Shape Memory: A New Concept of Explanation and of Mathematical Modelling

Abstract

The shape memory effect and pseudoelasticity that are observed typically with some binary and ternary alloys are explained on the basis of interaction of the sets of different atoms of the elements constituting the alloy. The concrete discussion is limited to binary alloys only, assuming that the processes in ternary alloys are similar in principle, but substantially more complicated and therefore difficult to be modelled. The differing thermal expansions of the two elements present in a binary alloy are assumed to be the cause of the changes of energy of the interatomic forces with changing temperature. Cooling of such an alloy in austenitic state leads to an increase of this energy, then the energy is partly dissipated and the structure of the alloy transforms to a martensitic one; the metastable austenitic configuration changes into the lower energy martensitic structure. The mechanism of the transformation consists in the following variations of the interatomic distances: the distances between the differing atoms in the binary alloy (pairs with the smallest distances and with the strongest bonds) remain nearly unchanged, whereas the distances between atoms of the same el ement (pairs with larger distances and with weaker bonds) do change with martensitic transforma tion substantially, which leads to the lowering of the bond energy. It is shown that this understanding of the process agrees with a number of observed phenomena and it opens the possibility of model ling the shape memory effect and pseudoelasticity by a continuum model consisting of two con tinuous infrastructures corresponding to the two sets of atoms present in the binary alloy.