Ab initio aided strain gradient elasticity theory in prediction of nanocomponent fracture. (September 2019) - Kotoul, Michal; Skalka, Petr; Profant, Tomáš; Friák, Martin; Řehák, Petr; Šesták, Petr; Černý, Miroslav; Pokluda, Jaroslav
Highlights: Strain gradient elasticity theory (SGET) was combined with ab-initio and molecular statics simulations. This hybrid approach proved to give reasonable predictions of fracture problems at micro and nano scales. Ab-initio calculations of the phonon-dispersion relations were fitted by the dispersion relations predicted by SGET. Ab-initio calculations of the displacement field near the screw dislocation was fitted by the SGET solution of this field. Ab-initio calculations were used to find the deformation mode of atoms when a single bond breaks at the crack tip. Abstract: The aim of the paper is to address fracture problems in nanoscale-sized cracked components using a simplified form of the strain gradient elasticity theory aided by ab initio calculations. Quantification of the material length scale parameter l 1 of the simplified form of the strain gradient elasticity theory plays a key role in the analysis. The parameter l 1 is identified for silicon and tungsten single crystals using first principles calculations. Specifically, the parameter l 1 is extracted from phonon-dispersions generated by ab-initio calculations and, for comparison, by adjusting the analytical strain gradient elasticity theory solution for the displacement field near the screw dislocation with the ab-initio calculations of this field. The obtained results are further used in the strain gradient elasticity modeling of crack stability in nano-panels made of silicon and tungsten single crystals, where due to size effects and nonlocal material point interactions the classical linear fracture mechanics breaks down. The cusp-like crack tip opening profiles determined by the gradient elasticity theory and a hybrid atomistic approach at the moment of nano-panels fracture revealed a very good mutual agreement.