{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,20]],"date-time":"2026-02-20T20:16:59Z","timestamp":1771618619557,"version":"3.50.1"},"reference-count":61,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2019,5,11]],"date-time":"2019-05-11T00:00:00Z","timestamp":1557532800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012336","name":"Major State Basic Research Development Program of China","doi-asserted-by":"publisher","award":["2015CB057704"],"award-info":[{"award-number":["2015CB057704"]}],"id":[{"id":"10.13039\/501100012336","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51808417, 51478080, 51475339, 51421064 and 51375354"],"award-info":[{"award-number":["51808417, 51478080, 51475339, 51421064 and 51375354"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>During the propagation of ultrasound in a polycrystalline material, ultrasonic energy losses due to the scattering at the boundaries between grains is usually described by the ultrasonic energy diffusion equation, and the boundaries of the grains in the material are influenced by the structural load. The aim of this research is to investigate the characterization of ultrasonic energy diffusion in a steel alloy sample under structural load by using lead zirconate titanate (PZT) transducers. To investigate the influence of structural load on ultrasonic energy diffusion, an experimental setup of a steel alloy plate under different tensile forces is designed and four samples with similar dimensions are fabricated. The experimental results of the four samples reveal that, during the loading process, the normalized ultrasonic energy diffusion coefficient fluctuates firstly, then decreases and at last increases as the tensile force increases. The proposed tensile force index shows a similar changing trend to the recorded displacement of the sample. Moreover, when the tensile force is less than the lower yield point or the sample deforms elastically, the index can be approximated by a cubic model. Therefore, the proposed tensile force index can be used to monitor the tensile force in the elastic deformation stage. Moreover, based on these findings, some force evaluation methods and their potential applications, such as the preloading detection of bolts, can be developed based on the linear relationships between the proposed index and the applied force.<\/jats:p>","DOI":"10.3390\/s19092185","type":"journal-article","created":{"date-parts":[[2019,5,13]],"date-time":"2019-05-13T05:35:39Z","timestamp":1557725739000},"page":"2185","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Characterization of Ultrasonic Energy Diffusion in a Steel Alloy Sample with Tensile Force Using PZT Transducers"],"prefix":"10.3390","volume":"19","author":[{"given":"Guangtao","family":"Lu","sequence":"first","affiliation":[{"name":"Key Laboratory for Metallurgical Equipment and Control of Ministry of Education, Wuhan University of Science and Technology, Wuhan 430081, China"}]},{"given":"Tao","family":"Wang","sequence":"additional","affiliation":[{"name":"Hubei Key Laboratory of Mechanical Transmission and Manufacturing Engineering, Wuhan University of Science and Technology, Wuhan 430081, China"}]},{"given":"Mingle","family":"Zhou","sequence":"additional","affiliation":[{"name":"Key Laboratory for Metallurgical Equipment and Control of Ministry of Education, Wuhan University of Science and Technology, Wuhan 430081, China"}]},{"given":"Yourong","family":"Li","sequence":"additional","affiliation":[{"name":"Hubei Key Laboratory of Mechanical Transmission and Manufacturing Engineering, Wuhan University of Science and Technology, Wuhan 430081, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,5,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1177\/05831024030356001","article-title":"Overview of piezoelectric impedance-based health monitoring and path forward","volume":"35","author":"Park","year":"2003","journal-title":"Shock. 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