An energy approach to the formation of twins in TiAl

Abstract

The energy criterion of stability of equilibrium is used to predict the formation of discrete twin bands running across the grains of polycrystalline solids. An uncontrolled rapid development of a twin band is assumed to occur when the associated release of elastic energy compensates the interfacial energy and intrinsic dissipation due to twinning. A simplified analysis is performed that leads to compact analytic formulae for the thickness of a twin band and for the critical resolved stress. The creation of subsequent discrete twin bands in a finite solid can be separated by the periods of quasistatic growth of existing twins under varying loads. An application of the energy criterion to twinning in TiAl intermetallics and its verification by observed data for the thickness of a twin band are presented.

Size effects on the martensitic phase transformation of NiTi nanograins

“…a Tw ¼ 0:041 for a Poisson's ratio n ¼ 0:2). Recently, Petryk et al (2003) and Fischer et al (2003) presented an estimation of the strain energy due to a single twin, based on dislocation mechanics. From their results, a coefficient a Tw ¼ã=4p À Á ln '=D À Á can be derived.…”

Mechanics of sheared bands – Applications to faults, twins and variants

“…If the variants exhibit different elastic properties, as it happens to be the case for shape memory alloys, then one has to resort to the finite element method to compute the stress fields as has been done by Waitz et al (2007). The solutions presented can be used to estimate the thickness of the banded twin-arrangements as outlined by Petryk et al (2003), Fischer et al (2003aFischer et al ( ,b, 2006, Yan et al (1997) and Waitz et al (2007). Particular attention is devoted to the stress state near the twin edges.…”

“…Petryk et al (2003) could prove the reduction of the energy content by applying a general stability criterion. A further outcome of this study is the magnitude of the twin-band width resulting in a morphology that minimizes the barrier terms inhibiting the formation of the twin.…”

Interfacial energy and dissipation in martensitic phase transformations. Part I: Theory

“…e.g. Fischer and Reisner (1998), Levitas (1998) and Petryk et al (2003). The major difficulty in applying it is to determine appropriately the dissipationDD during the transition from G 0 toĜ.…”