{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T11:17:55Z","timestamp":1775215075620,"version":"3.50.1"},"reference-count":40,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,12,31]],"date-time":"2020-12-31T00:00:00Z","timestamp":1609372800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"China Postdoctoral Science Foundation Funded Project","award":["No. 2018M642775"],"award-info":[{"award-number":["No. 2018M642775"]}]},{"DOI":"10.13039\/501100001809","name":"National Science Foundation of China","doi-asserted-by":"publisher","award":["(No. U1833116"],"award-info":[{"award-number":["(No. U1833116"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Carbon fiber-reinforced polymer (CFRP) laminates, a key composite material, are widely used in aircraft structures and are susceptible to low-velocity impact (LVI) damage from bird strikes, lightning strikes, hail impacts and other situations. Therefore, finding a method that repairs the damaged structure and detects the effect of these repairs under LVI is a very important goal. In this work, the repair effect of LVI damage in CFRP laminates repaired with patches of various sizes is investigated via experimental and numerical nonlinear Lamb wave analyses. An integrated numerical procedure that combines LVI with nonlinear Lamb wave detection is developed to predict the nonlinear Lamb wave behavior in LVI-damaged patch-repaired CFRP laminates. The CFRP laminate damage in the nonlinear Lamb wave simulation is evaluated based on relative acoustic nonlinearity parameters (RANPs). As a result, the integrated numerical procedure is validated with drop-weight impact tests and RAM-5000 SNAP nonlinear ultrasonic detection system. An optimal patch design is established via interpolation to optimize the absorbed energy, delamination surface area, second RANP and third RANP with different patch repair sizes. These parameters exhibit consistent curve fitting trends, indicating that they can be used as important indicators of impact damage. The optimal circular patch design with a radius of 2.5 r has better impact resistance behavior and repair performance.<\/jats:p>","DOI":"10.3390\/s21010219","type":"journal-article","created":{"date-parts":[[2020,12,31]],"date-time":"2020-12-31T14:31:49Z","timestamp":1609425109000},"page":"219","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Impact Damage Detection in Patch-Repaired CFRP Laminates Using Nonlinear Lamb Waves"],"prefix":"10.3390","volume":"21","author":[{"given":"Zhenhua","family":"Yin","sequence":"first","affiliation":[{"name":"School of Mechanical and Power Engineering, Zhengzhou University, Science Road 100,  Zhengzhou 450001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cheng","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mechanical and Power Engineering, Zhengzhou University, Science Road 100,  Zhengzhou 450001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ying","family":"Tie","sequence":"additional","affiliation":[{"name":"School of Mechanical and Power Engineering, Zhengzhou University, Science Road 100,  Zhengzhou 450001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6980-1864","authenticated-orcid":false,"given":"Yuechen","family":"Duan","sequence":"additional","affiliation":[{"name":"School of Mechanical and Power Engineering, Zhengzhou University, Science Road 100,  Zhengzhou 450001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Salmanpour, M.S., Sharif, K.Z., and Mhf, A. (2017). Impact damage localisation with piezoelectric sensors under operational and environmental conditions. Sensors, 17.","DOI":"10.3390\/s17051178"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1521","DOI":"10.1111\/ffe.13006","article-title":"Multiscale carbon fibre-reinforced polymer (CFRP) composites containing carbon nanotubes with tailored interfaces","volume":"42","author":"Santos","year":"2019","journal-title":"Fatigue Fract. Eng. M."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1252","DOI":"10.1109\/TIM.2019.2893701","article-title":"Locating defects in anisotropic CFRP plates using ToF-based probability matrix and neural networks","volume":"68","author":"Feng","year":"2019","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"111869","DOI":"10.1016\/j.compstruct.2020.111869","article-title":"Impact damage assessment in orthotropic CFRP laminates using nonlinear Lamb wave: Experimental and numerical investigations","volume":"236","author":"Tie","year":"2020","journal-title":"Compos. Struct."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1016\/j.compositesb.2017.09.020","article-title":"Effects of stacking sequence and rotation angle of patch on low velocity impact performance of scarf repaired laminates","volume":"133","author":"Cheng","year":"2018","journal-title":"Compos. Part B Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"105407","DOI":"10.1016\/j.ijmecsci.2019.105407","article-title":"Optimization for maximizing the impact-resistance of patch repaired CFRP laminates using a surrogate-based model","volume":"172","author":"Tie","year":"2020","journal-title":"Int. J. Mech. Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1016\/j.compstruct.2018.01.075","article-title":"An insight into the low-velocity impact behavior of patch-repaired CFRP laminates using numerical and experimental approaches","volume":"190","author":"Tie","year":"2018","journal-title":"Compos. Struct."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"638","DOI":"10.3390\/s16050638","article-title":"Rapid multi-damage identification for health monitoring of laminated composites using piezoelectric wafer sensor arrays","volume":"16","author":"Liang","year":"2016","journal-title":"Sensors"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/j.ultras.2015.02.011","article-title":"A Lamb waves based statistical approach to structural health monitoring of carbon fibre reinforced polymer composites","volume":"60","author":"Carboni","year":"2015","journal-title":"Ultrasonics"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.ultras.2018.02.005","article-title":"Mixing of ultrasonic Lamb waves in thin plates with quadratic nonlinearity","volume":"87","author":"Li","year":"2018","journal-title":"Ultrasonics"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1016\/j.compstruct.2016.09.073","article-title":"Detection of delamination in composite laminates using Lamb wave based nonlinear method","volume":"159","author":"Yelve","year":"2017","journal-title":"Compos. Struct."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"8528","DOI":"10.3390\/s140508528","article-title":"Numerical simulation of nonlinear lamb waves used in a thin plate for detecting buried micro-cracks","volume":"15","author":"Wan","year":"2014","journal-title":"Sensors"},{"key":"ref_13","first-page":"1","article-title":"An extensive overview of lamb wave technique for detecting fatigue damage in composite structures","volume":"2","author":"Altabey","year":"2017","journal-title":"Ind. Syst. Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1016\/j.apacoust.2014.10.010","article-title":"Detection of stiffener disbonding in a stiffened aluminium panel using nonlinear Lamb wave","volume":"89","author":"Yelve","year":"2015","journal-title":"Appl. Acoust."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/j.jsv.2007.07.029","article-title":"Characterization of elastic anisotropy of a solid plate using nonlinear Lamb wave approach","volume":"308","author":"Deng","year":"2007","journal-title":"J. Sound Vib."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/j.ultras.2017.05.004","article-title":"Nonlinear Lamb waves for fatigue damage identification in CFRP reinforced steel plates","volume":"80","author":"Wang","year":"2017","journal-title":"Ultrasonics"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"114903","DOI":"10.1016\/j.jsv.2019.114903","article-title":"Second-order harmonic generation of Lamb wave in prestressed plates","volume":"460","author":"Yang","year":"2019","journal-title":"J. Sound Vib."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1080\/15376494.2014.907950","article-title":"Impact Damage Detection in Composite Structures Considering Nonlinear Lamb Wave Propagation","volume":"22","author":"Rauter","year":"2014","journal-title":"Mech. Adv. Mater. Struct."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"448","DOI":"10.1016\/j.ymssp.2016.05.035","article-title":"Uncertainty quantification for acoustic nonlinearity parameter in Lamb wave-based prediction of barely visible impact damage in composites","volume":"82","author":"Hong","year":"2017","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"014001","DOI":"10.1088\/1361-6501\/ab382e","article-title":"Impact damage detection in composites using a guided wave mixing technique","volume":"31","author":"Li","year":"2020","journal-title":"Meas. Sci. Technol."},{"key":"ref_21","unstructured":"Takahashi, I., Ito, Y., and Takeda, S. (2007, January 8\u201313). Impact damage detection on scarf-repaired composites using Lamb wave sensing. Proceedings of the 16th International Conference on Composite Materials (ICCM-16), Kyoto, Japan."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/j.ndteint.2016.10.006","article-title":"Nonlinear Lamb wave-mixing technique for micro-crack detection in plates","volume":"85","author":"Jiao","year":"2017","journal-title":"NDT E Int."