A Semi-Analytical Solution for Temperature Distribution in Friction Stir Welding

A Semi-Analytical Solution for Temperature Distribution in Friction Stir Welding | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article A Semi-Analytical Solution for Temperature Distribution in Friction Stir Welding Armin Rahmati Darvazi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-521499/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 5 You are reading this latest preprint version Abstract In this paper, a semi-analytical thermal model of friction stir welding processes is developed in which the heat-generating regions are divided into many elements as point heat sources. The heat generation in each element involves the friction and plastic deformation, and the temperature rise caused by each element is calculated by solving the heat conduction equation of a moving heat source in a solid body. The heat loss through the top and bottom surfaces are considered in the model as heat sinks. The asymmetric distribution of the temperature is calculated through the whole process and over the whole volume of the workpiece by integrating the effects of all heat sources and sinks. The temperature-dependent material properties are updated by a numerical routine. The comparison between the calculated results and the experimental data clearly approved the validity of the proposed method for some aluminum and steel alloys. Mechanical Engineering Semi-analytical thermal model Friction stir welding Asymmetric distribution of temperature Heat sources and sinks Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 Figure 18 Figure 19 Figure 20 Figure 21 Figure 22 Figure 23 Figure 24 Figure 25 Full Text Supplementary Files GraphicalAbstract.docx Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Major Revisions Needed 11 Aug, 2021 Reviews received at journal 29 May, 2021 Reviewers invited by journal 29 May, 2021 Editor assigned by journal 20 May, 2021 First submitted to journal 12 May, 2021 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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02:33:39","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-521499/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-521499/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":9867188,"identity":"2652529a-c619-4d59-ad58-dfa16e72107e","added_by":"auto","created_at":"2021-06-01 23:05:40","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":69426,"visible":true,"origin":"","legend":"(a) Schematic diagram of the friction stir welding process and (b) the different heat generation regions","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-521499/v1/45f96514452a26ffb1adad26.png"},{"id":9867163,"identity":"02844d4f-fa45-429f-b7af-56cced0fc2c9","added_by":"auto","created_at":"2021-06-01 23:05:38","extension":"png","order_by":2,"title":"Figure 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4","display":"","copyAsset":false,"role":"figure","size":36703,"visible":true,"origin":"","legend":"The velocity of one point on the tool shoulder.","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-521499/v1/6fc96698c0442f0b3b6efd81.png"},{"id":9867266,"identity":"ae901520-0ae1-4934-9429-163e72943a18","added_by":"auto","created_at":"2021-06-01 23:08:38","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":23255,"visible":true,"origin":"","legend":"Definition of an element on the surface of the tool shoulder.","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-521499/v1/698d6f7aa5010bfab3e584f2.png"},{"id":9867267,"identity":"d3fea2db-f1f5-4a1a-a943-4ee7cde58c58","added_by":"auto","created_at":"2021-06-01 23:08:38","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":94019,"visible":true,"origin":"","legend":"The distance of one arbitrary point C from an element center.","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-521499/v1/7ab69412b6727e7ff7ebd79f.png"},{"id":9867275,"identity":"cba7ccbb-879f-448f-87f9-bb158097b812","added_by":"auto","created_at":"2021-06-01 23:08:39","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":35531,"visible":true,"origin":"","legend":"Definition of an element on the pin side.","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-521499/v1/5ffaaf8915cb7411fe1dfe1c.png"},{"id":9867273,"identity":"cee61475-4817-495d-9828-41f18f26e53d","added_by":"auto","created_at":"2021-06-01 23:08:39","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":42208,"visible":true,"origin":"","legend":"The