2015 Volume 101 Issue 8 Pages 435-444
This study investigates mechanical stability of ideal b.c.c. crystals (α-Fe, Mo and Nb) under finite deformation. Strain energy density W is introduced using a lattice dynamics model with the second- and third-order elastic constants measured by experiments. Critical stress and strains are determined from the failure of strong ellipticity condition for stress equilibrium equation. Present numerical analysis for (001) in-plane deformation revealed that mechanical stability of the crystals depends on the deformation mode including the sign. It also revealed that the number and direction of emerging characteristic curves vary with the critical point reflecting on the nature of inter-atomic bonding. We also conducted the stability analyses for simple shear deformations on the principal planes: (100), (110) and (111). The critical shear stress show semi-quantitative agreement with those reported by first-principle calculation. Average of the shear stress over shear modulus ratio turns out to be 11%, which is close to the displacement burst condition measured by nano-indentation experiments.