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.
Highlights
Size-affected dislocation-mediated plasticity is important in a wide range of materials and technologies
In the following, we present a study on size-dependent dislocationmediated plasticity by utilizing a large set of 3D discrete dislocation dynamics (DDD) simulations
The strength is computed between 0.5 and 1.0% strain, and at these strain levels the dislocation density does not increase or decrease more than a factor of 2–3 times from its initial value[23,27,28]. These results clearly show, for each crystal size, the strength scales with the dislocation density following a power-law relationship of the form t 1⁄4 rn, having negative and positive exponents below and above a critical dislocation density, rcrit respectively
Summary
Size-affected dislocation-mediated plasticity is important in a wide range of materials and technologies. We develop a generalized size-dependent dislocation-based model that predicts strength as a function of crystal/grain size and the dislocation density. In the following, we present a study on size-dependent dislocationmediated plasticity by utilizing a large set of 3D discrete dislocation dynamics (DDD) simulations These simulations span 2 orders of magnitude in crystal size and 5 orders of magnitude of dislocation density. The results show a correlation between crystal strength and dislocation density for micron and sub-micron crystal sizes, and a minimum crystal strength marked by a transition from dislocation-source strengthening to forestdominated strengthening at a size-dependent critical dislocation density These results are validated by a large set of experimental results on micro- and macro-crystals reported previously[19,20,21]. The developed model is shown to agree well with grain size strengthening in polycrystals and provide a microstructurally based understanding of the Hall–Petch relationship
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