Skip to main content Accessibility help

Effect of Crack Geometry on Dislocation Nucleation and Cleavage Thresholds

  • L.L. Fischer (a1) and G.E. Beltz (a1)


A continuum model based upon the Peierls-Nabarro description of a dislocation ahead of a crack is used to evaluate the critical mode I loading for dislocation nucleation at the tip of a finite, pre-blunted crack. A similar approach is used to evaluate the critical mode I loading for atomic decohesion. Results are presented for various crack tip root radii (a measure of bluntness), for several crack lengths. It is shown that increasing the crack length increases the critical energy release rate for both material behaviors. Increasing the bluntness of a crack tip always increases the required loading for atomic decohesion but nucleation thresholds are initially decreased by very small increases in crack tip bluntness. Nucleation thresholds are later increased after reaching significant crack tip blunting. Implications for ductile versus brittle competition are discussed by comparing the ongoing competition between these two different material behaviors.



Hide All
1. Rice, J. R. and Thomson, R., Phil. Mag. 29, p. 73 (1974).
2. Mason, D. D., Phil. Mag. 39, p. 455 (1979).
3. Rice, J. R., J. Mech. Phys. Solids 40, p. 239 (1992).
4. Peierls, R. E., Proc. phys. Soc. 52, p. 23 (1940).
5. Nabarro, F. R. N., Proc. phys. Soc. 59, p. 256 (1947).
6. Rice, J. R., Beltz, G. E., and Sun, Y., “Peierls Framework for Dislocation Nucleation from a Crack tip,” in Topics on Fracture and Fatigue ed. Argon, A. S. (New York: Springer-Verlag, 1992), p. 1.
7. Xu, G., Argon, A. S., and Ortiz, M., Phil. Mag. A 72, p. 415 (1995).
8. Gumbsch, P., J. Mater. Res. 10, p. 2897 (1995).
9. Gumbsch, P. and Beltz, G. E., Modelling Simul. Mater. Sci. Eng. 3, p. 597 (1995).
10. Schiotz, J., Carlsson, A. E., Canel, L. M., and Thomson, R., Mat. Res. Soc. Symp. Proc. 409, p. 95 (1996).
11. Schiotz, J., Canel, L. M., and Carlsson, A. E., Phys. Rev. B 55, p. 6211 (1997).
12. Frenkel, J., Z. Phys 37, p. 572 (1929).
13. Vitek, V., J. Mech. Phys. Solids, 24, p. 67 (1975).
14. Muskhelishvili, N. I., Some Basic Problems on the Mathematical Theory of Elasticity: Fundamental Equations, Plane Theory of Elasticity, Torsion and Bending (Noordhoff, 1975), p. 347.
15. Tada, H., Paris, P. C., and Irwin, G. R., The stress Analysis of Cracks Handbook (Del Research Corporation: St. Louis, 1985), p. 1.4b.
6. Timoshenko, S. P. and Goodier, J. N., Theory of Elasticity (McGraw-Hill, Inc.: New York, 1987), p. 90.
17. Beltz, G. E., Ph.D. Thesis, Division of Applied Sciences, Harvard University, Cambridge, Massachusetts, (1992).
18. Dundurs, J. and Mura, T., J. Mech. Phys. Solids 12, p. 177 (1964).


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed