Nanotwin orientation on history-dependent stress decay in Cu nanopillar under constant strain

Cu with nanotwin (NT) possesses great electrical, mechanical, and thermal properties and has potential for electronic applications. Various studies have reported the effect of NT orientation on Cu mechanical properties. However, its effect on Cu stress-relaxation behavior has not been clarified, particularly in nano-scale. In this study, Cu nanopillars with various orientations were examined by a picoindenter under constant strain and observed by in-situ TEM. The angles between the twin plane and the loading direction in the examined nanopillars were 0°, 60°, to 90°, and a benchmark pillar of single-crystal Cu without NT was examined. The stress drops were respectively 10%, 80%, 4%, and 50%. Owing to the interaction by NT, the dislocation behavior in nanopillars was different from that in bulk or in thin film samples. Especially, the rapid slip path of dislocations to go to the free surface of the nanopillar induced a dislocation-free zone in the 0° nanopillar, which led to work-softening. On the contrary, a high dislocation density was observed in the 90° nanopillar, which was generated by dislocation interaction and obstruction of dislocation slip by twin planes, and it led to work-hardening. The findings reveal the NT orientation in Cu nanopillars affected stress relaxation significantly.

A stochastic solver based on the residence time algorithm for crystal plasticity models

The deformation of crystalline materials by dislocation motion takes place in discrete amounts determined by the Burgers vector. Dislocations may move individually or in bundles, potentially giving rise to intermittent slip. This confers plastic deformation with a certain degree of variability that can be interpreted as being caused by stochastic fluctuations in dislocation behavior. However, crystal plasticity (CP) models are almost always formulated in a continuum sense, assuming that fluctuations average out over large material volumes and/or cancel out due to multi-slip contributions. Nevertheless, plastic fluctuations are known to be important in confined volumes at or below the micron scale, at high temperatures, and under low strain rate/stress deformation conditions. Here, we develop a stochastic solver for CP models based on the residence-time algorithm that naturally captures plastic fluctuations by sampling among the set of active slip systems in the crystal. The method solves the evolution equations of explicit CP formulations, which are recast as stochastic ordinary differential equations and integrated discretely in time. The stochastic CP model is numerically stable by design and naturally breaks the symmetry of plastic slip by sampling among the active plastic shear rates with the correct probability. This can lead to phenomena such as intermittent slip or plastic localization without adding external symmetry-breaking operations to the model. The method is applied to body-centered cubic tungsten single crystals under a variety of temperatures, loading orientations, and imposed strain rates.