Skip to main content
Top

2019 | OriginalPaper | Chapter

65. Crack-Dislocation Interactions Ahead of a Crack Tip

Authors : R. Goswami, C. S. Pande

Published in: Handbook of Mechanics of Materials

Publisher: Springer Singapore

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

An overview of interactions of crack and dislocations emitted from the crack is provided with particular emphasis on theoretical approaches. Several existing models, such as due to Bilby, Cottrell and Swinden, Burns and Majumdar, Lin and Thomson, and Pande and Masamura, are presented. These models provide a formalism that gives the equilibrium positions of dislocations in an array ahead of crack tip, from which important parameters such as plastic zone size, dislocation-free zone, and dislocation stress intensity factor can be determined, which are useful in discussing the phenomenon of fatigue. Following these overviews, the experimental results on the dislocation-free zone and plastic zone observed ahead of the cracks in aluminum using transmission electron microscopy are presented and compared with the existing models. The experimentally measured values of these zones are shown to be in reasonably good agreement with theoretical models of crack-dislocation configuration based on a continuum distribution of dislocations ahead of the crack. However, these models fail to predict the total number of emitted dislocations, underlying the need for better analytical models. We also provide a brief overview on crack tip dislocation behavior under fatigue loading.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Ohr SM, Narayan J. Electron microscope observation of shear cracks in stainless steel single crystals. Philos Mag. 1980;41(1):81–9.CrossRef Ohr SM, Narayan J. Electron microscope observation of shear cracks in stainless steel single crystals. Philos Mag. 1980;41(1):81–9.CrossRef
2.
go back to reference Kobayashi S, Ohr SM. Insitu observations of the formation of plastic zone ahead of a crack tip in copper. Scr Metall. 1981;15(3):343–8.CrossRef Kobayashi S, Ohr SM. Insitu observations of the formation of plastic zone ahead of a crack tip in copper. Scr Metall. 1981;15(3):343–8.CrossRef
3.
go back to reference Kobayashi S, Ohr SM. In situ fracture experiments in BCC metals. Philos Mag A. 1980;42(6):763–72.CrossRef Kobayashi S, Ohr SM. In situ fracture experiments in BCC metals. Philos Mag A. 1980;42(6):763–72.CrossRef
4.
go back to reference Horton JA, Ohr SM. Determination of emmision condition from the experiments and theory. Scr Metall. 1982;16(5):621–6.CrossRef Horton JA, Ohr SM. Determination of emmision condition from the experiments and theory. Scr Metall. 1982;16(5):621–6.CrossRef
5.
go back to reference Horton JA, Ohr SM. TEM observations of dislocation emission at crack tip in aluminum. J Mater Sci. 1982;17(11):3140–8.CrossRef Horton JA, Ohr SM. TEM observations of dislocation emission at crack tip in aluminum. J Mater Sci. 1982;17(11):3140–8.CrossRef
6.
go back to reference Ohr SM. An electron microscope study of crack tip deformation and its impact on the dislocation theory of fracture. Mater Sci Eng. 1985;72(1):1–35.CrossRef Ohr SM. An electron microscope study of crack tip deformation and its impact on the dislocation theory of fracture. Mater Sci Eng. 1985;72(1):1–35.CrossRef
7.
go back to reference Majumdar B, Burns S. Crack tip shielding-anelastic theory of dislocation and dislocation arrays near a sharp crack. Acta Metall. 1981;29(4):579–88.CrossRef Majumdar B, Burns S. Crack tip shielding-anelastic theory of dislocation and dislocation arrays near a sharp crack. Acta Metall. 1981;29(4):579–88.CrossRef
8.
go back to reference Majumdar B, Burns S. A Griffith crack shielded by a dislocation pile-up. Int J Fract Mech. 1983;21(3):229–40.CrossRef Majumdar B, Burns S. A Griffith crack shielded by a dislocation pile-up. Int J Fract Mech. 1983;21(3):229–40.CrossRef
