  Citation: Yuan, X.; ¸ Sopu, D.; Song, K.; Eckert, J. Relaxation and Strain-Hardening Relationships in Highly Rejuvenated Metallic Glasses. Materials 2022, 15, 1702. https:// doi.org/10.3390/ma15051702 Academic Editor: Lukasz Hawelek Received: 31 December 2021 Accepted: 22 February 2022 Published: 24 February 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2022 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 (https:// creativecommons.org/licenses/by/ 4.0/). materials Article Relaxation and Strain-Hardening Relationships in Highly Rejuvenated Metallic Glasses Xudong Yuan 1 , Daniel ¸ Sopu 1,2, * , Kaikai Song 3 and Jürgen Eckert 1,4 1 Erich Schmid Institute of Materials Science, Austrian Academy of Sciences, Jahnstraße 12, A-8700 Leoben, Austria; xudong.yuan@oeaw.ac.at (X.Y.); juergen.eckert@unileoben.ac.at (J.E.) 2 Fachgebiet Materialmodellierung, Institut für Materialwissenschaft, Technische Universität Darmstadt, Otto-Berndt-Straße 3, D-64287 Darmstadt, Germany 3 School of Mechanical, Electrical and Information Engineering, Shandong University (Weihai), Weihai 264209, China; songkaikai@sdu.edu.cn 4 Department of Materials Science, Chair of Materials Physics, Montanuniversität Leoben, Jahnstraße 12, A-8700 Leoben, Austria * Correspondence: daniel.sopu@oeaw.ac.at Abstract: One way to rejuvenate metallic glasses is to increase their free volume. Here, by randomly removing atoms from the glass matrix, free volume is homogeneously generated in metallic glasses, and glassy states with different degrees of rejuvenation are designed and further mechanically tested. We find that the free volume in the rejuvenated glasses can be annihilated under tensile or compressive deformation that consequently leads to structural relaxation and strain-hardening. Additionally, the deformation mechanism of highly rejuvenated metallic glasses during the uniaxial loading–unloading tensile tests is investigated, in order to provide a systematic understanding of the relaxation and strain-hardening relationship. The observed strain-hardening in the highly rejuvenated metallic glasses corresponds to stress-driven structural and residual stress relaxation during cycling deformation. Nevertheless, the rejuvenated metallic glasses relax to a more stable state but could not recover their initial as-cast state. Keywords: metallic glass; molecular dynamics simulations; rejuvenation; relaxation; strain-hardening 1. Introduction Metallic glasses (MGs) are obtained by fast cooling from the melt to avoid crystalliza- tion and exhibit a disordered structure with higher-energy states [1–3]. As-cast MGs are thermodynamically metastable and can spontaneously convert to a lower energy state via aging (relaxation) [4,5]. However, many strategies can push MGs to undergo an opposite process and reach a more disordered state which is called rejuvenation. Rejuvenation can be induced by reheating [6–8] and faster quenching [9], thermal cycling [10], elastostatic and heavy plastic deformation [11–15], irradiation [16], etc. Rejuvenation is an effective way to inspire the structure of MGs to restore flexibility with the increase of free volume and enthalpy [17–20] and it is regarded as a promising approach for tuning the deformability of MGs. It is now seen as a common way to improve the plasticity of MGs [11,21] since it can ameliorate the highly localized deformation mechanism and could ultimately eliminate the formation of critical shear bands [7,11]. Moreover, structural rejuvenation can also provide strain-hardening under certain loading conditions [21]. Although rejuvenation has captured increasing attention due to its scientific significance, the precise control of the degree of rejuvenation in MGs and the design of highly rejuvenated MGs is still a challenge in experimental work. Rejuvenation is usually associated with free volume accumulation that results to structural softening and hardness reduction. Strain softening is the Achilles’ heel of MGs. While strain-hardening is familiar in polycrystalline metals, it is not found in most MGs [22,23]. However, in some particular cases, strain- hardening has been also observed in monolithic MGs. Here, the suppression of shearing Materials 2022, 15, 1702. https://doi.org/10.3390/ma15051702 https://www.mdpi.com/journal/materials