Size Effects in Plasticity: From Macro to Nano PDF
Preview Size Effects in Plasticity: From Macro to Nano
Size Effects in Plasticity: From Macro to Nano Size Effects in Plasticity: From Macro to Nano George Z. Voyiadjis Boyd Professor,Department of Civil and Environmental Engineering, Louisiana State University,Baton Rouge, LA,UnitedStates Mohammadreza Yaghoobi Research Faculty, Materials ScienceandEngineering,University of Michigan, Ann Arbor, MI, United States AcademicPressisanimprintofElsevier 125LondonWall,LondonEC2Y5AS,UnitedKingdom 525BStreet,Suite1650,SanDiego,CA92101,UnitedStates 50HampshireStreet,5thFloor,Cambridge,MA02139,UnitedStates TheBoulevard,LangfordLane,Kidlington,OxfordOX51GB,UnitedKingdom ©2019ElsevierInc.Allrightsreserved. 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LibraryofCongressCataloging-in-PublicationData AcatalogrecordforthisbookisavailablefromtheLibraryofCongress BritishLibraryCataloguing-in-PublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary ISBN:978-0-12-812236-5 ForinformationonallAcademicPresspublicationsvisitour websiteathttps://www.elsevier.com/books-and-journals Publisher:MatthewDeans AcquisitionEditor:BrianGuerin EditorialProjectManager:ThomasVanDerPloeg ProductionProjectManager:SelvarajRaviraj CoverDesigner:MatthewLimbert TypesetbySPiGlobal,India Dedication LovinglydedicatedtomywifeChristinawhoselove, understanding, and support made this possible. George Z. Voyiadjis Lovingly dedicated to Mohammad Ebrahim and Pouran. Mohammadreza Yaghoobi About the Authors Dr.VoyiadjisisaMemberoftheEuropeanAcademyofSciences,andForeign MemberofboththePolishAcademyofSciences,andtheNationalAcademyof EngineeringofKorea.GeorgeZ.VoyiadjisistheBoydProfessorattheLoui- sianaStateUniversity,intheDepartmentofCivilandEnvironmentalEngineer- ing. This is the highest professorial rank awarded by the Louisiana State UniversitySystem.HeisalsotheholderoftheFreeport-MacMoRanEndowed Chair in Engineering. He joined the faculty of Louisiana State University in 1980.HeiscurrentlytheChairoftheDepartmentofCivilandEnvironmental Engineering.HeholdsthispositionsinceFebruaryof2001.Healsoservedfrom 1992to1994astheActingAssociateDeanoftheGraduateSchool.Hecurrently alsoservessince2012astheDirectoroftheLouisianaStateUniversityCenter for GeoInformatics (LSU C4G; http://c4gnet.lsu.edu/c4g/). Voyiadjis’primaryresearchinterestisinplasticityanddamagemechanics of metals, metal matrix composites, polymers and ceramics with emphasis on the theoretical modeling, numerical simulation of material behavior, and experimental correlation. Research activities of particular interest encompass macro-mechanicalandmicro-mechanicalconstitutivemodeling,experimental procedures for quantification of crack densities, inelastic behavior, thermal effects,interfaces,damage,failure,fracture,impact,andnumerical modeling. Dr. Voyiadjis’ research has been performed on developing numerical models that aim at simulating the damage and dynamic failure response of advancedengineeringmaterialsandstructuresunderhigh-speedimpactloading conditions.Thisworkwillguidethedevelopmentofdesigncriteriaandfabri- cation processes of high performance materials and structures under severe loading conditions. Emphasis is placed on survivability area that aims to develop and field a contingency armor that is thin and lightweight, but with a very high level of anoverpressure protection system that provides low pen- etrationdepths.Theformationofcracksandvoidsintheadiabaticshearbands, which are the precursors tofracture, are mainlyinvestigated. Hehastwopatents,over332refereedjournalarticlesand19books(11as editor) to his credit. He gave over 400 presentations as plenary, keynote and invited speaker as well as other talks. Over sixty two graduate students (37 PhD) completed their degrees under his direction. He has also supervised numerous postdoctoral associates. Voyiadjis has been extremely successful in securing more than $30.0 million in research funds as a principal xi xii AbouttheAuthors investigator/investigator from the National Science Foundation, the Depart- mentofDefense,theAirForceOfficeofScientificResearch,theDepartment ofTransportation,NationalOceanicandAtmosphericAdministration(NOAA), andmajor companies such as IBM andMartinMarietta. Affiliationsand Expertise Boyd Professor Department of Civil and EnvironmentalEngineering LouisianaState University BatonRouge, LA, United States MohammadrezaYaghoobiisaresearchfacultyintheMaterialScienceand EngineeringDepartmentatUniversityofMichigan,AnnArbor.Hisprimary research interest is in multiscale computational plasticity and damage mechanics of crystalline materials, composites, and ceramics with emphasis on the theoretical modeling, numerical simulation of material behavior, and experimental correlation. Research activities of particular interest include modeling at different length scales including atomistic simulation, crystal plasticityfiniteelementmethod,andlocalandnonlocalcontinuumplasticity. Central to his research is serving as a lead developer of PRISMS-Plasticity software (http://www.prisms-center.org), which is an open-source parallel 3-D crystal plasticity and continuum plasticity finite element code (https:// github.com/prisms-center/plasticity/). Affiliationsand Expertise Research Faculty