9.
go back to reference Chang S, Ohr SM. Dislocation-free zone model of fracture. J Appl Physiol. 1981;52(12):7174–81.CrossRef Chang S, Ohr SM. Dislocation-free zone model of fracture. J Appl Physiol. 1981;52(12):7174–81.CrossRef
10.
go back to reference Dai SH, Li JCM. Dislocation free zone at the crack tip. Scr Metall. 1982;16(2):183–8.CrossRef Dai SH, Li JCM. Dislocation free zone at the crack tip. Scr Metall. 1982;16(2):183–8.CrossRef
11.
12.
go back to reference Sadananda K, Glinka G. Dislocation processes that affect kinetics of fatigue crack growth. Philos Mag. 2005;85(2–3):189–203.CrossRef Sadananda K, Glinka G. Dislocation processes that affect kinetics of fatigue crack growth. Philos Mag. 2005;85(2–3):189–203.CrossRef
13.
go back to reference Bilby B, Cottrell A, Swinden K. The spread of plastic yield from a notch. Proc Roy Soc A. 1963;272(1350):304–14. Bilby B, Cottrell A, Swinden K. The spread of plastic yield from a notch. Proc Roy Soc A. 1963;272(1350):304–14.
14.
go back to reference Lin IH, Thomson R. Cleavage, dislocation emission, and shielding for cracks under general loading. Acta Metall. 1986;34(2):187–206.CrossRef Lin IH, Thomson R. Cleavage, dislocation emission, and shielding for cracks under general loading. Acta Metall. 1986;34(2):187–206.CrossRef
15.
go back to reference Pande CS, Masumura RA, Chou YT. Shielding of crack tips by inclined pile-ups of dislocations. Acta Metall. 1988;36(1):49–54.CrossRef Pande CS, Masumura RA, Chou YT. Shielding of crack tips by inclined pile-ups of dislocations. Acta Metall. 1988;36(1):49–54.CrossRef
16.
go back to reference Weertman J. Theory of fatigue crack growth based on a BCS crack theory with work hardening. Int J Fract. 1973;9(2):125–31.CrossRef Weertman J. Theory of fatigue crack growth based on a BCS crack theory with work hardening. Int J Fract. 1973;9(2):125–31.CrossRef
17.
go back to reference Park CG, Lee CS, Chang YW. In situ TEM observations of crack tip dislocation behaviors under a mixed mode loading. In: Mechanical behaviour of materials – VI; Proceedings of the 6th international conference, Kyoto, July 29–Aug 2; 1991. vol. 4 (A93–40776 16–39), p. 3–9. Park CG, Lee CS, Chang YW. In situ TEM observations of crack tip dislocation behaviors under a mixed mode loading. In: Mechanical behaviour of materials – VI; Proceedings of the 6th international conference, Kyoto, July 29–Aug 2; 1991. vol. 4 (A93–40776 16–39), p. 3–9.
18.
go back to reference Ding Y, Wang C, Li M, Wang W. In situ TEM observation of microcrack nucleation and propagation in pure tin solder. Mater Sci Eng B. 2006;127(1):62–9.CrossRef Ding Y, Wang C, Li M, Wang W. In situ TEM observation of microcrack nucleation and propagation in pure tin solder. Mater Sci Eng B. 2006;127(1):62–9.CrossRef
19.
go back to reference Weertman J. Fracture mechanics-unified view for Griffith-Irwin-Orowan cracks. Acta Metall. 1978;26(11):1731–8.CrossRef Weertman J. Fracture mechanics-unified view for Griffith-Irwin-Orowan cracks. Acta Metall. 1978;26(11):1731–8.CrossRef
20.
go back to reference Weertman J. Fracture stress obtained from the elastic crack tip enclave model. J Mater Sci. 1980;15(5):1306–10.CrossRef Weertman J. Fracture stress obtained from the elastic crack tip enclave model. J Mater Sci. 1980;15(5):1306–10.CrossRef
21.
go back to reference Weertman J, Lin IH, Thomson R. Double slip plane crack model. Acta Metall. 1983;31(4):473–82.CrossRef Weertman J, Lin IH, Thomson R. Double slip plane crack model. Acta Metall. 1983;31(4):473–82.CrossRef
22.
go back to reference Weertman J. Dislocation emmision into a mode III plastic zone. Scr Metall. 1986;20(11):1483–8.CrossRef Weertman J. Dislocation emmision into a mode III plastic zone. Scr Metall. 1986;20(11):1483–8.CrossRef
