A nano-embryonic mechanism for superelasticity, elastic softening, invar and elinvar effects in defected pre-transitional materials

A vast amount of physically-different materials near their structural phase transitions have been widely used due to their rich and extraordinary properties, e.g., superelasticity, elastic softening and invar/elinvar effects. These pre-transitional materials are known to have complex microstructures consisting of stress-generating defects such as dislocations and coherent nano-precipitates. However, effects of such defects on properties have not been well understood, which hinders fully exploiting the potential applications of these materials. In this paper we investigated a nano-embryonic mechanism in a generic case of pre-transitional materials with stress-generating defects at temperatures close but above the starting temperature of phase transformation, M_s. We demonstrated that the stress concentration generated by defects could induce localized displacive phase transformation near defects, producing equilibrium nano-size embryos of orientation variants of the product phase. The obtained mixed state consisting of nano embryos is in a thermoelastic equilibrium in which the total volume and sizes of embryos are equilibrium internal thermodynamic parameters. The subsequent imposition of an applied stress causes these embryos to grow, generating superelastic responses with an increasing applied field. If the defects are stationary the growth maintains thermoelastic equilibrium, and is, hence, fully reversible and anhysteretic. Moreover, cooling toward the M_s also causes embryo growth resulting in a diffuse phase transformation, which increases the volume and softens the modulus. These effects counteract the thermal contraction and modulus increase in the untransformed matrix, and may explain the invar and elinvar affects in alloys with low-temperature displacive transformations.