Skip to main content Accessibility help

Shielding of cracks in a plastically polarizable material

  • S.J. Zhou (a1) and Robb Thomson (a1)


In this paper, we address some fundamental questions regarding the response of a crack to externally generated dislocations. We note that since dislocations that formed at external sources in the material must be in the form of loops or dipoles, the theory must be couched in terms of crack shielding in a plastically polarizable medium. There are strong analogies to dielectric theory. We prove two general theorems: (1) Dipoles formed in the emission geometry relative to a crack tip always antishield the crack and (2) when dipoles are induced during uniform motion of a crack through a uniformly plastically polarizable material, then the net shielding is always positive. We illustrate these general theorems with a number of special cases for fixed and polarizable sources. Finally, we simulate the self consistent time dependent response of a crack to a polarizable source as the crack moves past it. The results show that the crack is initially antishielded, but that positive shielding always dominates during later stages of configuration evolution. The crack may be arrested by the source, or it may break away from it, depending upon the various parameters (source strength and geometry, dislocation mobility, Griffith condition for the crack, etc.). The results indicate that the time dependence of crack shielding in the presence of a nonuniform density of sources will be very important in practical cases of brittle transitions in materials.



Hide All
1. Rice, J. and Thomson, R., Philos. Mag. 29, 73 (1974).
2. Lin, I-H. and Thomson, R., Acta Metall. 34, 187 (1986).
3. Anderson, P. M. and Rice, J., J. Mech. Phys. Sol. 35, 743 (1987).
4. Ashby, M. and Embury, J., Scripta Metall. 19, 557 (1985).
5. Narita, N., Higashida, K., and Kitano, S., Scripta Metall. 27, 1273 (1987).
6. Suzuki, T. and Koizumi, H., unpublished report.
7. Ohr, S. M., Scripta Metall. 21, 1681 (1987).
8. Kanninen, M. and Popelar, C., Advanced Fracture Mechanics (Oxford, 1985).
9. Rice, J. R., Mech. of Mater. 6, 317 (1987); J. R. Rice, D. E. Hawk, and R.J. Asaro, Int. J. Fract. 42, 301 (1990).
10. Mataga, P., Freund, L., and Hutchinson, H., J. Phys. Chem. Solids 48, 985 (1987).
11. Zhou, S. and Lung, C., J. Phys.: Condens. Matter 1,1, 2297 (1989).
12. Eshelby, J. D., Solid State Physics, edited by Seitz, F. and Turnbull, D. (Academic Press, New York, 1956), Vol. 3, p. 79.
13. Thomson, R., Solid State Physics, edited by Turnbull, D. and Ehrenreich, H. (Academic Press, New York, 1986), Vol. 39, p. 1.
14. Rice, J., J. Appl. Mech. 35, 379 (1968).
15. Eshelby, J. D., in Physics of Strength and Plasticity (The Orowan 65th Anniversary Volume, edited by Argon, A.) (MIT Press, Cambridge, MA, 1969), p. 263.

Shielding of cracks in a plastically polarizable material

  • S.J. Zhou (a1) and Robb Thomson (a1)


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