Physics-Informed Neural Network Framework for Phase-Field Modeling of Intergranular Fracture

Physics-Informed Neural Network Framework for Phase-Field Modeling of Intergranular Fracture | 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 Physics-Informed Neural Network Framework for Phase-Field Modeling of Intergranular Fracture P G Kubendran Amos This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9407614/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Intergranular fracture, characterised by the preferential growth of crack along the grain boundaries is a critical failure mode in polycrystalline materials. While phase-field models have been widely used to simulate such fracture within finite-element frameworks, their combination with physics-informed neural networks (PINNs) for microstructure-dependent crack growth remains largely unexplored. This work develops a PINN-based phase-field formulation to model intergranular fracture. Introducing a reduced resistance to an interface, by representing the grain boundary through a spatially varying fracture toughness field, the fracture problem is solved, in the present work, using a staggered two-network architecture. While one network handles the displacement field, the other solves the phase-field damage variable, collectively mirroring the classical operator-split approach, which in this formulation replaces finite-element discretization with neural-network approximation. Comparing the evolution of the crack in two distinct cases of homogeneous and spatially-varying fracture-toughness, under identical loading condition, demostrates that the crack in the latter intergranular medium ($G_c^{gb} = 0.20$) elongates preferentially along the weakened interface, producing greater vertical extension, whereas the damage-field higher restricted in the intragranular setting ($G_c = 1.0$). Correspondingly, this work offers novel evidence for the ability of the PINN-based phase-field approach to model intergranular cracking. Physics-informed neural networks Phase-field fracture Intergranular cracking Grain boundary Spatially varying fracture toughness Staggered solution Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted 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. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9407614","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":622515996,"identity":"93aad1dc-17ce-4561-a84c-63fa6b58c744","order_by":0,"name":"P G Kubendran Amos","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAqElEQVRIiWNgGAWjYFACxgYgYcPABuawEa8ljYGNjZloLWBwGKiaWC3m0ofbHvyoOJ/HJ99/gOFD2WHCWiz7EtsNe87cLgY5jHHGOSK0GJxhbJNmbLud2AbUwszbRrSWf+cgWv4Sr6XhAEQLIzFaLHsY2yR7jiUDtSQbHOw5l05YizkP+zOJHzV2ifObDz588KPMmgiHIXMOEFaPrmUUjIJRMApGAVYAACkkNBFKVWbGAAAAAElFTkSuQmCC","orcid":"","institution":"National Institute of Technology Tiruchirappalli","correspondingAuthor":true,"prefix":"","firstName":"P","middleName":"G Kubendran","lastName":"Amos","suffix":""}],"badges":[],"createdAt":"2026-04-13 18:52:05","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-9407614/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9407614/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":106971104,"identity":"635a8b68-20c5-4ca2-aaf1-0ec5ac80f08c","added_by":"auto","created_at":"2026-04-15 10:17:38","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2083527,"visible":true,"origin":"","legend":"","description":"","filename":"InterGPINNL.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9407614/v1_covered_5a93aef4-86cb-4351-a095-acca21d505b5.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003ePhysics-Informed Neural Network Framework for Phase-Field Modeling of Intergranular Fracture\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"National Institute of Technology Tiruchirappalli","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","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":"Physics-informed neural networks, Phase-field fracture, Intergranular cracking, Grain boundary, Spatially varying fracture toughness, Staggered solution","lastPublishedDoi":"10.21203/rs.3.rs-9407614/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9407614/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIntergranular fracture, characterised by the preferential growth of crack along the grain boundaries is a critical failure mode in polycrystalline materials. While phase-field models have been widely used to simulate such fracture within finite-element frameworks, their combination with physics-informed neural networks (PINNs) for microstructure-dependent crack growth remains largely unexplored. This work develops a PINN-based phase-field formulation to model intergranular fracture. Introducing a reduced resistance to an interface, by representing the grain boundary through a spatially varying fracture toughness field, the fracture problem is solved, in the present work, using a staggered two-network architecture. While one network handles the displacement field, the other solves the phase-field damage variable, collectively mirroring the classical operator-split approach, which in this formulation replaces finite-element discretization with neural-network approximation. Comparing the evolution of the crack in two distinct cases of homogeneous and spatially-varying fracture-toughness, under identical loading condition, demostrates that the crack in the latter intergranular medium ($G_c^{gb} = 0.20$) elongates preferentially along the weakened interface, producing greater vertical extension, whereas the damage-field higher restricted in the intragranular setting \u0026nbsp;($G_c = 1.0$). Correspondingly, this work offers novel evidence for the ability of the PINN-based phase-field approach to model intergranular cracking.\u003c/p\u003e","manuscriptTitle":"Physics-Informed Neural Network Framework for Phase-Field Modeling of Intergranular Fracture","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-15 09:58:45","doi":"10.21203/rs.3.rs-9407614/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","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":"a661425f-f59b-49bd-a9c5-f08342bd540f","owner":[],"postedDate":"April 15th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-04-15T09:58:45+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-15 09:58:45","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9407614","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9407614","identity":"rs-9407614","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}