{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,3]],"date-time":"2026-09-03T10:46:08Z","timestamp":1788432368536,"version":"build-2803163510"},"reference-count":29,"publisher":"Acoustical Society of America (ASA)","issue":"2","funder":[{"DOI":"10.13039\/100006133","name":"Advanced Research Projects Agency - Energy","doi-asserted-by":"publisher","award":["DE-AR0001137"],"award-info":[{"award-number":["DE-AR0001137"]}],"id":[{"id":"10.13039\/100006133","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2024,8,1]]},"abstract":"<jats:p>The objective of this research is to demonstrate the effectiveness of a phased array-based nonlinear wave mixing technique to characterize internal, localized microscale damage in an additively manufactured (AM) component. By using phased arrays for the generation of the incident waves, it is possible to produce a nonlinear wave mixing scanning technique without the need for immersion or changing coupling conditions. The phased arrays can be configured to generate incident waves in multiple directions that meet the resonance conditions required for nonlinear wave mixing at a variety of internal locations. This allows for the scanning of a specimen without the removal and re-coupling of the source transducers, leading to greater scanning speed and repeatability. To demonstrate the accuracy of this phased array wave mixing approach, measurements of acoustic nonlinearity in an AM component are first made with a bulk wave second harmonic generation through thickness measurement. Next, nonlinear wave mixing measurements are made with single element transducers to confirm the sensitivity of the proposed nonlinear wave mixing approach to lack-of-fusion porosity in AM metals. Finally, phased arrays are used to highlight the effectiveness of the proposed nonlinear wave mixing technique in these same AM components.<\/jats:p>","DOI":"10.1121\/10.0028171","type":"journal-article","created":{"date-parts":[[2024,8,14]],"date-time":"2024-08-14T13:21:00Z","timestamp":1723641660000},"page":"1081-1090","update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":7,"title":["Phased array-based nonlinear wave mixing technique: Application to lack-of-fusion porosity characterization in additively manufactured metals"],"prefix":"10.1121","volume":"156","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9024-2331","authenticated-orcid":false,"given":"Aurelio","family":"Bellotti","sequence":"first","affiliation":[{"name":"George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology 1 , Atlanta, Georgia 30332, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5518-0032","authenticated-orcid":false,"given":"Jin-Yeon","family":"Kim","sequence":"additional","affiliation":[{"name":"School of Civil and Environmental Engineering, Georgia Institute of Technology 2 , Atlanta, Georgia 30332, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Donald","family":"VanderLaan","sequence":"additional","affiliation":[{"name":"School of Electrical and Computer Engineering, Georgia Institute of Technology 3 , Atlanta, Georgia 30332, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0358-7973","authenticated-orcid":false,"given":"Laurence","family":"Jacobs","sequence":"additional","affiliation":[{"name":"George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology 1 , Atlanta, Georgia 30332, USA"},{"name":"School of Civil and Environmental Engineering, Georgia Institute of Technology 2 , Atlanta, Georgia 30332, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"231","published-online":{"date-parts":[[2024,8,14]]},"reference":[{"issue":"3","key":"2024081413192899000_c1","doi-asserted-by":"publisher","first-page":"1266","DOI":"10.1121\/1.2221557","article-title":"Experimental characterization of fatigue damage in a nickel-base superalloy using nonlinear ultrasonic waves","volume":"120","year":"2006","journal-title":"J. Acoust. Soc. Am."},{"issue":"10","key":"2024081413192899000_c2","doi-asserted-by":"publisher","first-page":"5469","DOI":"10.1063\/1.368309","article-title":"Nonlinear acoustic response from precipitate-matrix misfit in a dislocation network","volume":"84","year":"1998","journal-title":"J. Appl. Phys."},{"key":"2024081413192899000_c3","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1016\/j.ndteint.2012.11.009","article-title":"Application of ultrasonic methods for early detection of thermal damage in 2205 duplex stainless steel","volume":"54","year":"2013","journal-title":"NDT&E Int."