{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,23]],"date-time":"2026-04-23T10:46:09Z","timestamp":1776941169759,"version":"3.51.4"},"reference-count":21,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2021,10,23]],"date-time":"2021-10-23T00:00:00Z","timestamp":1634947200000},"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":["51475372"],"award-info":[{"award-number":["51475372"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>Determination of the fracture angle and maximum exposure value of extended Puck\u2019s 3D inter-fiber failure (IFF) criterion is of great importance for predicting the failure mechanism of unidirectional fiber-reinforced composites. In this paper, a reliable semi-analytical algorithm (RSAA) is presented for searching fracture angle and corresponding exposure value for the extended Puck\u2019s failure criterion. One hundred million cases are tested for verifying the accuracy of the present and other algorithms on Python using the strength-value-stress-state combinations more universal than those in previous literatures. The reliability of previous algorithms is discussed and counterexamples are provided for illustration. The statistical results show RSAA is adequate for implementation in extended Puck\u2019s criterion and much more reliable than previous algorithms. RSAA can correctly predict the results with a probability of over 99.999%.<\/jats:p>","DOI":"10.3390\/ma14216325","type":"journal-article","created":{"date-parts":[[2021,10,24]],"date-time":"2021-10-24T22:07:11Z","timestamp":1635113231000},"page":"6325","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Reliable Fracture Angle Determination Algorithm for Extended Puck\u2019s 3D Inter-Fiber Failure Criterion for Unidirectional Composites"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6134-6940","authenticated-orcid":false,"given":"Yaohua","family":"Gong","sequence":"first","affiliation":[{"name":"School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi\u2019an 710129, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tao","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi\u2019an 710129, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xun\u2019an","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi\u2019an 710129, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Purong","family":"Jia","sequence":"additional","affiliation":[{"name":"School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi\u2019an 710129, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yongyong","family":"Suo","sequence":"additional","affiliation":[{"name":"School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi\u2019an 710129, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuyi","family":"Zhao","sequence":"additional","affiliation":[{"name":"AECC Commercial Aircraft Engine Co., Ltd., Shanghai 201100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1045","DOI":"10.1016\/S0266-3538(96)00140-6","article-title":"Failure analysis of FRP laminates by means of physically based phenomenological models","volume":"58","author":"Puck","year":"1998","journal-title":"Compos. 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