{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,22]],"date-time":"2026-07-22T03:20:20Z","timestamp":1784690420145,"version":"3.55.0"},"reference-count":26,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,2,28]],"date-time":"2023-02-28T00:00:00Z","timestamp":1677542400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001348","name":"Agency for Science, Technology and Research (A*STAR), Singapore","doi-asserted-by":"publisher","award":["A19F1a0104"],"award-info":[{"award-number":["A19F1a0104"]}],"id":[{"id":"10.13039\/501100001348","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper presents a method for measuring surface cracks based on the analysis of Rayleigh waves in the frequency domain. The Rayleigh waves were detected by a Rayleigh wave receiver array made of a piezoelectric polyvinylidene fluoride (PVDF) film and enhanced by a delay-and-sum algorithm. This method employs the determined reflection factors of Rayleigh waves scattered at a surface fatigue crack to calculate the crack depth. In the frequency domain, the inverse scattering problem is solved by comparing the reflection factor of the Rayleigh waves between the measured and the theoretical curves. The experimental measurement results quantitatively matched the simulated surface crack depths. The advantages of using the low-profile Rayleigh wave receiver array made of a PVDF film for detecting the incident and reflected Rayleigh waves were analyzed in contrast with those of a Rayleigh wave receiver using a laser vibrometer and a conventional lead zirconate titanate (PZT) array. It was found that the Rayleigh waves propagating across the Rayleigh wave receiver array made of the PVDF film had a lower attenuation rate of 0.15 dB\/mm compared to that of 0.30 dB\/mm of the PZT array. Multiple Rayleigh wave receiver arrays made of the PVDF film were applied for monitoring surface fatigue crack initiation and propagation at welded joints under cyclic mechanical loading. Cracks with a depth range of 0.36\u20130.94 mm were successfully monitored.<\/jats:p>","DOI":"10.3390\/s23052665","type":"journal-article","created":{"date-parts":[[2023,2,28]],"date-time":"2023-02-28T06:09:52Z","timestamp":1677564592000},"page":"2665","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Surface Crack Monitoring by Rayleigh Waves with a Piezoelectric-Polymer-Film Ultrasonic Transducer Array"],"prefix":"10.3390","volume":"23","author":[{"given":"Xiaotian","family":"Li","sequence":"first","affiliation":[{"name":"Institute of Materials Research and Engineering, A*STAR (Agency for Science, Technology and Research), 2 Fusionopolis Way, Innovis #08-03, Singapore 138634, Singapore"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Voon-Kean","family":"Wong","sequence":"additional","affiliation":[{"name":"Institute of Materials Research and Engineering, A*STAR (Agency for Science, Technology and Research), 2 Fusionopolis Way, Innovis #08-03, Singapore 138634, Singapore"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yasmin Mohamed","family":"Yousry","sequence":"additional","affiliation":[{"name":"Institute of Materials Research and Engineering, A*STAR (Agency for Science, Technology and Research), 2 Fusionopolis Way, Innovis #08-03, Singapore 138634, Singapore"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6046-469X","authenticated-orcid":false,"given":"David Boon Kiang","family":"Lim","sequence":"additional","affiliation":[{"name":"Institute of Materials Research and Engineering, A*STAR (Agency for Science, Technology and Research), 2 Fusionopolis Way, Innovis #08-03, Singapore 138634, Singapore"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Percis Teena","family":"Christopher Subhodayam","sequence":"additional","affiliation":[{"name":"Institute of Materials Research and Engineering, A*STAR (Agency for Science, Technology and Research), 2 Fusionopolis Way, Innovis #08-03, Singapore 138634, Singapore"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5875-4815","authenticated-orcid":false,"given":"Kui","family":"Yao","sequence":"additional","affiliation":[{"name":"Institute of Materials Research and Engineering, A*STAR (Agency for Science, Technology and Research), 2 Fusionopolis Way, Innovis #08-03, Singapore 138634, Singapore"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Liuyang","family":"Feng","sequence":"additional","affiliation":[{"name":"Department of Civil and Environmental Engineering, Centre for Offshore Research and Engineering, National University of Singapore, Singapore 117576, Singapore"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xudong","family":"Qian","sequence":"additional","affiliation":[{"name":"Department of Civil and Environmental Engineering, Centre for Offshore Research and Engineering, National University of Singapore, Singapore 117576, Singapore"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zheng","family":"Fan","sequence":"additional","affiliation":[{"name":"School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,28]]},"reference":[{"key":"ref_1","unstructured":"Gurney, T.R. (1979). Fatigue of Welded Structures, Cambridge UP. [2nd ed.]."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1339","DOI":"10.1016\/j.mcm.2011.10.013","article-title":"Application of ANFIS for analytical modeling of JIC of functionally graded steels","volume":"55","author":"Nazari","year":"2012","journal-title":"Math. Comput. Model."},{"key":"ref_3","unstructured":"Paik, J.K., and Robert, E.M. (2014). Condition Assessment of Aged Structures, Elsevier."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1016\/j.marstruc.2018.06.011","article-title":"Low cycle fatigue test and enhanced lifetime estimation of high-strength steel S550 under different strain ratios","volume":"61","author":"Feng","year":"2018","journal-title":"Mar. Struct."