suggested TMAZ profile for 304L stainless steel at advancing and retreating side. ","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-521499/v1/fadb62dd579cd81e4970239c.png"},{"id":9867177,"identity":"04bbdd20-8745-4111-a215-242edbc58210","added_by":"auto","created_at":"2021-06-01 23:05:39","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":282915,"visible":true,"origin":"","legend":"The shape of the TMAZ and definition of its boundary.","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-521499/v1/70d4032c8b5f878c318d394c.png"},{"id":9867190,"identity":"a6bbbed7-8248-4dd2-82ba-636394607e59","added_by":"auto","created_at":"2021-06-01 23:05:40","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":250734,"visible":true,"origin":"","legend":"Modeling of heat loss due to convection and radiation as a heat sink at the top 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12","display":"","copyAsset":false,"role":"figure","size":22399,"visible":true,"origin":"","legend":"The algorithm of the numerical code for material updating written in Fortran language (in the present paper δT=1°C).","description":"","filename":"12.png","url":"https://assets-eu.researchsquare.com/files/rs-521499/v1/6e4d938b2730748edeaf41d7.png"},{"id":9867301,"identity":"a5627113-d811-4ca0-a660-82cd4e117275","added_by":"auto","created_at":"2021-06-01 23:11:39","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":816944,"visible":true,"origin":"","legend":"Experimental installation (a) workpiece and thermocouple installation and (b) the Tool geometry.","description":"","filename":"13.png","url":"https://assets-eu.researchsquare.com/files/rs-521499/v1/ee282092a7d5b0b05c2f0541.png"},{"id":9867176,"identity":"530df4ef-42bd-4fe8-adee-362298c9d70a","added_by":"auto","created_at":"2021-06-01 23:05:39","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":23869,"visible":true,"origin":"","legend":"Comparison between the experimental data [13] and calculated temperature histories on the top of the retreating side of the workpiece at various distance from the weld line for the translational speed of 102 mm/min and the rotational speed of 300 rpm.","description":"","filename":"14.png","url":"https://assets-eu.researchsquare.com/files/rs-521499/v1/aca6ee7a92ca23b229ca457a.png"},{"id":9867184,"identity":"f9597676-4812-4d0d-9b14-cb4755656bcf","added_by":"auto","created_at":"2021-06-01 23:05:39","extension":"png","order_by":15,"title":"Figure 15","display":"","copyAsset":false,"role":"figure","size":29240,"visible":true,"origin":"","legend":"Comparison between the experimental data [13]and calculated temperature histories on the top of the retreating side of the workpiece at various distance from the weld line for the translational speed of 102 mm/min and the rotational speed of 500 rpm.","description":"","filename":"15.png","url":"https://assets-eu.researchsquare.com/files/rs-521499/v1/f28bd0387aa37a9fa5003b6f.png"},{"id":9867269,"identity":"be42507e-7035-40b5-b4a4-6e4a326fea45","added_by":"auto","created_at":"2021-06-01 23:08:38","extension":"png","order_by":16,"title":"Figure 16","display":"","copyAsset":false,"role":"figure","size":19235,"visible":true,"origin":"","legend":"Comparison between the experimental [24] and calculated temperature histories on the advancing side at a point 12.7 mm from the weld line for the translational speed of 25 mm/min and the rotational speed of 450 rpm.","description":"","filename":"16.png","url":"https://assets-eu.researchsquare.com/files/rs-521499/v1/6c4e83355fdf943d76ca02b3.png"},{"id":9867182,"identity":"2f5143d6-880f-4141-8888-4c12dceafb0e","added_by":"auto","created_at":"2021-06-01 23:05:39","extension":"png","order_by":17,"title":"Figure 17","display":"","copyAsset":false,"role":"figure","size":28190,"visible":true,"origin":"","legend":"The temperature histories at various distance from the weld line for the rotational speed of 800 rpm and the translational speed of 100 mm/min.","description":"","filename":"17.png","url":"https://assets-eu.researchsquare.com/files/rs-521499/v1/25abb50fcf9aff248a671e32.png"},{"id":9867194,"identity":"95106c02-90db-428a-84d3-6da101cc596c","added_by":"auto","created_at":"2021-06-01 23:05:40","extension":"png","order_by":18,"title":"Figure 18","display":"","copyAsset":false,"role":"figure","size":37702,"visible":true,"origin":"","legend":"The temperature histories at various distance from the