Metals 2021, 11, 1616. https://doi.org/10.3390/met11101616 www.mdpi.com/journal/metals Article Fatigue Damage Map of AZ31B-F Magnesium Alloys under Multiaxial Loading Conditions Vitor Anes 1,2, *, Luis Reis 2, * and Manuel Freitas 2 1 Instituto Superior de Engenharia de Lisboa, Instituto Politécnico de Lisboa, 1959-007 Lisboa, Portugal 2 IDMEC, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal; manuel.freitas@tecnico.ulisboa.pt * Correspondence: vitor.anes@isel.pt (V.A.); luis.g.reis@tecnico.ulisboa.pt (L.R.); Tel.: +351-916-222-536 (V.A.) Abstract: In this work, the mechanical behavior of the AZ31B-F magnesium alloy under cyclic load- ing is analyzed with the goal of contributing to the advancement of its use in the design of AZ31B- F components and structures. To achieve this goal, an experimental program was implemented to evaluate the cyclic response of the AZ31B-F under specific proportional loads with different stress amplitude ratios. Afterwards, regression methods were applied to extend the experimental data to a wide range of proportional loads. As a result, the AZ31B-F damage map, a material property that stablishes the damage scale between normal and shear stresses for finite life loading regimes, was obtained. In addition, a safety factor was developed for the AZ31B-F material when subjected to proportional loading. The achieved results have a direct application in mechanical design of com- ponents/structures made of AZ31B-F contributing to its reliability. Keywords: AZ31B-F magnesium alloy; multiaxial fatigue; fatigue damage; experimental testing 1. Introduction Nowadays, sustainability is a major concern for society. Over the years, industry in general has evolved without really thinking about the environmental impact of its strate- gies. However, societies are beginning to realize that change is needed, especially in the transportation industry, which today has a strong impact on the sustainability of planet Earth by contributing to the increase in greenhouse gas emissions [1–3]. In this sense, al- ternative strategies have been developed to reduce gas emissions by reducing the weight of transportation structures. In this context, the replacement of steels and aluminum al- loys with magnesium alloys has been strongly considered. Magnesium alloys are the lightest structural metals. They are 33% lighter than aluminum alloys and 75% lighter than steels. In fact, the use of magnesium alloys in the transportation industry is not new. The first magnesium alloys developed were used in the automotive and aircraft industries, especially for castings, but the low corrosion resistance of these alloys dampened the ex- pectations placed in them [4]. In the meantime, new structural magnesium alloys with better corrosion resistance and mechanical strength have been developed [5–7]. These new properties have encouraged the use of magnesium alloys for applications other than castings. Magnesium alloys have a very different mechanical behavior than steels or even aluminum alloys. The hexagonal close-packed structure gives these alloys various prop- erties such as polarity, twinning, mechanical behavior dependent on loading conditions, anisotropy due to slip-twin interactions, and different stress-strain behavior in tension and compression, making the mechanical behavior of these alloys quite different from that of other structural metals [8–12]. Citation: Anes, V.; Reis, L.; Freitas, M. Fatigue Damage Map of AZ31B-F Magnesium Alloys under Multiaxial Loading Conditions. Metals 2021, 11, 1616. https://doi.org/ 10.3390/met11101616 Academic Editor: Hamid Jahed Received: 18 September 2021 Accepted: 8 October 2021 Published: 11 October 2021 Publisher’s Note: MDPI stays neu- tral with regard to jurisdictional claims in published maps and institu- tional affiliations. Copyright: © 2021 by the authors. Li- censee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and con- ditions of the Creative Commons At- tribution (CC BY) license (http://crea- tivecommons.org/licenses/by/4.0/).