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1016\/j.engfailanal.2019.07.006","article-title":"Effect of low temperatures on constant amplitude fatigue properties of Q345qD steel butt-welded joints","volume":"105","author":"Liao","year":"2019","journal-title":"Eng. Fail. Anal."},{"key":"ref_6","first-page":"465","article-title":"A complete integrity assessment of welded connections under high and low cycle fatigue followed by fracture failure","volume":"43","author":"Feng","year":"2022","journal-title":"Steel Compos. Struct."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1016\/S0951-8339(02)00075-8","article-title":"Fatigue analysis of welded joints: State of development","volume":"16","author":"Fricke","year":"2003","journal-title":"Mar. Struct."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"108165","DOI":"10.1016\/j.engfracmech.2021.108165","article-title":"An adaptive learning approach to determine and update crack sizes from strain relaxation data for welded plate joints","volume":"259","author":"Feng","year":"2022","journal-title":"Eng. Fract. Mech."},{"key":"ref_9","unstructured":"Hellier, C.J. (2013). Handbook of Nondestructive Evaluation, McGraw-Hill Education."},{"key":"ref_10","first-page":"340","article-title":"Scattering by Surface-Breaking and Sub-Surface Cracks","volume":"58","author":"Achenbach","year":"1981","journal-title":"Proc. Darpa\/Afwal Rev. Prog. Quant. NDE"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"432","DOI":"10.1016\/j.ndteint.2010.04.003","article-title":"Interaction of Rayleigh surface waves with a tightly closed fatigue crack","volume":"43","author":"Na","year":"2010","journal-title":"NDT E Int."},{"key":"ref_12","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_13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ndteint.2012.03.002","article-title":"In-plane and out-of-plane measurements of Rayleigh waves using EMATs for characterising surface cracks","volume":"49","author":"Rosli","year":"2012","journal-title":"NDT E Int."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1016\/j.ndteint.2016.03.002","article-title":"Focused Rayleigh wave EMAT for characterisation of surface-breaking defects","volume":"81","author":"Thring","year":"2016","journal-title":"NDT E Int."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/0041-624X(79)90099-4","article-title":"A computer model of the interaction of acoustic surface waves with discontinuities","volume":"17","author":"Bond","year":"1979","journal-title":"Ultrasonics"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1121\/1.390473","article-title":"Reflection and transmission of obliquely incident Rayleigh waves by a surface-breaking crack","volume":"75","author":"Angel","year":"1984","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1016\/0165-2125(80)90008-6","article-title":"Scattering of elastic waves by a surface-breaking crack","volume":"2","author":"Mendelsohn","year":"1980","journal-title":"Wave Motion"},{"key":"ref_18","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":"Masserey","year":"2007","journal-title":"Ultrasonics"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"106309","DOI":"10.1016\/j.ultras.2020.106309","article-title":"So you think you can DAS? A viewpoint on delay-and-sum beamforming","volume":"111","author":"Perrot","year":"2021","journal-title":"Ultrasonics"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1016\/j.tws.2018.08.017","article-title":"Size effect and life estimation for welded plate joints under low cycle actions at room and low ambient temperatures","volume":"132","author":"Feng","year":"2018","journal-title":"Thin-Walled Struct."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"106048","DOI":"10.1016\/j.ijfatigue.2020.106048","article-title":"A uniform volume-based fatigue indicator for high-and low-cycle assessment of notched components","volume":"144","author":"Feng","year":"2021","journal-title":"Int. J. Fatigue"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"3354","DOI":"10.1109\/JSEN.2017.2694454","article-title":"Direct-Write Piezoelectric Ultrasonic Transducers for Non-Destructive Testing of Metal Plates","volume":"17","author":"Shen","year":"2017","journal-title":"IEEE Sens. J."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"102131","DOI":"10.1016\/j.ndteint.2019.102131","article-title":"Direct-write piezoelectric ultrasonic transducers for pipe structural health monitoring","volume":"107","author":"Guo","year":"2019","journal-title":"NDT E Int."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1016\/j.ndteint.2018.05.009","article-title":"Design and Fabrication of Direct-write Piezoelectric Ultrasonic Transducers for Determining Yielding of Aluminum Alloy","volume":"98","author":"Guo","year":"2018","journal-title":"NDT E Int."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1109\/TUFFC.2017.2768238","article-title":"Plastic Strain Determination with Nonlinear Ultrasonic Waves using In-situ Integrated Piezoelectric Ultrasonic Transducers","volume":"65","author":"Guo","year":"2018","journal-title":"IEEE Trans. Sonics Ultrason."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Wong, V.K., Rabeek, S.M., Lai, S.C., Philibert, M., Lim, D.B.K., Chen, S., Raja, M.K., and Yao, K. (2022). Active Ultrasonic Structural Health Monitoring Enabled by Piezoelectric Direct-write Transducers and Edge Computing Process. Sensors, 22.","DOI":"10.3390\/s22155724"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/5\/2665\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:44:08Z","timestamp":1760121848000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/5\/2665"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,28]]},"references-count":26,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2023,3]]}},"alternative-id":["s23052665"],"URL":"https:\/\/doi.org\/10.3390\/s23052665","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2,28]]}}}