23.
24.
go back to reference Rice JR, Thomson R. Ductile versus brittle behavior of crystals. Philos Mag. 1974;29(1):73–97.CrossRef Rice JR, Thomson R. Ductile versus brittle behavior of crystals. Philos Mag. 1974;29(1):73–97.CrossRef
25.
go back to reference Muskhelishvili N. Singular integral equations. Groningen: P. Noordhoof Ltd; 1953.MATH Muskhelishvili N. Singular integral equations. Groningen: P. Noordhoof Ltd; 1953.MATH
26.
go back to reference Zhang TY, Tong P, Ouyang H, Lee S. Interaction of an edge dislocation with a wedge crack. J Appl Physiol. 1995;78(8):4873–80.CrossRef Zhang TY, Tong P, Ouyang H, Lee S. Interaction of an edge dislocation with a wedge crack. J Appl Physiol. 1995;78(8):4873–80.CrossRef
27.
go back to reference Pande CS, Masumura RA, Chou YT. Shielding of crack tips by critical parameters for fatigue damage. Int J Fatigue. 2001;23(10–12):1170–4. Pande CS, Masumura RA, Chou YT. Shielding of crack tips by critical parameters for fatigue damage. Int J Fatigue. 2001;23(10–12):1170–4.
28.
go back to reference Goswami R, Pande CS. Investigations of crack-dislocation interactions ahead of mode-III crack. Mater Sci Eng A. 2015;627(03):217–22.CrossRef Goswami R, Pande CS. Investigations of crack-dislocation interactions ahead of mode-III crack. Mater Sci Eng A. 2015;627(03):217–22.CrossRef
29.
go back to reference Zacharopoulos N, Srolovitz DJ, Lesar R. Dynamic simulation of dislocation microstructures in mode III cracking. Acta Mater. 1997;45:3745–63.CrossRef Zacharopoulos N, Srolovitz DJ, Lesar R. Dynamic simulation of dislocation microstructures in mode III cracking. Acta Mater. 1997;45:3745–63.CrossRef
30.
go back to reference Pande CS, Imam MA, Srivatsan TS. Some thoughts, in fatigue of materials II: Advances and emergences in understanding. In: Srivatsan TS, Imam MA and Szini Vasan R (eds), Fundamentals of fatigue crack initiation and propagation. John Wiley & Sons, Inc., Hoboken, NJ; 2012. https://doi.org/10.1002/9781118533383.ch1 Pande CS, Imam MA, Srivatsan TS. Some thoughts, in fatigue of materials II: Advances and emergences in understanding. In: Srivatsan TS, Imam MA and Szini Vasan R (eds), Fundamentals of fatigue crack initiation and propagation. John Wiley & Sons, Inc., Hoboken, NJ; 2012. https://​doi.​org/​10.​1002/​9781118533383.ch1
31.
go back to reference Basinski ZS, Basinski SJ. Low amplitude fatigue of copper single crystals. Acta Metall. 1985;33(7):1319–27.CrossRef Basinski ZS, Basinski SJ. Low amplitude fatigue of copper single crystals. Acta Metall. 1985;33(7):1319–27.CrossRef
32.
go back to reference Mott NF. A theory of the origin of fatigue cracks. Acta Metall. 1958;6(3):195–7.CrossRef Mott NF. A theory of the origin of fatigue cracks. Acta Metall. 1958;6(3):195–7.CrossRef
33.
go back to reference Antonopoulos JG, Brown LM, Winter AT. Vacancy dipoles in fatigued copper. Philos Mag. 1976;34(4):549–63.CrossRef Antonopoulos JG, Brown LM, Winter AT. Vacancy dipoles in fatigued copper. Philos Mag. 1976;34(4):549–63.CrossRef
34.
go back to reference Differt K, Essmann U, Mughrabi H. A model of extrusions and intrusions infatigued metals – II. Surface roughening by random irreversible slip. Philos Mag. 1986;54(2):237–58.CrossRef Differt K, Essmann U, Mughrabi H. A model of extrusions and intrusions infatigued metals – II. Surface roughening by random irreversible slip. Philos Mag. 1986;54(2):237–58.CrossRef
35.
go back to reference Neumann P. Coarse slip model of fatigue. Acta Metall. 1969;17(9):1219–25.CrossRef Neumann P. Coarse slip model of fatigue. Acta Metall. 1969;17(9):1219–25.CrossRef
36.
go back to reference Riemelmoser FO, Gumbsch P, Pippan R. Dislocation modeling of fatigue cracks: an overview. Mater Trans. 2001;42(1):2–13.CrossRef Riemelmoser FO, Gumbsch P, Pippan R. Dislocation modeling of fatigue cracks: an overview. Mater Trans. 2001;42(1):2–13.CrossRef
