{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:18:37Z","timestamp":1760145517097,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2024,7,25]],"date-time":"2024-07-25T00:00:00Z","timestamp":1721865600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China as National Major Scientific Instruments Development Project","award":["61927807","202203021221099","EW202180221","XJZZ202006","51902294","11874386"],"award-info":[{"award-number":["61927807","202203021221099","EW202180221","XJZZ202006","51902294","11874386"]}]},{"name":"General Project of Basic Research Program in Shanxi Province","award":["61927807","202203021221099","EW202180221","XJZZ202006","51902294","11874386"],"award-info":[{"award-number":["61927807","202203021221099","EW202180221","XJZZ202006","51902294","11874386"]}]},{"name":"The Opening Fund for Key Research Bases of Nanchang Hangkong University","award":["61927807","202203021221099","EW202180221","XJZZ202006","51902294","11874386"],"award-info":[{"award-number":["61927807","202203021221099","EW202180221","XJZZ202006","51902294","11874386"]}]},{"name":"The Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi","award":["61927807","202203021221099","EW202180221","XJZZ202006","51902294","11874386"],"award-info":[{"award-number":["61927807","202203021221099","EW202180221","XJZZ202006","51902294","11874386"]}]},{"name":"The Opening Project of Key Laboratory of Biomedical Imaging and Image Data of Shanxi Province","award":["61927807","202203021221099","EW202180221","XJZZ202006","51902294","11874386"],"award-info":[{"award-number":["61927807","202203021221099","EW202180221","XJZZ202006","51902294","11874386"]}]},{"name":"The Opening Project of Shanxi Key Laboratory of Advanced Manufacturing Technology","award":["61927807","202203021221099","EW202180221","XJZZ202006","51902294","11874386"],"award-info":[{"award-number":["61927807","202203021221099","EW202180221","XJZZ202006","51902294","11874386"]}]},{"name":"The National Natural Science Foundation of China","award":["61927807","202203021221099","EW202180221","XJZZ202006","51902294","11874386"],"award-info":[{"award-number":["61927807","202203021221099","EW202180221","XJZZ202006","51902294","11874386"]}]},{"name":"The National Natural Science Foundation of China","award":["61927807","202203021221099","EW202180221","XJZZ202006","51902294","11874386"],"award-info":[{"award-number":["61927807","202203021221099","EW202180221","XJZZ202006","51902294","11874386"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this work, a two-parameter inversion problem is analyzed, related to surface crack widths for measuring depths of normal surface notches, based on a laser-based ultrasonic measurement method in the time domain. In determining the depth measurement formulas, the main technique is the time delay between reflected and scattered waves. Scattered waves are generated by two reflections along the bottom and three mode transformations at the surface of the crack tips. Moreover, the scattering angle of the mode-conversion waves is 30\u00b0. These two key factors lead to corrected item \u201c2w\u03b2\u201d in the depth measurement formula. A laser-based ultrasonic experimental platform is built to generate and receive surface waves in a non-contact manner on aluminum and steel specimens with surface cracks. The depth measurement method proposed in this paper has been validated through theoretical, simulation, and experimental methods. Finally, in this paper, an effective approach for quantitatively measuring crack depths, based on laser ultrasound, using the time-domain properties of surface wave propagation is provided.<\/jats:p>","DOI":"10.3390\/s24154849","type":"journal-article","created":{"date-parts":[[2024,7,26]],"date-time":"2024-07-26T06:17:44Z","timestamp":1721974664000},"page":"4849","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Estimating the Depths of Normal Surface Notches Using Mode-Conversion Waves at the Bottom Tip"],"prefix":"10.3390","volume":"24","author":[{"given":"Qianghua","family":"Pan","sequence":"first","affiliation":[{"name":"China Special Equipment Inspection and Research Institute, Beijing 100029, China"}]},{"given":"Jiawei","family":"Xu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Advanced Manufacturing Technology, North University of China, Taiyuan 030051, China"}]},{"given":"Wenbo","family":"Li","sequence":"additional","affiliation":[{"name":"China Special Equipment Inspection and Research Institute, Beijing 100029, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3842-7806","authenticated-orcid":false,"given":"Haiyang","family":"Li","sequence":"additional","affiliation":[{"name":"Key Laboratory of Advanced Manufacturing Technology, North University of China, Taiyuan 030051, China"},{"name":"Shanghai Acoustic Laboratory, Chinese Academy of Sciences, Shanghai 201815, China"}]},{"given":"Zehui","family":"Li","sequence":"additional","affiliation":[{"name":"Key Laboratory of Advanced Manufacturing Technology, North University of China, Taiyuan 030051, China"}]},{"given":"Pengfei","family":"Wang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Advanced Manufacturing Technology, North University of China, Taiyuan 030051, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"865","DOI":"10.1016\/j.proeng.2010.03.093","article-title":"Fatigue crack growth behavior of surface crack in rails","volume":"2","author":"Seo","year":"2010","journal-title":"Procedia Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/j.cemconcomp.2008.09.008","article-title":"Characterization of surface crack depth and repair evaluation using Rayleigh waves","volume":"31","author":"Aggelis","year":"2009","journal-title":"Cem. Concr. Compos."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1063\/1.90486","article-title":"Length and depth resonances of surface cracks and their use for crack size estimation","volume":"33","author":"Domarkas","year":"1978","journal-title":"Appl. Phys. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/S0041-624X(02)00393-1","article-title":"Finite element analysis of Rayleigh wave interaction with finite-size, surface-breaking cracks","volume":"41","author":"Hassan","year":"2003","journal-title":"Ultrasonics"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1016\/S0963-8695(98)80013-3","article-title":"Characterization of surface cracks with Rayleigh waves: A numerical model","volume":"31","author":"Abraham","year":"1998","journal-title":"NDT E Int."