{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,5]],"date-time":"2026-03-05T06:36:09Z","timestamp":1772692569904,"version":"3.50.1"},"reference-count":48,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T00:00:00Z","timestamp":1772496000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"crossref","award":["FRF-TP-20-028A1"],"award-info":[{"award-number":["FRF-TP-20-028A1"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"crossref","award":["FRF-BD-25-002"],"award-info":[{"award-number":["FRF-BD-25-002"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"crossref","award":["FRF-BD-23-02"],"award-info":[{"award-number":["FRF-BD-23-02"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Fundamental Research Funds for the Central Universities and The Youth Teacher International Exchange and Growth Program","award":["QNXM20210044"],"award-info":[{"award-number":["QNXM20210044"]}]},{"name":"Research Grants Council of Hong Kong Special Administrative Region, China","award":["15236225"],"award-info":[{"award-number":["15236225"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Nanomaterials"],"abstract":"<jats:p>Despite their excellent mechanical properties, metallic glasses (MGs) are significantly hindered by poor plasticity and toughness, which are essential for structural applications. The brittleness arises from the rapid propagation of shear bands (SBs), leading to strain softening and catastrophic failure. Recent advancements in microstructural engineering, particularly boundary engineering, such as nano-glass, focus on the utilization of heterogeneous structures to promote the proliferation and delocalization of SBs. Various attempts have been made experimentally to address these issues, but with very limited improvement in tensile strength and toughness. Under tensile loading, micro- or nano-pillar samples exhibit strain softening and continue to undergo plastic deformation after reaching yield or peak stress, especially the nano-glass micro-pillar. Reports on tensile strain-hardening in MG micro-pillars are rare. In this finite element simulation study, we optimize appropriate statistical and spatial distributions of free volume within the microsamples. Both the post-yield strength and the mean tangent modulus increase with progressive gradient structural modifications, thereby inducing a transition from strain-softening to strain-hardening behavior, as well as a concurrent transition from plastic fracture to brittle fracture. We systematically investigate the deformation mechanisms and transition mechanisms of fracture modes, which are closely associated with heterogeneous microstructures and their evolution in MGs. These insights into the transition mechanism could significantly facilitate the design and optimization of MGs to achieve enhanced toughness and strain hardening.<\/jats:p>","DOI":"10.3390\/nano16050319","type":"journal-article","created":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T09:45:12Z","timestamp":1772531112000},"page":"319","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Transition from Strain Softening to Strain Hardening in Metallic Glasses"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8126-4643","authenticated-orcid":false,"given":"Yongwei","family":"Wang","sequence":"first","affiliation":[{"name":"Collaborative Innovation Center of Steel Technology, University of Science and Technology Beijing, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guangping","family":"Zheng","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong 10000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6800-8776","authenticated-orcid":false,"given":"Mo","family":"Li","sequence":"additional","affiliation":[{"name":"School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,3,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1038\/nmat2930","article-title":"A damage-tolerant glass","volume":"10","author":"Demetriou","year":"2011","journal-title":"Nat. Mater."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"759","DOI":"10.1016\/j.pmatsci.2010.04.002","article-title":"Mechanical properties of bulk metallic glasses","volume":"55","author":"Trexler","year":"2010","journal-title":"Prog. Mater. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.mser.2013.04.001","article-title":"Shear bands in metallic glasses","volume":"74","author":"Greer","year":"2013","journal-title":"Mat. Sci. Eng. R"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"101283","DOI":"10.1016\/j.pmatsci.2024.101283","article-title":"Manufacturing of metallic glass components: Processes, structures, and properties","volume":"144","author":"Sohrabi","year":"2024","journal-title":"Prog. Mater. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1085","DOI":"10.1038\/nature06598","article-title":"Designing metallic glass matrix composites with high toughness and tensile ductility","volume":"451","author":"Hofmann","year":"2008","journal-title":"Nature"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"205501","DOI":"10.1103\/PhysRevLett.94.205501","article-title":"\u201cWork-hardenable\u201d ductile bulk metallic glass","volume":"94","author":"Das","year":"2005","journal-title":"Phys. Rev. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1038\/nmat2622","article-title":"Transition from a strong-yet-brittle to a stronger-and-ductile state by size reduction of metallic glasses","volume":"9","author":"Jang","year":"2010","journal-title":"Nat. Mater."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"735","DOI":"10.1038\/nmat1984","article-title":"Tensile ductility and necking of metallic glass","volume":"6","author":"Guo","year":"2007","journal-title":"Nat. Mater."