weld line for the rotational speed of 1100 rpm and the translational speed of 100 mm/min.","description":"","filename":"18.png","url":"https://assets-eu.researchsquare.com/files/rs-521499/v1/badbe5b12b713e8182c6ce8a.png"},{"id":9867277,"identity":"d15c3bbf-bca7-45e7-962c-0ddae5d33354","added_by":"auto","created_at":"2021-06-01 23:08:40","extension":"png","order_by":19,"title":"Figure 19","display":"","copyAsset":false,"role":"figure","size":39526,"visible":true,"origin":"","legend":"The temperature histories at various distance from the weld line for the rotational speed of 1400 rpm and the translational speed of 100 mm/min.","description":"","filename":"19.png","url":"https://assets-eu.researchsquare.com/files/rs-521499/v1/5ecd7af53dc7afeaf5591860.png"},{"id":9867174,"identity":"47bc91ed-c839-4d82-acee-10b216ce575c","added_by":"auto","created_at":"2021-06-01 23:05:39","extension":"png","order_by":20,"title":"Figure 20","display":"","copyAsset":false,"role":"figure","size":33806,"visible":true,"origin":"","legend":"Comparison between the experimental [25] and calculated temperature histories at points 2 mm below the top surface at a distance of ( a) 8 mm and ( b) 16 mm from the centerline for the rotational speed of 1400 rpm and the translational speed of 100 mm/min.","description":"","filename":"20.png","url":"https://assets-eu.researchsquare.com/files/rs-521499/v1/63790e64ec7985345a7f728b.png"},{"id":9867169,"identity":"93f1a8ec-e8c8-4fee-89f1-46d8d89f0132","added_by":"auto","created_at":"2021-06-01 23:05:38","extension":"png","order_by":21,"title":"Figure 21","display":"","copyAsset":false,"role":"figure","size":60664,"visible":true,"origin":"","legend":"Comparison between the experimental [23] and calculated temperature histories at different locations for welding conditions of (a) 220 rpm and 220 mm/min, and ( b) 457 rpm and 457 mm/min.","description":"","filename":"21.png","url":"https://assets-eu.researchsquare.com/files/rs-521499/v1/9ef4840d715e25fceef80399.png"},{"id":9867268,"identity":"aa10cf84-6388-4447-ab87-f203992dae1c","added_by":"auto","created_at":"2021-06-01 23:08:38","extension":"png","order_by":22,"title":"Figure 22","display":"","copyAsset":false,"role":"figure","size":55316,"visible":true,"origin":"","legend":"Schematic of any element of the shoulder region as a heat source.","description":"","filename":"22.png","url":"https://assets-eu.researchsquare.com/files/rs-521499/v1/94664ae27c0237235d52b0dd.png"},{"id":9867191,"identity":"1bcd0212-d863-4d79-9fd5-a191f2e17b79","added_by":"auto","created_at":"2021-06-01 23:05:40","extension":"png","order_by":23,"title":"Figure 23","display":"","copyAsset":false,"role":"figure","size":36372,"visible":true,"origin":"","legend":"Modeling of heat source: (a) the Ferro and Bonollo model [4] and (b) the present model.","description":"","filename":"23.png","url":"https://assets-eu.researchsquare.com/files/rs-521499/v1/398baa78007f3f2e8094fd0d.png"},{"id":9867180,"identity":"78cf4cb0-14b3-4a9d-b7b3-ab2ee007e52d","added_by":"auto","created_at":"2021-06-01 23:05:39","extension":"png","order_by":24,"title":"Figure 24","display":"","copyAsset":false,"role":"figure","size":169090,"visible":true,"origin":"","legend":"The Computed temperature profiles on the top surface of workpiece for the rotational speed of 300 rpm and the translational speed of 102 mm/min: (a) Nandan et al. [26], (b) Darvazi et al. [20], (c) He et al. [27] and (d) The present work.","description":"","filename":"24.png","url":"https://assets-eu.researchsquare.com/files/rs-521499/v1/5291d20ae06968c655032366.png"},{"id":9867185,"identity":"75c6b51f-4325-4b86-91df-69c9db490c59","added_by":"auto","created_at":"2021-06-01 23:05:39","extension":"png","order_by":25,"title":"Figure 25","display":"","copyAsset":false,"role":"figure","size":30447,"visible":true,"origin":"","legend":"The cross-sectional temperature distribution of the FSW in the transverse direction computed by: a) Darvazi et al. [20] and b) the present method.","description":"","filename":"25.png","url":"https://assets-eu.researchsquare.com/files/rs-521499/v1/c9f73b7d3e4a94f6788dff28.png"},{"id":13637790,"identity":"975d71c1-cb8e-457b-aa2a-3e009818e1ea","added_by":"auto","created_at":"2021-09-17 08:47:19","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":5205969,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-521499/v1_covered.pdf"},{"id":9867313,"identity":"65b131d6-48a0-4167-9c95-e37a2d0c1bf8","added_by":"auto","created_at":"2021-06-01 