Describing internal subloops due to incomplete phase transformations in shape memory alloys

Abstract

The hysteretic response of shape memory alloys (SMAs) is one of their essential characteristics and is related to the martensitic phase transformation. The hysteresis loop may be observed either in stressstrain or strain-temperature curves. In brief, it is possible to say that the major (or external) hysteresis loop can be defined as the envelope of all minor (or internal) hysteresis loops, usually denoted as subloops. The macroscopic description of the SMA hysteresis loops, together with their subloops due to incomplete phase transformations, is an important aspect in the phenomenological description of the thermomechanical behavior of SMAs, being of great interest in technological applications. This contribution exploits the description of these internal subloops and employs a constitutive model previously proposed by [1,20,25]. Numerical investigations of the phenomenon are carried out to show the capability of this model to describe these inner subloops. Comparisons between numerical and experimental results show that they are in close agreement. Moreover, numerical simulations are carried out to elucidate different aspects of this hysteretic behavior.

A three-dimensional constitutive model for shape memory alloys

“…The model is inspired on the one-dimensional model that is able to describe different thermomechanical behaviors of SMAs in a flexible way, and its numerical simulations are in a close agreement with the experimental uniaxial tests [3,18,22,28,29]. Numerical simulations are carried out for both uniaxial and multiaxial tests considering a single-point analysis that shows that the introduced model is able to capture the general thermomechanical behavior of SMAs.…”

Finite Element Analysis of Shape Memory Alloy Adaptive Trusses with Geometrical Nonlinearities

“…Moreover ∂ n J χ (n = 1,2,3) are the sub-differentials of the indicator function J χ with respect toβ n [36]. This indicator function is related to the convex set χ , establishing conditions for the correct description of internal sub-loops due to incomplete phase transformations and also avoids phase transformations of the type: M + → M or M-→ M [38].…”

“…Here, a constitutive model presented by Paiva et al [33,34] is employed [6,38,40]. This model describes different aspects related to the thermomechanical behavior of SMAs, considering different material properties and four macroscopic phases.…”

Nonlinear dynamics of a SMA large-scale space structure

“…Lagoudas (2008) and Paiva and Savi (2006) for an overview of constitutive models. Here, a constitutive model with internal variables previously discussed in different references (Savi et al, 2002b;Baêta-Neves et al, 2004;Savi and Paiva, 2005;Monteiro et al, 2009;Aguiar et al, 2010;Oliveira et al, 2010) is employed.…”

“…Concerning the parameters definition, temperature dependent relations are adopted for Λ M and Λ A as follows: In order to contemplate different characteristics of the kinetics of phase transformation for loading and unloading processes, it is possible to consider different values to the internal dissipation parameter η n (n = +, − , A): n L η and n U η during loading and unloading process, respectively. For more details about the constitutive model, see and Savi and Paiva (2005).…”