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1103","DOI":"10.1016\/j.pmatsci.2013.04.002","article-title":"Phase separation in metallic glasses","volume":"58","author":"Kim","year":"2013","journal-title":"Prog. Mater. Sci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/j.scriptamat.2017.03.019","article-title":"Mechanical properties of spinodal decomposed metallic glass composites","volume":"135","author":"Wang","year":"2017","journal-title":"Scr. Mater."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1016\/0022-3093(89)90007-0","article-title":"Modified atomic structure in a Pd-Fe-Si nanoglass: A M\u00f6ssbauer study","volume":"113","author":"Jing","year":"1989","journal-title":"J. Non-Cryst. Solids"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"517","DOI":"10.3762\/bjnano.4.61","article-title":"Nanoglasses: A new kind of noncrystalline materials","volume":"4","author":"Gleiter","year":"2013","journal-title":"Beilstein J. Nanotechnol."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"6051","DOI":"10.1021\/acs.nanolett.1c01283","article-title":"Metallic Nanoglasses with Promoted \u03b2-Relaxation and Tensile Plasticity","volume":"21","author":"Yang","year":"2021","journal-title":"Nano Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1016\/j.mattod.2020.04.005","article-title":"Nanostructural metallic materials: Structures and mechanical properties","volume":"38","author":"Sun","year":"2020","journal-title":"Mater. Today"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"458","DOI":"10.1021\/nl2038216","article-title":"Atomic structure and structural stability of Sc75Fe25 nanoglasses","volume":"12","author":"Fang","year":"2012","journal-title":"Nano Lett."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/j.scriptamat.2016.01.036","article-title":"Sample size effects on strength and deformation mechanism of Sc75Fe25 nanoglass and metallic glass","volume":"116","author":"Wang","year":"2016","journal-title":"Scr. Mater."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1016\/j.scriptamat.2014.11.010","article-title":"Plasticity of a scandium-based nanoglass","volume":"98","author":"Wang","year":"2015","journal-title":"Scr. Mater."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1038\/s41586-020-2016-3","article-title":"Strain-hardening and suppression of shear-banding in rejuvenated bulk metallic glass","volume":"578","author":"Pan","year":"2020","journal-title":"Nature"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"10147","DOI":"10.1038\/s41467-025-65120-4","article-title":"Transformation-mediated and relaxation assisted macroscopic tensile plasticity with strain-hardening in metallic glass","volume":"16","author":"Hu","year":"2025","journal-title":"Nat. Commun."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"560","DOI":"10.1016\/j.jmst.2013.11.014","article-title":"Structure heterogeneity in metallic glass: Modeling and experiment","volume":"30","author":"Ke","year":"2014","journal-title":"J. Mater. Sci. Technol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1016\/j.actamat.2016.05.002","article-title":"Interfaces and interphases in nanoglasses: Surface segregation effects and their implications on structural properties","volume":"113","author":"Adjaoud","year":"2016","journal-title":"Acta Mater."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"322","DOI":"10.1016\/j.actamat.2017.12.014","article-title":"Microstructure formation of metallic nanoglasses: Insights from molecular dynamics simulations","volume":"145","author":"Adjaoud","year":"2018","journal-title":"Acta Mater."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"105806","DOI":"10.1016\/j.jmps.2024.105806","article-title":"Unravelling the relation between free volume gradient and shear band deflection induced extra plasticity in metallic glasses","volume":"192","author":"Lu","year":"2024","journal-title":"J. Mech. Phys. Solids"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/j.scriptamat.2016.11.003","article-title":"Free volume gradient effect on mechanical properties of metallic glasses","volume":"130","author":"Wang","year":"2017","journal-title":"Scr. Mater."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.scriptamat.2015.09.038","article-title":"Toughen and harden metallic glass through designing statistical heterogeneity","volume":"113","author":"Wang","year":"2016","journal-title":"Scr. Mater."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1016\/0001-6160(77)90232-2","article-title":"A microscopic mechanism for steady state inhomogeneous flow in metallic glasses","volume":"25","author":"Spaepen","year":"1977","journal-title":"Acta Metall."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/0001-6160(79)90055-5","article-title":"Plastic deformation in metallic glasses","volume":"27","author":"Argon","year":"1979","journal-title":"Acta Metall."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1329","DOI":"10.1088\/0965-0393\/14\/8\/004","article-title":"An implicit finite element method for simulating inhomogeneous deformation and shear bands of amorphous alloys based on the free-volume model","volume":"14","author":"Gao","year":"2006","journal-title":"Modell. Simul. Mater. Sci. Eng."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"241906","DOI":"10.1063\/1.3050462","article-title":"Interpreting the change in shear band inclination angle in metallic glasses","volume":"93","author":"Zhao","year":"2008","journal-title":"Appl. Phys. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1557\/s43577-022-00347-w","article-title":"From patterning heterogeneity to nanoglass: A new approach to harden and toughen metallic glasses","volume":"48","author":"Wang","year":"2023","journal-title":"MRS Bull."