Mobility of twin and phase boundaries

Abstract

Abstract.This paper reviews sorne recent advances in understanding the mobility of twin and phase boundaries in martensites, and discusses the design of systematic experiments.

Micro-to-Meso Scale Limit for Shape-Memory-Alloy Models with Thermal Coupling

“…It has been argued in [13] that such a choice is necessary as "boundaries require an unboundedly increasing driving force for the propagation speeds to reach towards some sound speed", cf. also [12]. This is also consistent with experiments, see again [13] and the references therein.…”

Mathematical models of martensitic microstructure

“…In principle, one might expect the concepts of dynamical systems theory, such as invariant manifolds and attractors, to be important in such an analysis. Unfortunately, to carry out such a programme at present seems out of reach, firstly because it is not clear what dynamic equations to use (a key issue being the laws governing the motion of interfaces -see Bhattacharya, Purohit and B. Craciun [22]), and secondly because the mathematical analysis of such systems is poorly developed. For example, the author is not aware of a satisfactory three-dimensional treatment of motion of a single austenite martensite interface.…”

An experimentally-fitted thermodynamical constitutive model for polycrystalline shape memory alloys

“…Indeed, as demonstrated in [31], in quasi-static loading under strictly isothermal conditions, NiTi SMA behave in a rate-independent manner. However, to conform also to high-driving-rates situations, the model shall be extended by a rate-dependent contribution; this is justified by the fact that phase boundaries require an unlimitedly increasing driving force to propagate at speeds reaching towards some sound speed [10]. For the rate-dependent part, we choose the simplest possible option and take (uncoupled) terms quadratic in the rates.…”

“…In this section, we show that the model devised in Section 2 is mathematically well-posed in the sense that it possesses weak solutions and simultaneously we devise a stable and convergent approximation.When scrutinizing a suitable notion of weak solutions, we have to deal with doubly-nonlinear structure of the balance equations for the mechanic variables; cf. (10). In isothermal situations, analysis of such structures has been pioneered in [23] but here the situation is more general because we allow for a state-dependence of the dissipation function and thermal coupling.…”