SOFT PHONON MODE AND ELASTIC INSTABILITIE S IN STRESS-INDUCED PHASE-TRANSFORMATION

A stress-induced phase transformation phenomenon is one of the hierarc hical mechanical behaviors in which atomistic rearrangements the simul taneously and dually reflected to macroscopic strength of material. It has so far been recognized as one of the bifurcation problems in the fields of thermodynamics and continuum mechanics. Softening of phonon dispersion curves has also been acknowledged as precedence of transfor mation as well. Movements of atoms in an alpha-iron under uniaxial ten sion are first traced by the molecular dynamics (MD) simulations on th e assumption oi a constant applied stress ensemble proposed by Parrine llo & Rahman. Stress dependency a phonon dispresion curves obtained fr om the deformed lattice structures are then examined. Bifurcation cond itions derived from positive definiteness of strain energy in the whol e deformed matters are, at the same time, investigated using analytica l elastic constants defined from only an atomic configuration and the force constants which are the second derivative of an employed Interat omic potential. It is found that softening of phonon dispersion curves , especially the long-wavelength acoustic branch, could correspond to the macroscopic bifurcation conditions over the scale.