{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:32:57Z","timestamp":1760239977907,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2019,2,12]],"date-time":"2019-02-12T00:00:00Z","timestamp":1549929600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Chongqing Technology and Business University, China","award":["950117041"],"award-info":[{"award-number":["950117041"]}]},{"name":"National Key Research &amp; Development Program of China","award":["2016YFE0205600"],"award-info":[{"award-number":["2016YFE0205600"]}]},{"name":"MoST Science &amp; Technology Partnership Program","award":["KY201802006"],"award-info":[{"award-number":["KY201802006"]}]},{"name":"Program of Chongqing Municipal Education Commission, China","award":["KJZH17123"],"award-info":[{"award-number":["KJZH17123"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Conventional sensor structure design and related fracture mechanics analysis are based on the single J-integral parameter approach of elastic-plastic fracture mechanics (EPFM). Under low crack constraint cases, the EPFM one-parameter approach generally gives a stress overestimate, which results in a great cost waste of labor and sensor components. The J-A two-parameter approach overcomes this limitation. To enable the extensive application of the J-A approach on theoretical research and sensor engineering problem, under small scale yielding (SSY) conditions, the authors developed an estimate method to conveniently and quickly obtain the constraint (second) parameter A values directly from T-stress. Practical engineering application of sensor structure analysis and design focuses on three-dimensional (3D) structures with biaxial external loading, while the estimate method was developed based on two-dimensional (2D) plain strain condition with uniaxial loading. In the current work, the estimate method was successfully extended to a 3D structure with biaxial loading cases, which is appropriate for practical sensor design. The estimate method extension and validation process was implemented through a thin 3D single edge cracked plate (SECP) specimen. The process implementation was completed in two specified planes of 3D SECP along model thickness. A wide range of material and geometrical properties were applied for the extension and validation process, with material hardening exponent value 3, 5 and 10, and crack length ratio 0.1, 0.3 and 0.7.<\/jats:p>","DOI":"10.3390\/s19030735","type":"journal-article","created":{"date-parts":[[2019,2,13]],"date-time":"2019-02-13T02:49:44Z","timestamp":1550026184000},"page":"735","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["3D SSY Estimate of EPFM Constraint Parameter under Biaxial Loading for Sensor Structure Design"],"prefix":"10.3390","volume":"19","author":[{"given":"Ping","family":"Ding","sequence":"first","affiliation":[{"name":"National Research Base of Intelligent Manufacturing Service, Chongqing Technology and Business University, Chongqing 400067, China"},{"name":"Department of Mechanical and Aerospace Engineering, Carleton University, Ottawa, ON K1S 5B6, Canada"}]},{"given":"Xin","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Aerospace Engineering, Carleton University, Ottawa, ON K1S 5B6, Canada"}]}],"member":"1968","published-online":{"date-parts":[[2019,2,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1287","DOI":"10.1007\/s00466-018-1564-y","article-title":"Static and free-vibration analyses of cracks in thin-shell structures based on an isogeometric-meshfree coupling approach","volume":"62","author":"Li","year":"2018","journal-title":"Comput. 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