{"paper_id":"077dfbfe-bb5c-4d6b-be70-bcbf3abe5f71","body_text":"An improved unified creep‐plasticity constitutive model for viscoplastic solder materials of electronic packaging subjected to high-strain-rate impact loadings | 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 An improved unified creep‐plasticity constitutive model for viscoplastic solder materials of electronic packaging subjected to high-strain-rate impact loadings Ning An, Bofeng Li, Yuexing Wang, Xiangyu Sun, Xu He This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8219436/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 17 Jan, 2026 Read the published version in Journal of Materials Science: Materials in Electronics → Version 1 posted You are reading this latest preprint version Abstract With the increasing demand for reliability in electronic packaging under extreme dynamic loading environments, accurate characterization of solder joint deformation behavior has become critical for optimizing structural design and enhancing product durability. This paper addresses this imperative by focusing on the deformation mechanisms and constitutive modeling challenges of solder joints under high-strain-rate conditions. Traditional metallic material models are unable to adequately capture the complex thermo-mechanical responses of solders, highlighting the need for advanced constitutive frameworks. By integrating split Hopkinson pressure bar (SHPB) experimental data with a unified creep-plasticity theory, an improved constitutive model is developed that incorporates the strengths of the Johnson-Cook formulation while addressing its limitations in temperature-dependent behavior. Experimental validation utilizes Pb37Sn63 solder specimens tested at temperatures of 25°C, 60°C, and 100°C under strain rates up to 5500 s⁻¹, enabling quantitative analysis of coupled temperature-strain rate effects on stress-strain behavior. The proposed model demonstrates exceptional accuracy in predicting solder deformation across extreme thermo-mechanical conditions. Following rigorous parameter calibration through SHPB test replication via user-defined material subroutines in finite element simulations, the model exhibits high predictive fidelity. Implementation in package-level structural simulations further reveals critical dynamic mechanical response characteristics under impact loading, confirming its efficacy in enhancing reliability analysis for electronics packaging design. Solder joint High strain rate SHPB Unified creep-plasticity Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 17 Jan, 2026 Read the published version in Journal of Materials Science: Materials in Electronics → Version 1 posted 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. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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materials of electronic packaging subjected to high-strain-rate impact loadings\",\"fulltext\":[],\"fulltextSource\":\"\",\"fullText\":\"\",\"funders\":[],\"hasAdminPriorityOnWorkflow\":false,\"hasManuscriptDocX\":false,\"hasOptedInToPreprint\":true,\"hasPassedJournalQc\":\"\",\"hasAnyPriority\":false,\"hideJournal\":true,\"highlight\":\"\",\"institution\":\"\",\"isAcceptedByJournal\":true,\"isAuthorSuppliedPdf\":true,\"isDeskRejected\":\"\",\"isHiddenFromSearch\":false,\"isInQc\":false,\"isInWorkflow\":false,\"isPdf\":true,\"isPdfUpToDate\":true,\"isWithdrawnOrRetracted\":false,\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"researchsquare\",\"isNatureJournal\":false,\"hasQc\":true,\"allowDirectSubmit\":true,\"externalIdentity\":\"\",\"sideBox\":\"\",\"snPcode\":\"\",\"submissionUrl\":\"/submission\",\"title\":\"Research Square\",\"twitterHandle\":\"researchsquare\",\"acdcEnabled\":true,\"dfaEnabled\":false,\"editorialSystem\":\"\",\"reportingPortfolio\":\"\",\"inReviewEnabled\":false,\"inReviewRevisionsEnabled\":true},\"keywords\":\"Solder joint, High strain rate, SHPB, Unified creep-plasticity\",\"lastPublishedDoi\":\"10.21203/rs.3.rs-8219436/v1\",\"lastPublishedDoiUrl\":\"https://doi.org/10.21203/rs.3.rs-8219436/v1\",\"license\":{\"name\":\"CC