A novel approach to representative orientation distribution functions for modeling and simulation of polycrystalline shape memory alloys

Abstract

SUMMARYA micromechanical model for polycrystalline shape memory alloys (SMAs) was introduced in a series of papers by Hackl and coauthors. In order to model the polycrystalline aspect, they assumed a specific set of orientation distribution functions that had to be resolved with high numerical effort. Although this model displays interesting aspects, its use to simulate macroscopic specimens is problematic due to the long calculation time.In this paper, we present a new approach to modeling and simulation of polycrystalline SMAs that is based on parameterization of a class of orientation distribution functions by using only a few parameters. A variational concept is applied to derive evolution equations for these parameters. The resultant material model drastically reduces the calculation time and may thus provide an approach to efficient micromechanical simulation of specimens that are of engineering interest.This study presents a variety of different numerical examples, such as pseudoelastic and pseudoplastic material behavior for CuAlNi and NiTi SMAs, to demonstrate the broad applicability of the material model. The numerical benefit of the presented modeling approach is demonstrated by comparative calculations of the new model versus the previous model. Copyright © 2014 John Wiley & Sons, Ltd.

A coupled dissipation functional for modeling the functional fatigue in polycrystalline shape memory alloys

“…Condensed versions can be found in [23,22] and for the thermo-mechanically coupled case in [24] where the principle of the minimum of the dissipation potential for non-isothermal processes [27] has been applied. The micromechanical state for shape memory alloys undergoing functional fatigue is described by use of two internal variables for both the phases λ and the irreversible strains ε p :…”

“…This might influence the local and consequently the global stress response. To account for this, we adapt in this subsection the approach in [16] to calculate the Young measure for the volume fraction of grains ξ j bȳ ξ j = max k=1,...,6 n pref · R j · n {1,0,0},k −q (23) with the set of {1, 0, 0}-austenite normal vectors…”

Finite element implementation and simulation of the functional fatigue in shape memory alloys

“…Therefore, the quantity ρ accounts for the stabilized martensite during cyclic loading until a maximum value ρ max . In addition, we introduce a set of Euler angles α = {ϕ, ϑ, ω} (see [2]) which describes the averaged orientation of the transforming grains and hence, takes into account the polycrystalline structure. The presented model is based on the principle of the minimum of the dissipation potential, see e.g.…”

“…Thus, we take into account a reversible and an irreversible volume fraction for the austenitic and several martensitic phases. To consider the material's polycrystalline structure and hence, differently oriented grains, we use an orientation distribution function which depends on three Euler angles and affects a high numerical efficiency as presented in [2]. …”

A variational viscosity-limit approach to the evolution of microstructures in finite crystal plasticity

“…Several material models were designed using this variational framework, e.g. those in references [23][24][25][26]. The principle of the minimum of the dissipation potential for non-isothermal processes was presented in reference [27] and applied to shape memory alloys in reference [28].…”