Materials Science and Engineering Department Universityof Michigan Ann Arbor,MI, United States Acknowledgments The partial financial support provided by a grant from the National Science Foundation EPSCoR Consortium for Innovation in manufacturing and Mate- rials, CIMM (Grant Number #OIA-1541079) at Louisiana State University is gratefully acknowledged by the authors. The second author also wishes to acknowledge the partial support by the U.S.DepartmentofEnergy,OfficeofBasicEnergySciences,DivisionofMate- rials Sciences and Engineering under Award #DE-SC0008637 as part of the CenterforPredictiveIntegratedStructuralMaterialsScience(PRISMSCenter) at University ofMichigan. Finally,theauthorswanttothankReemAboZnemahandYooseobSongfor their help with proofreading the book. xiii Chapter 1 Introduction: Size effects in materials Inmaterialscience,sizeeffectsaredescribedasthevariationofmaterialprop- erties as the sample size changes. The size effects include various properties such as optical and Photocatalytic properties, thermal conductivity, Young’s Modulus, material strength, diffusion processes, electrical conductivity, and magneticproperties.Inthisbook,thesizedependencyofthematerialstrength isaddressedassizeeffects.Thesizeeffectsunderlyingmechanismsdependon thenatureoftheconsideredmaterial.Thegoverningmechanismsofsizeeffects in brittle materials, quasibrittle materials, and crystalline metals are different fromeachother.Inthecaseofbrittlematerials,thesizeeffectshaveastatistical nature. It may be considered to be originated from the random nature of the materialstrengththatcanbegenerallycapturedusingWeibullstatisticaltheory (Weibull,1939).Thebasicassumptionsofthetheory,whichwasproposedby Weibull (1939), are the structure failure occurs by failing any element of the structure, and the strength of the structure elements is a random function that canbedescribedbytheWeibulldistribution.TheWeibulltheorycansuccess- fullycapturethesizeeffectsinbrittlematerials.Inthecaseofquasibrittlemate- rials,however,thenatureofthesizeeffectsisdeterministicandnotstatistical anditisduetothestressredistributionaroundthecracks.Inthecaseofcrys- tallinemetallicstructures,thesourcesofsizeeffectsaremoreversatile.Thesize effects in crystalline metallic samples can be related to some internal length scales,suchasgrainsize,theaveragedistanceofsecondphaseparticlesorpre- cipitates, and dislocations mean free path. Finally, the external geometrical properties of the specimen such as the thin film thickness, pillar diameter, or indentation depthmay leadto size effects. 1.1 Brittle materials StudyingthesizeeffectsinstrengthhavebeeninitiatedduringtheRenaissance periodbyLeonardodaVinci(1500s)who stated thatthe shorterthe cord,the strongeritisforcordsofequalthicknesses(Williams,1957).Lateron,Galileo (1638)rejectedtheruleproposedbydaVinciandstatedthatreducingthecord SizeEffectsinPlasticity:FromMacrotoNano.https://doi.org/10.1016/B978-0-12-812236-5.00001-3 ©2019ElsevierInc.Allrightsreserved. 1 2 SizeEffectsinPlasticity:FromMacrotoNano lengthdoesnotchangethecordstrength(Williams,1957).Mariotte(1686)ini- tiated the statistical theory of size effects in which he stated that the length should not affect the rope strength unless the longer rope has some defects whichmakesthelongerropeweaker.Lateron,Young(1807)rejectedthisthe- ory using the deterministic point of view and related the wire strength to its crosssectionarea.Hestatedthatthewirestrengthdoesnotdependonitslength. Griffith(1921)observedthesizeeffectsduringthemechanicaltestingofglass fibers where their nominal strength increases from 42,300psi for the sample with diameter of 0.00542in. to 491,000psi for the diameter of 0.00013in. He related the observed size effects to the defects and flaws in materials. The underlying mechanism for size effects proposed by Griffith (1921) was similar tothe one originallystated by Mariotte (1686). Weibull (1939) made a greatcontribution to size effects research topic by introducing the Weibull distribution to capture the sample strength based on its size. After the statistical framework of Weibull (1939), other researchers have applied, studied, and improved the method (see e.g. Bazˇant, 2005). The Weibulldistributioncansuccessfullycapturethebrittlematerialsthatfailafter themacroscopiccrackinitiationwheretheirfractureprocesszoneisverysmall. Fig.1.1illustratestheWeibulltheoryofsizeeffectsusingasystemof1Dstruc- turalelements.TheWeibulltheorydescribesthestructureasasysteminwhich thespecimenfailsbyfailureofthefirstelement(Fig.1.1).Thefailureproba- bility of each structural element subjected to the uniaxial stress σ can be described asfollows (Weibull,1939): (cid:1) (cid:3) σ(cid:2)σ m fðσÞ¼ u , (1.1) σ 0 wheremistheWeibullmodulusandσ isascaleparameter.Theelementdoes 0 notfailforσ(cid:3)σ .Accordingly,thefailureprobabilityofastructurecomposed u ofn small componentsat nominal strength σ can bedescribed asfollows: N Yn 1(cid:2)P ðσ Þ¼ ½1(cid:2)fðσÞ(cid:4) (1.2) f N i i¼1 FIG.1.1 A1Dbarwith10elementseachhasafailureprobabilityoff(σ)definedaccordingtothe Weibulldistribution.ThefailureprobabilityofthestructureP(σ )isdescribedusingtheWeibull f N theorythatstatesthestrengthofthestructureisequaltothestrengthoftheweakestelement.
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