photoelastic evaluation. Exp. Mech. 23, 1–9 (1983)

    Article  Google Scholar 

  29. K. Ravi-Chandar, W.G. Knauss, An experimental Investigation into Dynamic Fracture: III. On Stready-state Crack Propagation and Crack Branching. Int. J. Fracture. 26, 141–154; 198–200 (1984)

    Google Scholar 

  30. W.G. Knauss, K. Ravi-Chandar, Some basic problems in stress wave dominated fracture. Int. J. Fracture 27, 127 (1985)

    Article  Google Scholar 

  31. N.A. Fleck, J.W. Hutchinson, Z. Suo, Crack path selection in a brittle adhesive layer. Int. J. Solids Struct. 27, 1683–1703 (1991)

    Article  Google Scholar 

  32. L. Banks-sills, J. Schwartz, Fracture testing of Brazilian disk sandwich specimens. Int. J. Fracture 118, 191–209 (2002)

    Article  CAS  Google Scholar 

  33. M.T. Kirk, K.C. Koppenhoefer, C.F. Shih, Effect of constraint on specimen dimensions needed to obtain structurally relevant toughness measures, in Constraint in Fracture, ASTM STP 1171, ed. by E.M. Hachett, K.-H. Schwalbe, R.H. Dodds (American Society for testing and Materials, Philadelphia, 1993), pp. 79–103

    Chapter  Google Scholar 

  34. W.A. Sorem, R.H. Dodds, S.T. Rolfe, Effects of crack depth on elastic plastic fracture toughness. Int. J. Fracture 47, 105–126 (1991)

    Article  Google Scholar 

  35. J.W. Hancock, W.G. Reuter, D.M. Parks, Constraint and toughness parameterized by T, in Constraint effects in Fracture, ASTM STP 1171, ed. by E.M. Hackett, K.-H. Schwalbe, R.H. Dodds (American Society for Testing and Materials, Philadelphia, 1993), pp. 21–40

    Chapter  Google Scholar 

  36. J.D.S. Sumpter, An experimental investigation of the T stresses approach, in Constraint effects in Fracture, ASTM STP 1171, ed. by E.M. Hackett, K.-H. Schwalbe, R.H. Dodds (American Society for Testing and Materials, Philadelphia, 1993), pp. 492–502

    Chapter  Google Scholar 

  37. S. Ganti, D.M. Parks, Elastic plastic fracture mechanics of strength-mismatch interface cracks, in Recent Advances in Fracture, ed. by R.K. Mahudhara, et al. (The Minerals, Metals and Material Society, London, 1997), pp.13–25

    Google Scholar 

  38. Z.L. Zhang, M. Hauge, C. Taulow, The effect of T -stress on the near tip stress field of an elastic-plastic interface crack, in Proceedings of the Ninth International Conference on Fracture, ed. by B.L. Karihaloo, et al., vol 4 (Pergamon, Amsterdam, 1997), pp. 2643–2650

    Google Scholar 

  39. X.F. Li, L.R. Xu, T-stresses across static crack kinking. J. Appl. Mech. 74, N2, 181–190 (2007)

    Google Scholar 

  40. S. Melin, The influence of the T-Stress on the directional stability of cracks. Int. J. Fracture 114, 259–65 (2002)

    Article  Google Scholar 

  41. D.E. Richardson, J.G. Goree, Experimental verification of a new two parameter fracture model, in Fracture Mechanics: Twenty-Third Symposiums. ASTM STP 1189, 1993, pp. 738–750

    Google Scholar 

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

    Article  Google Scholar 

  43. Z.B. Kuang, X.P. Xu, Stress and strain fields at the tip of a sharp V-notch in a power-hardening material. Int. J. Fracture 35, 39–50 (1987)

    Google Scholar 

  44. M. Yang, S.W. Yu, in: V.V.Panasijuket. al. ed., Advances in fracture resistance in materials, in Proceedings of the International Conference Fracture (ICF9), Turin, 1993, pp. 301–308

    Google Scholar 

  45. S. Yang, Y.J. Chao, Asymptotic deformation and stress fields at the tip of a sharp notch in an elastic-plastic material. Int. J. Fracture 54, 211–224 (1992)

    CAS  Google Scholar 

  46. G. Pluvinage, Fracture and Fatigue Emanating from Stress Concentrators (Kluwer, Dordrecht, 2003)

    Google Scholar 

  47. M.H. Meliani, M. Benarous, A. Ghoul, Z. Azari, Volumetric method to understand the effect of T-stress and stress intensity factor in arc of pipe. African Phys. Rev. 1 Special Issue (Microfluidics):0006 12 (2007)

