Cohesive Zone Model ReviewMotivationleFM breaks down incases when(amongothersaThe process zone is tooarge relative to the cracklengthStress Intensity Factorslose meaning and value!Toughness"for a givenmaterial is no longer amaterial state valueThe process zone is toolarge relative to otherstructural dimensionsConditions for crack growthvery sensitive to BCs andgeometryLocal fields need to becomputedStress singularity at the crack tip is not . realisticDhruv Bhate, Purdue Universitywww.cfg.cornelledu/education/cee%20770%202002/lecture9NlfmCtoa.pdfFebruary 2006Non-Linear Fracture Mechanics(NLFMCrack Tip Opening Angle(CTOA)Fracture CriterionWhen Ctoa at a specified distance d from the crack tipeaches a critical value CTOA, the crack will growCTOACrack TipCTOD6,96:B,290.01 inch lDetermination of ctoac involves use of finite elements to find acritical value that fits results from testElastoplastic J-IntegralDhruv Bhate, Purdue UniversityFebruary 2006www.cfg.cornelledu/education/cee%20770%202002/lecture9nlfmCtoa.pdfWhy Cohesive Zone Modeling?Seems to mimic many process zone effects in many materialsIsolates fracture process model from surrounding continuumconstitutive modelThe fracture process model is simple: traction vs crackdisplacementA step towards micromechanical modeling of the process zoneEasy to implement in the FEm using interface elementsDhruv Bhate, Purdue UniversityFebruary 2006www.cfg.cornelledu/education/cee%20770%202002/lecture11NlfmcohesivepafHistorical DevelopmentSeminal Papers in Cohesive Zone ModelingDugdaleBarenblatt19601962crack length ay世.First to overcome singularity by dividing cracks into two parts: stress freecrack region and region loaded by cohesive(and finite)stressdugdale -cohesive stress =yield stress(only true for plane stress)Barenblatt- cohesive stress varies as per a prescribed distributionGoogleImagesDhruv Bhate, Purdue UniversityScheider I, " Cohesive model for crack propagation of structures with elastic-plastic material behavior", April 2001February 2006Historical DevelopmentLandmark PapersGurson1977Developed theory for void nucleation andgrowth to explain ductile ruptureEarly CZMs work within the constitutiveframework of Gurson's model to explainvoid nucleation and growthRose. smith Ferrante1981Showed for the first time that a universalcuzuu>咀+β·)x-pMbinding law existed and proposed itse Sm -4f 6d, 63extension to continuum scales0.6s,6口0.61 Ba◇A|3.From a fracture perspective, strictly validou-c≌oonly for atomistically sharp interfacesSCAL[ D SEPARATION,°SCALED CHANGE IN WIGNER SEITZ RADIUS, es=(3/4TnA)3Dhruv Bhate, Purdue UniversityFebruary2006All metal curves scaled by Thomas-Fermi screening lengthHistorical DevelopmentDuctile and brittle model pioneerserborg et alNeedleman19761987,1990. Applied CZM to brittle fracture(concrete)using FEM for the first timeTurning point in the fracture of brittleFirst to use CzM for crack propagation inmaterialsductile materialsProposed 2 traction separation laws( basedon Gurson' s models)PeterssonCarpinteri19811986Showed further use of CzM as a modelingtool for brittle fractureTvergaard Hutchinson1990.1992First ( to extend needleman, s work tounloadingDhruv Bhate, Purdue UniversityFebruary 2006Scheider I, Cohesive model for crack propagation of structures with elastic-plastic material behavior", april 2001Historical DevelopmentFatigue and Mixed Mode Fracturede andresNeedleman, xuOrtiz. PandolfiPerez. ortiz1987,199419991999Among first to use Czm to describeFirst (? to apply CZM to describemixed mode fracture and apply it in a3D environmentfatigue failure(aluminum shaftsAnd closer to homeRoe, SiegmundJin, Sun20032005Modified Needleman 's cohesive lawsArgue against simple extension of Modeto develop sophisticated irreversibleCZM for mixed mode fractureCZMs for fatigue failureApproach CzM primarily from the point ofview of removing stress singularity at thecrack tipDhruv Bhate, Purdue UniversityFebruary 2006Basic ConceptsWhere is the zone?Crack growthFar-Field Loading●Larger lnclusionsVaidsAa20-100pm.’:∵· Inclusionssmaller.Stress-FreeMacrocrackDamaging Process ZoneCementitious compositeMetals(Nucleation of voids atinclusion sites ahead of crack tip).While modeling, direction of crack growth must be known a prioriTreatment of micromechanics scaleallows definition of interface elementsalong grain boundaries that decohereto form cracksInterface elementsDhruv Bhate, Purdue UniversityFebruary 2006www.cfg.cornell.edu/education/cee%20770%202002/lecture9NlfmctOa.pdf