A modification to Hardy's thermomechanical theory for conserving fundamental properties more accurately: tensile and shear failures in iron

Abstract

A new normalization criterion has recently been proposed for constructing the localization function in Hardy's atomistic-to-continuum thermomechanical theory. The modification involves changing the normalization integral into a summation over the discrete volumes occupied by the atoms. The resulting thermomechanical quantities such as stress and heat flux have been shown to obey the conservation equations more accurately for some non-equilibrium thermomechanical processes in numerical tests. However, it is still uncertain if this modification is valid in ductile fractures, where more complex deformation mechanisms exist such as dislocation emission, slip band formation and twinning. As such, molecular dynamics simulation is conducted to investigate crack in bcc iron (Fe) crystal under tensile and shearing loading and the validity of Hardy's formulas are tested at the defective region. Stress fields are constructed around the defective crack-tip region using the ensemble averaged Hardy's formulas and are used to explain the fracture mechanism in the cracked Fe system. The validity of the conservation equations using Hardy's quantities based on the proposed modification can be established at the crack tip where slip bands and other defects exist, but some discrepancy between two sides of the balance of energy can be observed at the crack region.