On a unified approach to the description of phase transitions and strain localization

Summary

Two contradictions are stated in the paper: (1) The standard approach to the description of the onset of strain localization (SL) cannot describe known results related to the onset of phase transition (PT) although PT can also be considered as a form of SL. (2) In the course of PT, traction continuity is violated across the phase interface. To remove tje contradictions, the concept of stress fluctuating across the discontinuity surface is introduced. The stress overcomes the energy barrier and restores the traction continuity. It is shown that the unified approach to the two types of instabilities can be found by a kinetic method only. A simplest macroscopic counterpart of the known microscopic kinetic method is considered. For SL, it results in a kinetic theory of surface damage, time-dependent behaviour and fracture at the stress smaller than the peak value of the stress-strain diagram. The classical description of SL can be obtained for vanishing velocity of damage accumulation, i.e. when the fluctuating stress is absent. The fluctuating stress is necessary for equilibrium PT. In the last part of the paper, the equilibrium PT is considered by taking into account both the energy of internal stresses and the threshold-type thermodynamical dissipative forcek. Known experimental results on the deformation of pseudoelastic material are described. A simple dependence ofk on the volume fraction of martensite and PT history is determined. A kinetic equation is suggested which includes the above thermodynamical description.