Ab initio aided strain gradient elasticity theory in prediction of nanocomponent fracture

• Published in: Mechanics of materials 2019-09, Vol.136, p.103074, Article 103074
• Main Authors: Kotoul, Michal, Skalka, Petr, Profant, Tomáš, Friák, Martin, Řehák, Petr, Šesták, Petr, Černý, Miroslav, Pokluda, Jaroslav
• Format: Article
• Language: English
• Subjects: DFT; FEM; Fracture nanomechanics; Size dependent phenomena; Strain gradient elasticity
• ISSN: 0167-6636; 1872-7743
• DOI: 10.1016/j.mechmat.2019.103074

•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. 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 l1 of the simplified form of the strain gradient elasticity theory plays a key role in the analysis. The parameter l1 is identified for silicon and tungsten single crystals using first principles calculations. Specifically, the parameter l1 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.