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"113846","DOI":"10.1016\/j.matdes.2025.113846","article-title":"Manage local deformation by patterning structural heterogeneity: Controlling toughness in honeycomb patterned metallic glass composites","volume":"253","author":"Wang","year":"2025","journal-title":"Mater. Des."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"123702","DOI":"10.1016\/j.jnoncrysol.2025.123702","article-title":"Orientation effects on strengthening mechanism of network-structured metallic glass composites and nanoglasses","volume":"666","author":"Wang","year":"2025","journal-title":"J. Non-Cryst. Solids"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"4467","DOI":"10.1021\/acs.nanolett.6b01636","article-title":"Brittle-to-Ductile Transition in Metallic Glass Nanowires","volume":"16","author":"Foroughi","year":"2016","journal-title":"Nano Lett."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"121902","DOI":"10.1063\/5.0039755","article-title":"Unravel unusual hardening behavior of a Pd\u2013Ni\u2013P metallic glass in its supercooled liquid region","volume":"118","author":"Cao","year":"2021","journal-title":"Appl. Phys. Lett."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"083523","DOI":"10.1063\/1.4704688","article-title":"Characteristic free volume change of bulk metallic glasses","volume":"111","author":"Hu","year":"2012","journal-title":"J. Appl. Phys."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"135504","DOI":"10.1103\/PhysRevLett.111.135504","article-title":"Densification and strain hardening of a metallic glass under tension at room temperature","volume":"111","author":"Wang","year":"2013","journal-title":"Phys. Rev. Lett."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1080\/14786430701864753","article-title":"Energy dissipation in fracture of bulk metallic glasses via inherent competition between local softening and quasi-cleavage","volume":"88","author":"Jiang","year":"2008","journal-title":"Philos. Mag."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"7076","DOI":"10.1038\/s41598-017-07669-9","article-title":"Hardening of shear band in metallic glass","volume":"7","author":"Wang","year":"2017","journal-title":"Sci. Rep."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"034108","DOI":"10.1103\/PhysRevE.109.034108","article-title":"Universality of random-site percolation thresholds for two-dimensional complex noncompact neighborhoods","volume":"109","author":"Malarz","year":"2024","journal-title":"Phys. Rev. E"},{"key":"ref_40","first-page":"333","article-title":"An overview of biomass solid fuels: Biomass sources, processing methods, and morphological and microstructural properties","volume":"8","author":"Ibitoye","year":"2023","journal-title":"J. Bioresour. Bioprod."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"2655","DOI":"10.1557\/JMR.2007.0351","article-title":"Strain-rate dependence of hardening and softening in compression of a bulk metallic glass","volume":"22","author":"Jiang","year":"2007","journal-title":"J. Mater. Res."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"2798","DOI":"10.1038\/srep02798","article-title":"Localized shear deformation and softening of bulk metallic glass: Stress or temperature driven?","volume":"3","author":"Ketov","year":"2013","journal-title":"Sci. Rep."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1405","DOI":"10.1557\/jmr.2009.0167","article-title":"Role of free volume in strain softening of as-cast and annealed bulk metallic glass","volume":"24","author":"Yoo","year":"2009","journal-title":"J. Mater. Res."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"105503","DOI":"10.1103\/PhysRevLett.96.105503","article-title":"Softening Caused by Profuse Shear Banding in a Bulk Metallic Glass","volume":"96","author":"Bei","year":"2006","journal-title":"Phys. Rev. Lett."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1210","DOI":"10.1016\/j.scriptamat.2008.08.021","article-title":"Stress-induced softening and hardening in a bulk metallic glass","volume":"59","author":"Chen","year":"2008","journal-title":"Scr. Mater."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"025502","DOI":"10.1103\/PhysRevLett.126.025502","article-title":"Theory of Pressure-Induced Rejuvenation and Strain Hardening in Metallic Glasses","volume":"126","author":"Phan","year":"2021","journal-title":"Phys. Rev. Lett."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"121792","DOI":"10.1016\/j.jnoncrysol.2022.121792","article-title":"Transition from softening to hardening related with strain rate in Zr-based metallic glasses","volume":"593","author":"Liu","year":"2022","journal-title":"J. Non-Cryst. Solids"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"106877","DOI":"10.1016\/j.intermet.2020.106877","article-title":"Work hardening and homogeneous elongation in metallic glass matrix composite at cryogenic temperature","volume":"126","author":"Li","year":"2020","journal-title":"Intermetallics"}],"container-title":["Nanomaterials"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-4991\/16\/5\/319\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,5]],"date-time":"2026-03-05T05:16:31Z","timestamp":1772687791000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-4991\/16\/5\/319"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,3]]},"references-count":48,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2026,3]]}},"alternative-id":["nano16050319"],"URL":"https:\/\/doi.org\/10.3390\/nano16050319","relation":{},"ISSN":["2079-4991"],"issn-type":[{"value":"2079-4991","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,3]]}}}