23:12:03","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":5202311,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-521499/v1_covered.pdf"},{"id":9867192,"identity":"b8f96c21-a658-49ec-8c53-a31bfaaa894a","added_by":"auto","created_at":"2021-06-01 23:05:40","extension":"docx","order_by":4,"title":"","display":"","copyAsset":false,"role":"supplement","size":537714,"visible":true,"origin":"","legend":"","description":"","filename":"GraphicalAbstract.docx","url":"https://assets-eu.researchsquare.com/files/rs-521499/v1/81f48431eadce9441222a217.docx"}],"financialInterests":"","formattedTitle":"\u003cp\u003eA Semi-Analytical Solution for Temperature Distribution in Friction Stir Welding\u003c/p\u003e","fulltext":[{"header":"Full Text","content":"This preprint is available for \u003ca href='/article/rs-521499/latest.pdf' target='_blank'\u003edownload as a PDF\u003c/a\u003e."}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"the-international-journal-of-advanced-manufacturing-technology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jamt","sideBox":"Learn more about [The International Journal of Advanced Manufacturing Technology](https://www.springer.com/journal/170)","snPcode":"170","submissionUrl":"https://submission.nature.com/new-submission/170/3","title":"The International Journal of Advanced Manufacturing Technology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Semi-analytical thermal model, Friction stir welding, Asymmetric distribution of temperature, Heat sources and sinks","lastPublishedDoi":"10.21203/rs.3.rs-521499/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-521499/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this paper, a semi-analytical thermal model of friction stir welding processes is developed in which the heat-generating regions are divided into many elements as point heat sources. The heat generation in each element involves the friction and plastic deformation, and the temperature rise caused by each element is calculated by solving the heat conduction equation of a moving heat source in a solid body. The heat loss through the top and bottom surfaces are considered in the model as heat sinks. The asymmetric distribution of the temperature is calculated through the whole process and over the whole volume of the workpiece by integrating the effects of all heat sources and sinks. The temperature-dependent material properties are updated by a numerical routine. The comparison between the calculated results and the experimental data clearly approved the validity of the proposed method for some aluminum and steel alloys.\u003c/p\u003e","manuscriptTitle":"A Semi-Analytical Solution for Temperature Distribution in Friction Stir Welding","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2021-06-01 23:05:32","doi":"10.21203/rs.3.rs-521499/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Major Revisions Needed","date":"2021-08-11T08:21:40+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2021-05-29T18:31:00+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2021-05-29T06:13:00+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2021-05-20T08:06:00+00:00","index":"","fulltext":""},{"type":"submitted","content":"The International Journal of Advanced Manufacturing Technology","date":"2021-05-12T07:22:19+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"the-international-journal-of-advanced-manufacturing-technology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jamt","sideBox":"Learn more about [The International Journal of Advanced Manufacturing Technology](https://www.springer.com/journal/170)","snPcode":"170","submissionUrl":"https://submission.nature.com/new-submission/170/3","title":"The International Journal of Advanced Manufacturing Technology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"a15da79d-0cb2-4fda-8c0d-18e7f4dd3306","owner":[],"postedDate":"June 1st, 2021","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"in-revision","subjectAreas":[{"id":4707758,"name":"Mechanical Engineering"}],"tags":[],"updatedAt":"2021-08-12T00:52:37+00:00","versionOfRecord":[],"versionCreatedAt":"2021-06-01 23:05:32","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-521499","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-521499","identity":"rs-521499","version":["v1"]},"buildId":"ApUGefWb6u5IBVtyqm6d5","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}