37.
go back to reference Riemelmoser FO, Pippan R. Investigation of a growing fatigue crack by means of a discrete dislocation model. Mater Sci Eng A. 1997;135:234–6. Riemelmoser FO, Pippan R. Investigation of a growing fatigue crack by means of a discrete dislocation model. Mater Sci Eng A. 1997;135:234–6.
38.
go back to reference Riemelmoser FO, Pippan R, Stuwe HP. A comparison of a discrete dislocation model and a continuous description of cyclic crack tip plasticity. Int J Fract. 1997;85(2):157–68.CrossRef Riemelmoser FO, Pippan R, Stuwe HP. A comparison of a discrete dislocation model and a continuous description of cyclic crack tip plasticity. Int J Fract. 1997;85(2):157–68.CrossRef
39.
go back to reference Pippan R. Dislocation emission and fatigue crack growth threshold. Acta Metall Mater. 1991;39(3):255–62.CrossRef Pippan R. Dislocation emission and fatigue crack growth threshold. Acta Metall Mater. 1991;39(3):255–62.CrossRef
40.
go back to reference Wilkinson AJ, Roberts SG, Hirsch PB. Modelling the threshold conditions for propagation of stage-I fatigue cracks. Acta Mater. 1998;46(2):379–90.CrossRef Wilkinson AJ, Roberts SG, Hirsch PB. Modelling the threshold conditions for propagation of stage-I fatigue cracks. Acta Mater. 1998;46(2):379–90.CrossRef
41.
go back to reference Laird C, Smith GC. Crack propagation in high stress fatigue. Philos Mag. 1962;7(77):847–57.CrossRef Laird C, Smith GC. Crack propagation in high stress fatigue. Philos Mag. 1962;7(77):847–57.CrossRef
42.
go back to reference Katagiri K, Omura A, Koyanagi K, Awatani J, Shiraishi T, Kaneshiro H. Early stage in fatigued crack tip dislocation morphology in fatigued copper. Metall Trans A. 1977;8A:1769–73.CrossRef Katagiri K, Omura A, Koyanagi K, Awatani J, Shiraishi T, Kaneshiro H. Early stage in fatigued crack tip dislocation morphology in fatigued copper. Metall Trans A. 1977;8A:1769–73.CrossRef
43.
go back to reference Pham MS, Solenthaler C, Janssens KGF, Holdsworth SR. Dislocation structure evolution and its effects on cyclic deformation response of AISI 316L stainless steel. Mater Sci Eng A. 2011;528:3261–9.CrossRef Pham MS, Solenthaler C, Janssens KGF, Holdsworth SR. Dislocation structure evolution and its effects on cyclic deformation response of AISI 316L stainless steel. Mater Sci Eng A. 2011;528:3261–9.CrossRef
44.
go back to reference Miekk-Oja HM, Lindroos VK. The formation of dislocation networks. Surf Sci. 1972;31:422–55.CrossRef Miekk-Oja HM, Lindroos VK. The formation of dislocation networks. Surf Sci. 1972;31:422–55.CrossRef
45.
go back to reference Lindroos VK, Miekk-Oja HM. Knitting of dislocation networks by means of stress-induced climb in aluminium-magnesium alloy. Philos Mag. 1968;17:119–33.CrossRef Lindroos VK, Miekk-Oja HM. Knitting of dislocation networks by means of stress-induced climb in aluminium-magnesium alloy. Philos Mag. 1968;17:119–33.CrossRef
46.
go back to reference Grosskreutz JC. Formation of substructure in aluminum during alternate plastic strain. In: Proceedings of the fifth international congress for electron microscopy. New York: Academic; 1962. p. J-9. Grosskreutz JC. Formation of substructure in aluminum during alternate plastic strain. In: Proceedings of the fifth international congress for electron microscopy. New York: Academic; 1962. p. J-9.
47.
go back to reference McEvily AJ, Boettner RC. On fatigue crack propagation in FCC metals. Acta Metall. 1963;11(7):725–43.CrossRef McEvily AJ, Boettner RC. On fatigue crack propagation in FCC metals. Acta Metall. 1963;11(7):725–43.CrossRef
Metadata
Title
Crack-Dislocation Interactions Ahead of a Crack Tip
Authors
R. Goswami
C. S. Pande
Copyright Year
2019
Publisher
Springer Singapore
DOI
https://doi.org/10.1007/978-981-10-6884-3_52

Premium Partners