Dislocation Emission from Surface Crack/Notch under Mode I Loading and its Size Dependence

Abstract

Fatigue and fracture of structures often originate from the surface notch or crack. In this contribution, a Peierls type continuum model developed by Rice (1992, Dislocation Nucleation From a Crack Tip: An Analysis Based on the Peierls Concept, Journal of the Mechanics and Physics of Solids, 40: 239—271) is employed to analyze the critical stress of dislocation emission from the surface notch/crack in the plane strain state in a unified manner. Both the stress field in a notched/cracked half-plane under mode I loading and the stress field induced by an edge dislocation are obtained in closed forms using the Muskhelishvili method. Calculations are carried out to study the effects of the notch/crack depth and the root curvature radius on the dislocation emission. Results show that the critical stress for dislocation emission depends greatly on both of them. The shallower the surface notch/crack is, the higher the critical stress is. This depth dependence of the critical stress for the surface notch is more significant than that for the surface crack. Similarly, the dependence of the critical stress on the slip plane orientation angle for the surface notch is relatively stronger than that for the surface crack. Within a certain range of the slip orientation angle, the critical dislocation emission stress for the surface notch with small root curvature radius is even less than that for the surface crack at the same depth. These results are helpful for us to understand the ductile—brittle fracture behavior of materials with surface notches or cracks.

Keywords

dislocation emission Peierls model surface notch surface crack size effect.

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References

Ahn, D.C. , Sofronis, P. and Minich, R. ( 2006). On the Micromechanics of Void Growth by Prismatic-dislocation Loop Emission, Journal of the Mechanics and Physics of Solids , 54: 735-755.

Beltz, G.E. and Fischer, L.L. ( 2001). Multiscale Deformation and Fracture in Materials and Structures, Boston, Kluwer, p. 237.

Beltz, G.E. and Rice, J.R. ( 1992). Dislocation Nucleation at Metal-Ceramic Interfaces, Acta Metallurgica et Materialia, 40: S321-S331.

Carrasco, E. , González, M.A. , Rodríguez de la Fuente, O. and Rojo, J.M. (2004). Analysis at Atomic Level of Dislocation Emission and Motion Around Nanoindentations in Gold, Surface Science, 572: 467-475.

Chiao, Y.H. and Clarke, D.R. ( 1989). Direct Observation of Dislocation Emission From Crack Tips in Silicon at High Temperatures, Acta Metallurgica, 37: 203-219.

Cleri, F. , Wolf, D. , Yip, S. and Phillpot, S.R. ( 1997). Atomistic Simulation of Dislocation Nucleation and Motion from a Crack Tip, Acta Materialia, 45: 4993-5003.

Fischer, L.L. and Beltz, G.E. ( 2001). The Effect of Crack Blunting on the Competition Between Dislocation Nucleation and Cleavage, Journal of the Mechanics and Physics of Solids, 49: 635-654.

Frenkel, J. ( 1926). Zur theorie der elastizitXatsgrenze und der festigkeit kristallinischer korper, Zeitschrift für Physik, 37: 572-609.

Higashida, K. , Narita, N. , Asano, S. and Onodera, R. ( 2000). Dislocation Emission from a Crack Tip in MgO Thin Crystals , Materials Science & Engineering A, 285: 111-121.

10.

Hora, P. , Pelikán, V. , Machová A. , Spielmannová A. , Prahl, J. , Landa, M. and Červená, O. ( 2008). Crack Induced Slip Processes in 3D, Engineering Fracture Mechanics, 75: 3612-3623.

11.

Huang, M.S. , Li, Z.H. and Wang, C. ( 2007). Discrete Dislocation Dynamics Modelling of Microvoid Growth Andits Intrinsic Mechanism in Single Crystals, Acta Materialia, 55: 1387-1396.

12.

Huang, M.X. and Li, Z.H. ( 2004). Dislocation Emission Criterion from a Blunt Crack Tip , Journal of the Mechanics and Physics of Solids, 52: 1991-2003.

13.

Ju, J.W. and Oh, S. ( 2008). Investigation of the Crack-dislocation Interaction Effects , International Journal of Damage Mechanics, 17: 223-246.

