Contributions on the theory and computation of mono‐ and poly‐crystalline cyclic martensitic phase transformations

Abstract

In this article new contributions to the theory and computation of cyclic martensitic phase transformations (PT) in monoand poly-crystalline metallic shape memory alloys are presented. The PT models of the non-convex variational problem are based on the Cauchy-Born hypothesis and Bain's principle. A quasi-convexified C 1 -continuous thermo-mechanical micromacro constitutive model for metallic monocrystals is developed which is represented together with the phase transformation constraints by a unified Lagrangian variational functional including phase evolution equations with mass conservation. The unified setting presented here includes poly-crystalline shape memory alloys whose microstructure is modeled using lattice variants. A pre-averaging scheme for randomly distributed poly-crystalline variants of transformation strains is used to transform them into those of a fictitious monocrystal. Thus, the incremental integration in process time and the spatial integration algorithms of the discrete variational problems for both mono-and poly-crystalline phase transformations can be implemented into a unified algorithm with branching for mono-and poly-crystalline phase transformations. Furthermore, an error-controlled adaptive 3D finite element method in space is presented for phase transformation problems using explicit error indicator with gradient smoothing and mesh refinements via new mesh generation in each adaptive step. Computations of informative examples with convergence studies, and comparisons with published experimental results are presented using 3D finite elements. Shape memory alloys: phenomenology, physical effects, and applicationsShape memory alloys (SMAs) have immense technological potential because of various aspects of their special thermomechanical behavior, such as shape memory effect (SME) in form of reversible quasiplastic (QP) deformation, superelasticity (SE), and bio-compatibility. Nowadays, it is widely used for biomedical systems e.g. endovascular stents, orthodontic arc wires; for controlling and activating mechanical systems such as actuators and connectors and also for structural systems e.g. vibration control devices.SMAs exhibit a strong nonlinear thermomechanical behavior associated with abrupt changes in their lattice structure called martensitic phase transformation (PT). They have intrinsic ability to transform between austenite (parent phase) and a number of symmetry-related martensitic variants (product phases). Those SMAs considered here are copper based alloy CuAlNi and nickel based alloy NiTi, which both can behave as QP and SE depending on the operating temperature.Martensitic PT is considered as a diffusionless first-order transformation between 'high' temperature, θ > A s , austenite and 'low' temperature martensitic phases, θ < M s , Fig. 1. A s and M s are the so-called austenite and martensite start temperatures. Other critical temperatures are austenite and martensite finish temperatures which are denoted by A f and M f , respectively. SMAs exhibit a specific feature...

A micromechanics-based model for polycrystalline Ni–Ti wires

“…Phenomenological macroscoping models draw inspiration from plasticity by using inelastic strains as internal variables [1][2][3][4][5][6][7]. In micromechanical models, the internal variables (usually the volume fractions of the different phases) are directly related to the austenite-martensite microstructures that develop in the material [8][9][10][11][12][13][14]. Compared to phenomenological models, micromechanical models provide more information on the material behavior: in addition to the macroscopic stressstrain-temperature relation, they also give some insight in the microstructures that appear at a microscopic scale.…”