{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,14]],"date-time":"2026-07-14T04:29:47Z","timestamp":1784003387373,"version":"3.55.0"},"reference-count":60,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2021,3,15]],"date-time":"2021-03-15T00:00:00Z","timestamp":1615766400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Chinese National Natural Science Fund","award":["11632004 and 11604033"],"award-info":[{"award-number":["11632004 and 11604033"]}]},{"name":"Fund for Innovative Research Groups of Natural Science Foundation of Hebei Province","award":["A2020202002"],"award-info":[{"award-number":["A2020202002"]}]},{"name":"Key Project of Natural Science Foundation of Tianjin","award":["S20ZDF077"],"award-info":[{"award-number":["S20ZDF077"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This study experimentally and numerically investigated the nonlinear behavior of the resonant bulk waves generated by the two-way collinear mixing method in 5052 aluminum alloy with micro-crack damage. When the primary longitudinal and transverse waves mixed in the micro-crack damage region, numerical and experimental results both verified the generation of resonant waves if the resonant condition \u03c9L\/\u03c9T=2\u03ba\/(\u03ba\u22121) was satisfied. Meanwhile, we found that the acoustic nonlinearity parameter (ANP) increases monotonously with increases in micro-crack density, the size of the micro-crack region, the frequency of resonant waves and friction coefficient of micro-crack surfaces. Furthermore, the micro-crack damage in a specimen generated by low-temperature fatigue experiment was employed. It was found that the micro-crack damage region can be located by scanning the specimen based on the two-way collinear mixing method.<\/jats:p>","DOI":"10.3390\/s21062061","type":"journal-article","created":{"date-parts":[[2021,3,15]],"date-time":"2021-03-15T22:16:54Z","timestamp":1615846614000},"page":"2061","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Experimental and Numerical Investigation of the Micro-Crack Damage in Elastic Solids by Two-Way Collinear Mixing Method"],"prefix":"10.3390","volume":"21","author":[{"given":"Hongjun","family":"Liu","sequence":"first","affiliation":[{"name":"College of Aerospace Engineering, Chongqing University, Chongqing 400044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7412-8216","authenticated-orcid":false,"given":"Youxuan","family":"Zhao","sequence":"additional","affiliation":[{"name":"College of Aerospace Engineering, Chongqing University, Chongqing 400044, China"},{"name":"Chongqing Key Laboratory of Heterogeneous Material Mechanics, Chongqing University, Chongqing 400044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Han","family":"Zhang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Noise and Vibration, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mingxi","family":"Deng","sequence":"additional","affiliation":[{"name":"College of Aerospace Engineering, Chongqing University, Chongqing 400044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ning","family":"Hu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Reliability and Intelligence Electrical Equipment, Hebei University of Technology, Tianjin 300401, China"},{"name":"National Engineering Research Center for Technological Innovation Method and Tool, Hebei University of Technology, Tianjin 300401, China"},{"name":"School of Mechanical Engineering, Hebei University of Technology, Tianjin 300401, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaoyang","family":"Bi","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Hebei University of Technology, Tianjin 300401, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,3,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Berndt, T.P., and Green, R.E. 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