    Google Scholar 

  48. M. Hadj Meliani, Z. Azari, G. Pluvinge, Constraint Parameter for a Longitudinal Surface Notch in a Pipe Submitted to Internal Pressure. Key Eng. Mater. 399(Advances in Strength of Materials), 3–11 (2009)

    Article  Google Scholar 

  49. P. Hutar, S. Seitl, Z. Knésl, Quantification of the effect of specimen geometry on the fatigue crack growth response by two-parameter fracture mechanics. Mater. Sci. Eng. A 387–389, 491–494 (2004)

    Google Scholar 

  50. S. Stanislav, Z. Knésl, Two parameter fracture mechanics: fatigue crack behavior under mixed mode conditions. Eng. Fract. Mech. 75, 857–865 (2008)

    Article  Google Scholar 

  51. M. Creager, P.C. Paris, Elastic Celd equations for blunt cracks with reference to stress corrosion cracking. Int. J. Fracture 3, 247–251 (1967)

    CAS  Google Scholar 

  52. M.H. Meliani, Z. Azari, G. Pluvinge, Y. Matvienko, New approach for the T-stress estimation for specimens with a U-notch. New Trends in Fatigue and Fracture, 9th Meeting – NT2F9 –, Failures of materials and structures by fatigue and fracture, Belgrade, 12–14 Oct 2009

    Google Scholar 

  53. M.H. Meliani, G. Pluvinage, J. Capelle, Gouge assessment for pipes and associated transferability problems. Eng. Fail. Anal. 17(2010), 1117–1126 (2009)

    Google Scholar 

  54. M.H. Meliani, Z. Azari, G. Pluvinge, YuG Matvienko, The effective T-stress estimation and crack paths emanating from U-notches. Eng. Fract. Mech. 77, 1682–1692 (2010)

    Article  Google Scholar 

  55. B. Ozmat, A.S. Argon, D.M. Parks, Growth modes of cracks in creeping type 304 stainless steel. Mech. Mater. 11, 1–17 (1999)

    Article  Google Scholar 

  56. B. Nguyen, P. Onck, E. Van der Giessen, Crack-tip constraint effects on creep fracture. Eng. Fract. Mech. 65, 467–490 (2000)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire de Physique Théorique et Physique des Matériaux (LPTPM), FSSI, Université Hassiba Benbouali, Chlef, 02000, Algeria

    Mohamed Hadj Meliani

  2. Laboratoire de Mécanique, Biomécanique, Polymères et structures, LaBPS-ENIM, île de saulcy, Université Paul Verlaine de Metz, Metz, 57045, France

    Zitouni Azari & Guy Pluvinage

  3. Laboratory of Modelling Damage and Fracture, Mechanical Engineering Research Institute of the Russian Academy of Sciences, 4 M. Kharitonievsky Per, Moscow, 101990, Russia

    Yu. G. Matvienko

Authors
  1. Mohamed Hadj Meliani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zitouni Azari
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Guy Pluvinage
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yu. G. Matvienko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohamed Hadj Meliani .

Editor information

Editors and Affiliations

  1. , Dipartimento di Ingegneria Strutturale, Politecnico di Milano, Piazza Leonardo da Vinci 32, Milano, 20133, Italy

    Gabriella Bolzon

  2. Technologie Houari Boumediene (USTH, Dépt. Matériaux et Composants, Université des Sciences et de la, Algiers, Algeria

    Taoufik Boukharouba

  3. Eni E&P Division – TEMM, Via Emilia 1, San Donato Milanese (MI), 20097, Italy

    Giovanna Gabetta

  4. , Nat. Resources Canada, Govt. of Canada, CANMET Materials Technology Laboratory, Booth Street 568, Ottawa, K1A 0G1, Ontario, Canada

    Mimoun Elboujdaini

  5. , Faculté des Sciences et de la Techn., Université Mohamed Khider, Biskra, 07000, Algeria

    Mekki Mellas

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer Science+Business Media B.V.

About this paper

Cite this paper

Meliani, M.H., Azari, Z., Pluvinage, G., Matvienko, Y.G. (2011). Two Parameter Engineering Fracture Mechanics: Calculation of the Relevant Parameters and Investigation of Their Influence on the Surface Notch. In: Bolzon, G., Boukharouba, T., Gabetta, G., Elboujdaini, M., Mellas, M. (eds) Integrity of Pipelines Transporting Hydrocarbons. NATO Science for Peace and Security Series C: Environmental Security, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0588-3_16

Download citation

Publish with us

Policies and ethics

Search

Navigation