Metals 2021, 11, 1558. https://doi.org/10.3390/met11101558 www.mdpi.com/journal/metals Article Numerical Investigations of Shape Memory Alloy Fatigue Vanderson M. Dornelas 1 , Sergio A. Oliveira 2 , Marcelo A. Savi 1, * and Pedro Manuel Calas Lopes Pacheco 2 1 Center for Nonlinear Mechanics, Department of Mechanical Engineering, Universidade Federal do Rio de Janeiro, COPPE P.O. Box 68503, Rio de Janeiro 21941-972, Brazil; vm.dornelas@mecanica.coppe.ufrj.br 2 Department of Mechanical Engineering CEFET/RJ, Centro Federal de Educação Tecnológica Celso Suckow da Fonseca, Rio de Janeiro 20271-110, Brazil; amserol@yahoo.com.br (S.A.O.); pedro.pacheco@cefet-rj.br (P.M.C.L.P.) * Correspondence: savi@mecanica.coppe.ufrj.br Abstract: This work deals with numerical investigations of the functional and structural fatigue on shape memory alloys (SMAs). A thermodynamically consistent, three-dimensional constitutive model is employed, adopting a continuum damage perspective. Fatigue life is predicted by considering a macroscopic model. Numerical simulations are compared with experimental data taken from the literature to demonstrate the model’s ability to capture the general thermomechanical behavior of SMAs subjected to different loading conditions. Uniaxial and torsion tests are discussed; thermal loads are also analyzed considering the influence of the maximum temperature on the fatigue life of SMAs. Cyclic degradation of the shape memory effect is investigated in the sequence. Results show that numerical simulations are in good agreement with the experimental data, including the fatigue life estimation. Keywords: shape memory alloys; plasticity; transformation induced plasticity; cyclic loading; functional fatigue; structural fatigue; constitutive model; numerical simulations 1. Introduction Shape memory alloys belong to the class of smart materials and have a series of complex thermomechanical behaviors including one-way shape memory effect, two-way shape memory effect, pseudoelasticity, and phase transformation due to temperature variation. These phenomena are due to solid-solid martensitic phase transformations that can be induced either by stress or by temperature [1–3]. In recent years, shape memory alloys, especially nickel-titanium (NiTi) alloys, were used in a large variety of applications considering different fields including biomedical, automotive, aerospace, civil engineering, and robotics, due to unique characteristics such as good mechanical properties, biocompatibility, and corrosion resistance [4–10]. Devices developed from these materials are often subjected to cyclic loading processes and therefore, fatigue is an essential issue responsible to the loss of functionality, and eventually, to failure. In this regard, fatigue of shape memory alloys is an important issue to be analyzed with scientific and technological relevance. Fatigue is a kind of localized damage process associated with cyclic loadings, being related to the initiation and growth of cracks [11,12]. Fatigue is usually classified into low cycle fatigue when the material accumulates plastic strains during the cyclic loading and high cycle fatigue when the material undergoes only elastic strains. According to Eggeler et al. [13], the definition of SMA fatigue can be split into structural fatigue, associated with the material failure due to the growth and propagation of microcracks, and functional fatigue, related to the reduction of functional properties. SMA fatigue was explored by many researchers employing different approaches. From the experimental point of view, different phenomena related to shape memory alloys were explored to quantify the influence of structural and functional fatigue. For Citation: Dornelas, V.M.; Oliveira, S.A.; Savi, M.A.; Pacheco, P.M.C.L. Numerical Investigations of Shape Memory Alloy Fatigue. Metals 2021, 11, 1558. https://doi.org/ 10.3390/met11101558 Academic Editors: Anders E. W. Jarfors and Alexander V. Shelyakov Received: 19 August 2021 Accepted: 22 September 2021 Published: 29 September 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses /by/4.0/).