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1134\/S0020441221010048","article-title":"A Novel Method for Evaluation of Surface Breaking Crack Using Position-Time Graph","volume":"64","author":"Basit","year":"2021","journal-title":"Instrum. Exp. Tech."},{"key":"ref_7","first-page":"541","article-title":"Estimation of Surface Crack Depth using Rayleigh Waves by Electromagnetic Acoustic Transducers","volume":"22","author":"He","year":"2017","journal-title":"Int. J. Acoust. Vib."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"5333","DOI":"10.1016\/j.jsv.2011.05.034","article-title":"Surface wave transmission measurements across distributed surface-breaking cracks using air-coupled sensors","volume":"330","author":"Kee","year":"2011","journal-title":"J. Sound Vib."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"211","DOI":"10.20965\/ijat.2013.p0211","article-title":"Laser-Generated Surface Acoustic Wave Technique for Crack Monitoring\u2014A Review","volume":"7","author":"Chen","year":"2013","journal-title":"Int. J. Autom. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1367","DOI":"10.1007\/s10765-013-1428-9","article-title":"Noncontact, Nondestructive Evaluation of Realistic Cracks with Surface Acoustic Waves by Scanning Excitation and Detection Lasers","volume":"34","author":"Hess","year":"2013","journal-title":"Int. J. Thermophys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"064906","DOI":"10.1063\/1.2910897","article-title":"Depth evaluation of surface-breaking cracks using laser-generated transmitted Rayleigh waves","volume":"103","author":"Moura","year":"2008","journal-title":"J. Appl. Phys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1016\/j.apacoust.2018.07.013","article-title":"Mode conversion detection in an elastic plate based on Fizeau fiber interferometer","volume":"141","author":"Yan","year":"2018","journal-title":"Appl. Acoust."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"065104","DOI":"10.1063\/1.5028207","article-title":"Laser-generated Rayleigh wave for width gauging of subsurface lateral rectangular defects","volume":"124","author":"Wang","year":"2018","journal-title":"J. Appl. Phys."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"4179","DOI":"10.1364\/AO.52.004179","article-title":"Analysis of laser generated ultrasonic wave frequency characteristics induced by a partially closed surface-breaking crack","volume":"52","author":"Li","year":"2013","journal-title":"Appl. Opt."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Dutton, B., Rosli, M.H., and Edwards, R.S. (2009, January 26\u201331). Defect feature extraction using surface wave interactions and time-frequency behavior. Proceedings of the 36th Annual Review of Progress in Quantitative Nondestructive Evaluation, Kingston, RI, USA.","DOI":"10.1063\/1.3362455"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Li, H., Pan, Q., Zhang, X., and An, Z. (2020). An Approach to Size Sub-Wavelength Surface Crack Measurements Using Rayleigh Waves Based on Laser Ultrasounds. Sensors, 20.","DOI":"10.3390\/s20185077"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1016\/j.ultras.2007.02.001","article-title":"Ultrasonic sizing of short surface cracks","volume":"46","author":"Bernard","year":"2007","journal-title":"Ultrasonics"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"462","DOI":"10.1109\/T-UFFC.1986.26857","article-title":"Surface Acoustic Wave Interactions with Cracks and Slots: A Noncontacting Study Using Lasers","volume":"33","author":"Cooper","year":"1986","journal-title":"IEEE Trans Ultrason. Ferroelectr. Freq. Control."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1063\/1.3110885","article-title":"Sizing of partially closed surface-breaking microcracks with broadband Rayleigh waves","volume":"105","author":"Lomonosov","year":"2009","journal-title":"J. Appl. Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"312","DOI":"10.1016\/j.jsv.2019.05.011","article-title":"The role of non-slender inner structural designs on the linear and non-linear wave propagation attributes of periodic, two-dimensional architectured materials","volume":"455","author":"Karathanasopoulos","year":"2019","journal-title":"J. Sound Vib."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1016\/j.jsv.2018.06.006","article-title":"Wave propagation characteristics of periodic structures accounting for the effect of their higher order inner material kinematics","volume":"431","author":"Reda","year":"2018","journal-title":"J. Sound Vib."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2649","DOI":"10.1063\/1.109274","article-title":"Surface-breaking fatigue crack detection using laser ultrasound","volume":"62","author":"Shan","year":"1993","journal-title":"Appl. Phys. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"064907","DOI":"10.1063\/1.2353892","article-title":"Surface-breaking crack gauging with the use of laser-generated Rayleigh waves","volume":"100","author":"Jian","year":"2006","journal-title":"J. Appl. Phys."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1116","DOI":"10.1007\/BF02984033","article-title":"Finite element analysis of laser-generated ultrasound for characterizing surface-breaking cracks","volume":"19","author":"Jeong","year":"2005","journal-title":"J. Mech. Sci. Technol."},{"key":"ref_25","first-page":"121","article-title":"Research on photoacoustic detection method for depth measurement of surface \u201cnarrow defects\u201d","volume":"42","author":"Li","year":"2022","journal-title":"Acta Opt. Sin."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/15\/4849\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:23:37Z","timestamp":1760109817000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/15\/4849"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,25]]},"references-count":25,"journal-issue":{"issue":"15","published-online":{"date-parts":[[2024,8]]}},"alternative-id":["s24154849"],"URL":"https:\/\/doi.org\/10.3390\/s24154849","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2024,7,25]]}}}