14.

Lubarda, V.A. , Schneider, M.S. , Kalantar, D.H. , Remington, B.A. and Meyers, M.A. ( 2004). Void Growth by Dislocation Emission, Acta Materialia, 52: 1397-1408.

15.

Muskhelishvili, N.I. ( 1975). Some Basic Problems on the Mathematical Theory of Elasticity: Fundamental Equations, Plane Theory of Elasticity, Torsion and Bending, Holland , Noordhoff.

16.

Ohr, S.M. ( 1985). An Electron Microscopy Study of Crack Tip Deformation and Its Impact on Dislocation Theory of Fracture, Materials Science and Engineering, 72: 1-35.

17.

Peierls, R.E. ( 1940). The Size of a Dislocation, Proceedings of the Physical Society of London, 52: 34-37.

18.

Rice, J.R. ( 1992). Dislocation Nucleation from a Crack Tip: An Analysis Based on the Peierls Concept, Journal of the Mechanics and Physics of Solids, 40: 239-271.

19.

Rice, J.R. and Beltz, G.E. ( 1994). The Activation Energy for Dislocation Nucleation at a Crack, Journal of the Mechanics and Physics of Solids, 42: 333-360.

20.

Rice, J.R. , Beltz, G.E. and Sun, Y. ( 1992). Peierls Framework for Dislocation Nucleation from a Crack Tip. In: Argon, A.S. (ed.), Topics in Fracture and Fatigue, Chap. 1, Berlin, Springer pp. 1-58.

21.

Rice, J.R. and Thomson, R. ( 1974). Ductile Versus Brittle Behavior of Crystals, Philosophical Magazine, 29: 73-97.

22.

Schoeck, G. ( 1991). Dislocation Emission from Crack Tips, Philosophical Magazine A, 63: 111-120.

23.

Schoeck, G. ( 2003). The Emission of Dislocations From Crack Tips a Critical Assessment, Materials Science and Engineering A, 356: 93-101.

24.

Spearot, D.E. , Jacob, K.I. and McDowell, D.L. ( 2007). Dislocation Nucleation From Bicrystal Interfaces with Dissociated Structure, International Journal of Plasticity , 23: 143-160.

25.

Tadmor, E.B. and Hai, S. ( 2003). A Peierls Criterion for the Onset of Deformation Twinning at a Crack Tip, Journal of the Mechanics and Physics of Solids , 51: 765-793.

26.

Tang, Q. and Wang, T. ( 1998). Correlative Reference Model and Molecular Dynamics Simulation of Dislocation Emission Process, Computational Materials Science , 12: 73-83.

27.

Van Milder, J.G.M. and Man, H.K. ( 2009). Some Notes on Microcracking, Softening, Localization and Size Effects, International Journal of Damage Mechanics , 18: 283-309.

28.

Vitek, V. ( 1975). Yielding from a Crack with Finite Root-radius Loaded in Uniform Tension, Journal of the Mechanics and Physics of Solids, 24: 67-76.

29.

Warren, W. ( 1970). Interaction of Dislocations with Surface Notches and Protrusions, International Journal of Engineering Science , 8: 545-558.

30.

Xin, X.J. , Daehn, G.S. and Wagoner, R.H. ( 1998). Modeling the Generation, Equilibrium, and Emission of Dislocations at Elastically Misfitted Particles, Acta Materialia , 46: 6131-6144.

31.

Xu, G. , Argon, A.S. and Ortiz, M. ( 1995). Nucleation of Dislocations from Crack Tips Under Mixed Modes of Loading: Implications for Brittle Against Ductile Behavior of Crystals , Philosophical Magazine A, 72: 415-451.

32.

Xu, G. , Argon, A.S. and Ortiz, M. ( 1997). Critical Configurations for Dislocation Nucleation from Crack Tips, Philosophical Magazine A, 75: 341-367.

33.

Yang, W. , Tang, J. , Ing, J. and Ma, C. ( 2001). Transient Dislocation Emission from a Crack Tip, Journal of the Mechanics and Physics of Solids, 49: 2431-2453.