Abstract
Interaction of the cooperative grain boundary sliding and migration with a crack in deformed nanocrystalline materials is investigated using the complex variable method. Effects of the two disclination dipoles produced by the cooperative deformation on the emission of lattice dislocations from the crack tip are theoretically described. The complex form expressions of the stress field and the force field are derived. The critical stress intensity factors for the first dislocation emission are calculated. Influences of disclination strength, grain size, locations of the two disclination dipoles as well as crack length on the critical stress intensity factors are discussed in detail. Results show that, the cooperative deformation has great influence on dislocation emission from the crack tip. In general, the cooperative deformation can promote the lattice dislocation emission from the crack tip, thus improve the toughness of the nanocrystalline materials.
Highlights
Rapidly growing attention has been focused on a new physical mechanism or mode of plastic deformation in nanocrystalline metals and ceramics
When the disclination strength is larger than the critical value ω0, the dislocation can emit from the crack tip without any external loadings
We can see that, with the same disclination strength and the same crack length, the critical normalized stress intensity factors (SIFs) KI0IC is much smaller than KI0C, which means the mode II loadings are easier than the mode I loadings to make the dislocation emit form the crack tip
Summary
Let us consider a deformed nanocrystalline solid with a crack under remote mode I loadings and remote mode II loadings. Let us calculate the stress fields produced by the cooperative grain boundary sliding and migration in the deformed nanocrystalline solid with a flat crack. According the Romanov and Vladimirov [32], the elastic stress fields produced by a wedge disclination characterized by strength ω , located at the point zk ( = xk + iyk ) in an infinite homogeneous medium may be expressed as follows:. Assume that the elastic fields produced by the cooperative grain boundary sliding and migration in an infinite homogeneous medium can be evaluated by using two complex potentials ΦΔ0 ( z) and ΨΔ0 (z). (11) and (12) are singularity principal parts of complex potentials on the problem of the cooperative grain boundary sliding and migration in an infinite homogeneous medium without the crack. Substituting Eqs. (19) and (20) into formulae (4), (5) and (6), we obtain the stress fields due to the cooperative grain boundary sliding and migration
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