},{"issue":"5","key":"2024081413192899000_c4","doi-asserted-by":"publisher","first-page":"054911","DOI":"10.1063\/1.3692086","article-title":"Evaluation of radiation damage using nonlinear ultrasound","volume":"111","year":"2012","journal-title":"J. Appl. Phys."},{"issue":"1","key":"2024081413192899000_c5","doi-asserted-by":"publisher","first-page":"158","DOI":"10.1121\/10.0002960","article-title":"Nonlinear ultrasonic technique for the characterization of microstructure in additive materials","volume":"149","year":"2021","journal-title":"J. Acoust. Soc. Am."},{"issue":"2","key":"2024081413192899000_c6","doi-asserted-by":"publisher","first-page":"021008","DOI":"10.1115\/1.4053252","article-title":"Nonlinear acoustic technique for monitoring porosity in additively manufactured parts","volume":"5","year":"2022","journal-title":"J. Nondestr. Eval., Diagn. Prognostics Eng. Syst."},{"issue":"11","key":"2024081413192899000_c7","doi-asserted-by":"publisher","first-page":"3876","DOI":"10.3390\/ma15113876","article-title":"Microstructural characterization of additively manufactured metal components using linear and nonlinear ultrasonic techniques","volume":"15","year":"2022","journal-title":"Materials"},{"issue":"1","key":"2024081413192899000_c8","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1007\/s10921-014-0273-5","article-title":"Review of second harmonic generation measurement techniques for material state determination in metals","volume":"34","year":"2015","journal-title":"J. Nondestruct. Eval."},{"issue":"2","key":"2024081413192899000_c9","doi-asserted-by":"publisher","first-page":"024908","DOI":"10.1063\/1.4739746","article-title":"Measuring acoustic nonlinearity parameter using collinear wave mixing","volume":"112","year":"2012","journal-title":"J. Appl. Phys."},{"key":"2024081413192899000_c10","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1016\/j.ultras.2015.09.021","article-title":"Analytical and numerical modeling of non-collinear shear wave mixing at an imperfect interface","volume":"65","year":"2016","journal-title":"Ultrasonics"},{"issue":"14","key":"2024081413192899000_c11","doi-asserted-by":"publisher","first-page":"145102","DOI":"10.1063\/5.0086194","article-title":"Use of a non-collinear wave mixing technique to image internal microscale damage in concrete","volume":"131","year":"2022","journal-title":"J. Appl. Phys."},{"issue":"1","key":"2024081413192899000_c12","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1121\/1.1918405","article-title":"Interaction of elastic waves in an isotropic solid","volume":"35","year":"1963","journal-title":"J. Acoust. Soc. Am."},{"issue":"2","key":"2024081413192899000_c13","doi-asserted-by":"publisher","first-page":"591","DOI":"10.1121\/1.4861241","article-title":"Possible second-order nonlinear interactions of plane waves in an elastic solid","volume":"135","year":"2014","journal-title":"J. Acoust. Soc. Am."},{"issue":"4","key":"2024081413192899000_c14","doi-asserted-by":"publisher","first-page":"1934","DOI":"10.1121\/10.0002009","article-title":"Necessary and sufficient conditions for resonant mixing of plane waves in elastic solids with quadratic nonlinearity","volume":"148","year":"2020","journal-title":"J. Acoust. Soc. Am."},{"issue":"3A","key":"2024081413192899000_c15","doi-asserted-by":"publisher","first-page":"A591","DOI":"10.1103\/PhysRev.136.A591","article-title":"Ultrasonic study of three-phonon interactions. I. Theory","volume":"136","year":"1964","journal-title":"Phys. Rev."},{"issue":"8","key":"2024081413192899000_c16","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1063\/1.1753818","article-title":"Interaction of ultrasonic waves in solid media","volume":"2","year":"1963","journal-title":"Appl. Phys. Lett."},{"issue":"5","key":"2024081413192899000_c17","doi-asserted-by":"publisher","first-page":"EL117","DOI":"10.1121\/1.3231451","article-title":"The use of non-collinear mixing for nonlinear ultrasonic detection of plasticity and fatigue","volume":"126","year":"2009","journal-title":"J. Acoust. Soc. Am."},{"issue":"1","key":"2024081413192899000_c18","doi-asserted-by":"publisher","first-page":"060003","DOI":"10.1063\/1.4940509","article-title":"On the feasibility of nonlinear assessment of fatigue damage in hardened IN718 specimens based on non-collinear shear wave mixing","volume":"1706","year":"2016","journal-title":"AIP Conf. Proc."