BY 4.0\",\"url\":\"https://creativecommons.org/licenses/by/4.0/\"},\"manuscriptAbstract\":\"\\u003cp\\u003eWith the increasing demand for reliability in electronic packaging under extreme dynamic loading environments, accurate characterization of solder joint deformation behavior has become critical for optimizing structural design and enhancing product durability. This paper addresses this imperative by focusing on the deformation mechanisms and constitutive modeling challenges of solder joints under high-strain-rate conditions. Traditional metallic material models are unable to adequately capture the complex thermo-mechanical responses of solders, highlighting the need for advanced constitutive frameworks. By integrating split Hopkinson pressure bar (SHPB) experimental data with a unified creep-plasticity theory, an improved constitutive model is developed that incorporates the strengths of the Johnson-Cook formulation while addressing its limitations in temperature-dependent behavior. Experimental validation utilizes Pb37Sn63 solder specimens tested at temperatures of 25\\u0026deg;C, 60\\u0026deg;C, and 100\\u0026deg;C under strain rates up to 5500 s⁻\\u0026sup1;, enabling quantitative analysis of coupled temperature-strain rate effects on stress-strain behavior. The proposed model demonstrates exceptional accuracy in predicting solder deformation across extreme thermo-mechanical conditions. Following rigorous parameter calibration through SHPB test replication via user-defined material subroutines in finite element simulations, the model exhibits high predictive fidelity. Implementation in package-level structural simulations further reveals critical dynamic mechanical response characteristics under impact loading, confirming its efficacy in enhancing reliability analysis for electronics packaging design.\\u003c/p\\u003e\",\"manuscriptTitle\":\"An improved unified creep‐plasticity constitutive model for viscoplastic solder materials of electronic packaging subjected to high-strain-rate impact loadings\",\"msid\":\"\",\"msnumber\":\"\",\"nonDraftVersions\":[{\"code\":1,\"date\":\"2025-12-12 06:50:01\",\"doi\":\"10.21203/rs.3.rs-8219436/v1\",\"editorialEvents\":[{\"type\":\"communityComments\",\"content\":0}],\"status\":\"published\",\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"researchsquare\",\"isNatureJournal\":false,\"hasQc\":true,\"allowDirectSubmit\":true,\"externalIdentity\":\"\",\"sideBox\":\"\",\"snPcode\":\"\",\"submissionUrl\":\"/submission\",\"title\":\"Research Square\",\"twitterHandle\":\"researchsquare\",\"acdcEnabled\":true,\"dfaEnabled\":false,\"editorialSystem\":\"\",\"reportingPortfolio\":\"\",\"inReviewEnabled\":false,\"inReviewRevisionsEnabled\":true}}],\"origin\":\"\",\"ownerIdentity\":\"9070c2f8-ccd4-487c-afa0-948a31e790d2\",\"owner\":[],\"postedDate\":\"December 12th, 2025\",\"published\":true,\"recentEditorialEvents\":[],\"rejectedJournal\":[],\"revision\":\"\",\"amendment\":\"\",\"status\":\"posted\",\"subjectAreas\":[],\"tags\":[],\"updatedAt\":\"2026-01-19T16:46:35+00:00\",\"versionOfRecord\":{\"articleIdentity\":\"rs-8219436\",\"link\":\"https://doi.org/10.1007/s10854-026-16591-8\",\"journal\":{\"identity\":\"journal-of-materials-science-materials-in-electronics\",\"isVorOnly\":false,\"title\":\"Journal of Materials Science: Materials in Electronics\"},\"publishedOn\":\"2026-01-17 16:29:11\",\"publishedOnDateReadable\":\"January 17th, 2026\"},\"versionCreatedAt\":\"2025-12-12 06:50:01\",\"video\":\"\",\"vorDoi\":\"10.1007/s10854-026-16591-8\",\"vorDoiUrl\":\"https://doi.org/10.1007/s10854-026-16591-8\",\"workflowStages\":[]},\"version\":\"v1\",\"identity\":\"rs-8219436\",\"journalConfig\":\"researchsquare\"},\"__N_SSP\":true},\"page\":\"/article/[identity]/[[...version]]\",\"query\":{\"redirect\":\"/article/rs-8219436\",\"identity\":\"rs-8219436\",\"version\":[\"v1\"]},\"buildId\":\"XKTyCvWXoU3ODBz1xrDgd\",\"isFallback\":false,\"isExperimentalCompile\":false,\"dynamicIds\":[84888],\"gssp\":true,\"scriptLoader\":[]}","source_license":"CC-BY-4.0","license_restricted":false}