Non-localseparationconstitutivelawsforinterfacesand theirrelationtonanoscalesimulations DouglasE.Spearot a ,KarlI.Jacob b ,DavidL.McDowell a, * a George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, 801 Ferst Drive, Atlanta, GA 30332-0405, USA b School of Polymer, Textile and Fiber Engineering, Georgia Institute of Technology, 801 Ferst Drive, Atlanta, GA 30332-0295, USA Received6January2003;receivedinrevisedform17June2003 Abstract Aframeworkisproposedtocharacterizefracturethroughcontinuuminterfaceseparationconstitutivelawsthatare motivatedbymoleculardynamics(MD)simulationsusingembedded-atommethodpotentials.Theselawsaredistin- guishedfrompreviouscontinuummodelsinthatdiscreteatomisticsareusedtodetermineasetofnanoscaleeffects, accountingfortheinfluenceofatomicstructureandimperfectionsoninterfaceseparationorfracture.Thisconceptual framework utilizes internal state variable (ISV) theory to embed a set of interface attributes into cohesive interface separationconstitutiverelations.Structuralrearrangementoftheinterfaceregionduringseparationcanbeexplicitly trackedthroughasetofdifferentialequationsfortheISVs.Toguideformsfortheinterfaceconstitutivelaws,MD simulationsarepresentedforaplanar,tiltnanograinboundaryinterfacesubjectedtotensionandsheardeformations. TheproposedlistofISVsaccountsforgeometry,composition,defectdensity,anddamagewithintheinterfaceregion. Continuumcalculationsmotivatedbydiscretenanoscalecomputationsfacilitateamorecompletedescriptionofreal materialseparationprocesses. Ó 2003ElsevierLtd.Allrightsreserved. Keywords: Cohesive interface separation; Fracture; Multi-scale modeling; Internal state variables; Molecular dynamics; Atomistic simulations;Embedded-atommethod;Copper;Grainboundary 1. Introduction Formanynanostructuredmaterials,formation and propagation of interface or grain boundary cracks is the predominant mode of failure. The propagationofinterfacecracksmaybeaccompa- nied by dissipative mechanisms, such as disloca- tion motion and structural rearrangement, which play a powerful role in the deformation process. Ultimately, fracture is realized with the breaking of interatomic bonds and the formation of free surfaces. Atomic level defects, such as impurities and microvoids, influence fracture by magnifying the applied stress in localized regions around the imperfection,leadingtonon-uniformlydistributed bond ruptures. For metallic materials, such as * Correspondingauthor.Tel.:+1-404-894-5128;fax:+1-404- 894-0186. E-mail address: david.mcdowell@me.gatech.edu (D.L. McDowell). 0167-6636/$-seefrontmatter Ó 2003ElsevierLtd.Allrightsreserved. doi:10.1016/j.mechmat.2003.08.002 MechanicsofMaterials36(2004)825–847 www.elsevier.com/locate/mechmat