Unravelling the physics of size-dependent dislocation-mediated plasticity

Size-affected dislocation-mediated plasticity is important in a wide range of materials and technologies. The question of how to explain and predict the effect of size on the properties and response of materials has been at the forefront of mechanics and materials research.

In dislocation-mediated plasticity the fundamental building blocks are dislocations, which collectively govern the plastic deformation and damage evolution in metals, semiconductors, semicrystalline polymers and even ceramics under shock loading. It is well established that the strength of bulk crystals increases with increasing dislocation density generally following the well-known Taylor-strengthening power law with an exponent of 0.5. However, for micron and sub-micron crystals, strength has been observed to increase with decreasing crystal/grain size. Furthermore, it is also accepted that the initial dislocation density plays an important role in the strength of micron-sized single crystals, with several simulations and experimental studies showing that bulk like behaviour is recovered at large enough dislocation densities.

Recently, we have performed a large set of discrete dislocation dynamics (DDD) simulations spanning two orders of magnitude of crystal size, and five orders of magnitude of dislocation density to develop a generalized size-dependent dislocation-based model that predicts strength as a function of crystal/grain size and the dislocation density (i.e. a modified size dependent Taylor/forest "Hardening" model). The model was subsequently validated with a large set of published single and polycrystal experiments from submicron to bulk scales. The model is also shown to yield excellent agreement with size-effects in polycrystals (Hall-Petch) and gives further insights on possible reasons for the deviation from the -0.5 Hall-Petch scaling reported in some experiments. Also based on these simulations we proposed a deformation mechanism map as well as predict an apparent size dependent length distribution of dislocation networks.

Jaafar A. El-Awady, Unravelling the physics of size-dependent dislocation-mediated plasticity, Nature Communications, 5926, (2015) 10.1038/ncomms6926 (http://www.nature.com/ncomms/2015/150106/ncomms6926/full/ncomms6926.html)

Paper Abstract:

Size-affected dislocation-mediated plasticity is important in a wide range of materials and technologies. Here we develop a generalized size-dependent dislocation-based model that predicts strength as a function of crystal/grain size and the dislocation density. Three-dimensional (3D) discrete dislocation dynamics (DDD) simulations reveal the existence of a well-defined relationship between strength and dislocation microstructure at all length scales for both single crystals and polycrystalline materials. The results predict a transition from dislocation-source strengthening to forest-dominated strengthening at a size-dependent critical dislocation density. It is also shown that the Hall–Petch relationship can be physically interpreted by coupling with an appropriate kinetic equation of the evolution of the dislocation density in polycrystals. The model is shown to be in remarkable agreement with experiments. This work presents a micro-mechanistic framework to predict and interpret strength size-scale effects, and provides an avenue towards performing multiscale simulations without ad hoc assumptions.

The paper (open access) is attached along with the supplementary information.

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