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Park, S.J., Joo, Y.S., and Kim, H.W. (2020). Selective Generation of Lamb Wave Modes in a Finite-Width Plate by Angle-Beam Excitation Method. Sensors, 20.","DOI":"10.3390\/s20143868"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"760","DOI":"10.1016\/j.ymssp.2017.07.011","article-title":"Second harmonic generation at fatigue cracks by low-frequency Lamb waves: Experimental and numerical studies","volume":"79","author":"Yang","year":"2018","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1016\/j.ultras.2017.04.004","article-title":"Generation mechanism of nonlinear ultrasonic Lamb waves in thin plates with randomly distributed micro-cracks","volume":"79","author":"Zhao","year":"2017","journal-title":"Ultrasonics"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1016\/j.ndteint.2018.04.006","article-title":"Application of nonlinear ultrasonic technique to characterize the creep damage in ASME T92 steel welded joints","volume":"98","author":"Wang","year":"2018","journal-title":"NDT E Int."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1829","DOI":"10.1121\/1.3621714","article-title":"Baseline-free estimation of residual fatigue life using a third order acoustic nonlinear parameter","volume":"130","author":"Amura","year":"2011","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"669","DOI":"10.1016\/j.compositesb.2018.12.153","article-title":"Low-velocity impact behaviors of repaired CFRP laminates: Effect of impact location and external patch configurations","volume":"163","author":"Hou","year":"2019","journal-title":"Compos. Part B Eng."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"710","DOI":"10.1016\/j.compositesb.2012.07.049","article-title":"Towards optimization of patch shape on the performance of bonded composite repair using FEM","volume":"45","author":"Ramji","year":"2013","journal-title":"Compos. Part B Eng."},{"key":"ref_30","unstructured":"ASTM D7136\/D7136M-07 (2003). Standard Test Method for Measuring the Damage Resistance of a Fiber-Reinforced Polymer Matrix Composite to a Drop-Weight Impact Event, American Society for Testing and Materials."},{"key":"ref_31","unstructured":"Hibbitt, H.D., Karlsson, B.I., and Sorensen, P. (2011). ABAQUS\/Explicit: User\u2019s Manual, Inc.. Version 10.1."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/j.ijadhadh.2012.10.015","article-title":"Study of tensile failure mechanisms in scarf repaired CFRP laminates","volume":"41","author":"Cheng","year":"2013","journal-title":"Int. J. Adhes. Adhes."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1016\/j.compstruct.2014.12.048","article-title":"Design and optimization of bonded patch repairs of laminated composite structures","volume":"123","author":"Gong","year":"2015","journal-title":"Compos. Struct."},{"key":"ref_34","first-page":"3292334","article-title":"Failure criteria for unidirectional fiber composite","volume":"47","author":"Hashi","year":"1980","journal-title":"J. Appl. Mech."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1016\/j.compositesb.2015.08.082","article-title":"Progressive failure analysis of three-dimensional woven carbon composites in single-bolt, double-shear bearing","volume":"84","author":"Warren","year":"2016","journal-title":"Compos. Part B Eng."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1016\/j.compositesa.2014.02.013","article-title":"Simulating progressive failure of composite laminates including in-ply and delamination damage effects","volume":"61","author":"Chen","year":"2014","journal-title":"Compos. Part A Appl. Sci. Manuf."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"2383","DOI":"10.1016\/j.compscitech.2007.06.015","article-title":"Prediction of impact-induced delamination in cross-ply composite laminates using cohesive interface elements","volume":"68","author":"Aymerich","year":"2008","journal-title":"Compos. Sci. Technol."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1016\/j.ijadhadh.2008.04.004","article-title":"Cohesive and continuum mixed-mode damage models applied to the simulation of the mechanical behaviour of bonded joints","volume":"28","author":"Chousal","year":"2008","journal-title":"Int. J. Adhes. Adhes."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1016\/j.compositesb.2017.11.042","article-title":"Damage characterization of composite plates under low velocity impact using ultrasonic guided waves","volume":"138","author":"Caputo","year":"2018","journal-title":"Compos. Part B Eng."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1016\/j.compstruct.2017.01.015","article-title":"Damage localization and identification in WGF\/epoxy composite laminates by using Lamb waves: Experiment and simulation","volume":"165","author":"Yang","year":"2017","journal-title":"Compos. Struct."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/1\/219\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:48:31Z","timestamp":1760179711000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/1\/219"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,31]]},"references-count":40,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,1]]}},"alternative-id":["s21010219"],"URL":"https:\/\/doi.org\/10.3390\/s21010219","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,12,31]]}}}