},{"key":"2024081413192899000_c19","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.ndteint.2017.09.010","article-title":"Scanning non-collinear wave mixing for nonlinear ultrasonic detection and localization of plasticity","volume":"93","year":"2018","journal-title":"NDT&E"},{"key":"2024081413192899000_c20","unstructured":"A.\n            Bellotti\n          , \u201c\nNonlinear ultrasound for the characterization of additively manufactured metals,\u201d Ph.D. thesis, \nGeorgia Institute of Technology, \nAtlanta, GA, 2023."},{"issue":"3","key":"2024081413192899000_c21","doi-asserted-by":"publisher","first-page":"479","DOI":"10.1007\/s11837-016-2234-1","article-title":"Synchrotron-based x-ray microtomography characterization of the effect of processing variables on porosity formation in laser power-bed additive manufacturing of Ti-6Al-4V","volume":"69","year":"2017","journal-title":"JOM"},{"key":"2024081413192899000_c22","doi-asserted-by":"publisher","first-page":"106227","DOI":"10.1016\/j.ultras.2020.106227","article-title":"A review of ultrasonic testing applications in additive manufacturing: Defect evaluation, material characterization, and process control","volume":"108","year":"2020","journal-title":"Ultrasonics"},{"key":"2024081413192899000_c23","doi-asserted-by":"publisher","first-page":"110944","DOI":"10.1016\/j.measurement.2022.110944","article-title":"Nondestructive evaluation of porosity in additive manufacturing by laser ultrasonic surface wave","volume":"193","year":"2022","journal-title":"Measurement"},{"key":"2024081413192899000_c24","doi-asserted-by":"publisher","first-page":"101800","DOI":"10.1016\/j.addma.2020.101800","article-title":"Ultrasonic nondestructive evaluation of laser powder bed fusion 316L stainless steel","volume":"38","year":"2021","journal-title":"Addit. Manuf."},{"key":"2024081413192899000_c25","doi-asserted-by":"publisher","first-page":"494","DOI":"10.6028\/jres.119.019","article-title":"Porosity measurements and analysis for metal additive manufacturing process control","volume":"119","year":"2014","journal-title":"J. Res. Natl. Inst. Stand. Technol."},{"key":"2024081413192899000_c26","doi-asserted-by":"publisher","first-page":"101943","DOI":"10.1016\/j.addma.2021.101943","article-title":"Effect of processing parameters and strut dimensions on the microstructures and hardness of stainless steel 316L lattice-emulating structures made by powder bed fusion","volume":"40","year":"2021","journal-title":"Addit. Manuf."},{"key":"2024081413192899000_c27","unstructured":"M. P.\n            May\n          , \u201c\nProposal and analysis of a non-collinear wave mixing technique for the detection of micro-cracks using phased arrays,\u201d Master's thesis, \nGeorgia Institute of Technology, \nAtlanta, 2020."},{"issue":"10","key":"2024081413192899000_c28","doi-asserted-by":"publisher","first-page":"2352","DOI":"10.3390\/s19102352","article-title":"Acoustic field of a linear phased array: A simulation study of ultrasonic circular tube material","volume":"19","year":"2019","journal-title":"Sensors"},{"issue":"8","key":"2024081413192899000_c29","doi-asserted-by":"publisher","first-page":"4320","DOI":"10.1063\/1.325484","article-title":"On the determination of phase and group velocities of dispersive waves in solids","volume":"49","year":"1978","journal-title":"J. Appl. Phys."}],"container-title":["The Journal of the Acoustical Society of America"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/asa\/jasa\/article-pdf\/156\/2\/1081\/20112365\/1081_1_10.0028171.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/asa\/jasa\/article-pdf\/156\/2\/1081\/20112365\/1081_1_10.0028171.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,14]],"date-time":"2024-08-14T13:21:06Z","timestamp":1723641666000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/jasa\/article\/156\/2\/1081\/3308066\/Phased-array-based-nonlinear-wave-mixing-technique"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8,1]]},"references-count":29,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2024,8,1]]}},"URL":"https:\/\/doi.org\/10.1121\/10.0028171","relation":{},"ISSN":["0001-4966"],"issn-type":[{"value":"0001-4966","type":"print"}],"subject":[],"published-other":{"date-parts":[[2024,8]]},"published":{"date-parts":[[2024,8,1]]}}}