Mechanical stability of iron under hydrostatic stresses

Abstract

A comprehensive investigation of the mechanics of iron subjected to arbitrary fluid pressure has been carried out. Apart from the classical elastic moduli (k, μ, and μ′) and conventional elastic moduli (Green and stretch moduli) computations are carried out for a family of generalised moduli of which the conventional moduli are just specific members. With the generalised moduli the mechanical stability of iron is investigated through Born criteria. It is found that classical stability, Green stability and stretch stability are all represented uniquely by the present generalised scheme. The definition of effective classical moduli under stresses enabled the amalgamation of the Born criteria of lattice stability into the single classical criteria of lattice stability of cubic crystal under hydrostatic loading environment. Computations are also carried out to investigate the coordinate and stress dependence of Young's modulus of elasticity, Poisson's ratio, mean velocity of elastic wave, and Debye temperature. Surprisingly, it is found that all these properties of solids play an important role in representing the mechanical stability of the solid. The path of uniaxial loading of iron is also investigated along with its internal energy variation on this path. This indicated the existance of stress-free fcc phase of iron on the path of uniaxial deformation at cell length a=3.6444 A giving enthalpy of transformation (bcc→fcc) of 1.1 kJ/mol in good agreement with experimental results.