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.
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References
Ohr SM, Narayan J. Electron microscope observation of shear cracks in stainless steel single crystals. Philos Mag. 1980;41(1):81–9.
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.
Kobayashi S, Ohr SM. In situ fracture experiments in BCC metals. Philos Mag A. 1980;42(6):763–72.
Horton JA, Ohr SM. Determination of emmision condition from the experiments and theory. Scr Metall. 1982;16(5):621–6.
Horton JA, Ohr SM. TEM observations of dislocation emission at crack tip in aluminum. J Mater Sci. 1982;17(11):3140–8.
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.
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.
Majumdar B, Burns S. A Griffith crack shielded by a dislocation pile-up. Int J Fract Mech. 1983;21(3):229–40.
Chang S, Ohr SM. Dislocation-free zone model of fracture. J Appl Physiol. 1981;52(12):7174–81.
Dai SH, Li JCM. Dislocation free zone at the crack tip. Scr Metall. 1982;16(2):183–8.
Thomson R. Physics of fracture. J Phys Chem Solids. 1987;48(11):965–83.
Sadananda K, Glinka G. Dislocation processes that affect kinetics of fatigue crack growth. Philos Mag. 2005;85(2–3):189–203.
Bilby B, Cottrell A, Swinden K. The spread of plastic yield from a notch. Proc Roy Soc A. 1963;272(1350):304–14.
Lin IH, Thomson R. Cleavage, dislocation emission, and shielding for cracks under general loading. Acta Metall. 1986;34(2):187–206.
Pande CS, Masumura RA, Chou YT. Shielding of crack tips by inclined pile-ups of dislocations. Acta Metall. 1988;36(1):49–54.
Weertman J. Theory of fatigue crack growth based on a BCS crack theory with work hardening. Int J Fract. 1973;9(2):125–31.
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.
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.
Weertman J. Fracture mechanics-unified view for Griffith-Irwin-Orowan cracks. Acta Metall. 1978;26(11):1731–8.
Weertman J. Fracture stress obtained from the elastic crack tip enclave model. J Mater Sci. 1980;15(5):1306–10.
Weertman J, Lin IH, Thomson R. Double slip plane crack model. Acta Metall. 1983;31(4):473–82.
Weertman J. Dislocation emmision into a mode III plastic zone. Scr Metall. 1986;20(11):1483–8.
Weertman J. Complete crack shielding. J Appl Mech. 1991;58(4):1107–8.
Rice JR, Thomson R. Ductile versus brittle behavior of crystals. Philos Mag. 1974;29(1):73–97.
Muskhelishvili N. Singular integral equations. Groningen: P. Noordhoof Ltd; 1953.
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.
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.
Goswami R, Pande CS. Investigations of crack-dislocation interactions ahead of mode-III crack. Mater Sci Eng A. 2015;627(03):217–22.
Zacharopoulos N, Srolovitz DJ, Lesar R. Dynamic simulation of dislocation microstructures in mode III cracking. Acta Mater. 1997;45:3745–63.
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
Basinski ZS, Basinski SJ. Low amplitude fatigue of copper single crystals. Acta Metall. 1985;33(7):1319–27.
Mott NF. A theory of the origin of fatigue cracks. Acta Metall. 1958;6(3):195–7.
Antonopoulos JG, Brown LM, Winter AT. Vacancy dipoles in fatigued copper. Philos Mag. 1976;34(4):549–63.
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.
Neumann P. Coarse slip model of fatigue. Acta Metall. 1969;17(9):1219–25.
Riemelmoser FO, Gumbsch P, Pippan R. Dislocation modeling of fatigue cracks: an overview. Mater Trans. 2001;42(1):2–13.
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, 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.
Pippan R. Dislocation emission and fatigue crack growth threshold. Acta Metall Mater. 1991;39(3):255–62.
Wilkinson AJ, Roberts SG, Hirsch PB. Modelling the threshold conditions for propagation of stage-I fatigue cracks. Acta Mater. 1998;46(2):379–90.
Laird C, Smith GC. Crack propagation in high stress fatigue. Philos Mag. 1962;7(77):847–57.
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.
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.
Miekk-Oja HM, Lindroos VK. The formation of dislocation networks. Surf Sci. 1972;31:422–55.
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.
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.
McEvily AJ, Boettner RC. On fatigue crack propagation in FCC metals. Acta Metall. 1963;11(7):725–43.
Acknowledgment
This research was funded by the Office of Naval Research (ONR) through 6.1 program at Naval Research Laboratory (NRL).
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Goswami, R., Pande, C.S. (2019). Crack-Dislocation Interactions Ahead of a Crack Tip. In: Schmauder, S., Chen, CS., Chawla, K., Chawla, N., Chen, W., Kagawa, Y. (eds) Handbook of Mechanics of Materials. Springer, Singapore. https://doi.org/10.1007/978-981-10-6884-3_52
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DOI: https://doi.org/10.1007/978-981-10-6884-3_52
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