{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,11,5]],"date-time":"2026-11-05T05:57:43Z","timestamp":1793858263780,"version":"4.6.1"},"reference-count":73,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2020,10,5]],"date-time":"2020-10-05T00:00:00Z","timestamp":1601856000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11872023"],"award-info":[{"award-number":["11872023"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11372114"],"award-info":[{"award-number":["11372114"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>The superior fracture toughness of zirconia is closely correlated with stress-induced martensitic phase transformation around a crack tip. In this study, a modified phase field (PF) model coupling phase transformation and fracture is proposed to study the fracture behavior and toughening effect of tetragonal zirconia polycrystal (TZP). The stress-induced tetragonal to monoclinic (t\u2013m) phase transformation around a static or propagating crack is characterized with PF simulations. It is shown that the finite size and shape of the transformation zone under different loads and ambient temperatures can be well predicted with the proposed PF model. The phase transformation may decrease the stress level around the crack tip, which implies the toughening effect. After that, crack propagation in TZP is studied. As the stress field is perturbed by the phase transformation patterns, the crack may experience deflection and branching in the propagation process. It is found that the toughness of the grain boundaries (GBs) has important influences on the crack propagation mode. For TZP with strong GBs, the crack is more likely to propagate transgranularly while, for TZP with weak GBs, intergranular crack propagation is prevalent. Besides that, the crystal orientation and the external load can also influence the topology of crack propagation.<\/jats:p>","DOI":"10.3390\/ma13194430","type":"journal-article","created":{"date-parts":[[2020,10,5]],"date-time":"2020-10-05T08:35:57Z","timestamp":1601886957000},"page":"4430","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Study of the Fracture Behavior of Tetragonal Zirconia Polycrystal with a Modified Phase Field Model"],"prefix":"10.3390","volume":"13","author":[{"given":"Jingming","family":"Zhu","sequence":"first","affiliation":[{"name":"Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, China"},{"name":"Hubei Key Laboratory for Engineering Structural Analysis and Safety Assessment, Luoyu Road, Wuhan 430074, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jun","family":"Luo","sequence":"additional","affiliation":[{"name":"Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, China"},{"name":"Hubei Key Laboratory for Engineering Structural Analysis and Safety Assessment, Luoyu Road, Wuhan 430074, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuanzun","family":"Sun","sequence":"additional","affiliation":[{"name":"Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, China"},{"name":"Hubei Key Laboratory for Engineering Structural Analysis and Safety Assessment, Luoyu Road, Wuhan 430074, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,10,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"703","DOI":"10.1038\/258703a0","article-title":"Ceramic steel?","volume":"258","author":"Garvie","year":"1975","journal-title":"Nature"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2659","DOI":"10.1111\/j.1151-2916.1990.tb06743.x","article-title":"Crack-Tip Transformation Zones in Toughened Zirconia","volume":"73","author":"Marshall","year":"1990","journal-title":"J. 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