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

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.