NPTEL Syllabus

Engineering Fracture Mechanics - Videocourse

COURSE OUTLINE

T h e course covers the basic aspects of Engineering Fracture Mechanics.Spectacular failures that triggered the birth of fracture mechanics, Modes ofloading, Classification as LEFM and EPFM, Crack growth and fracturemechanisms, Energy release rate, Resistance, Griffith Theory of fracture,Extension of Griffith Theory by Irwin and Orowan, R-Curve, Pop-in phenomena,Crack branching. Necessary and sufficient conditions for fracture, Stress andDisplacement fields in the very near and near-tip fields, Westergaard, Williamsand Generalised Westergaard solutions, Influence of the T-stress and higherorder terms, Role of photoelasticity on the development of stress field equations infracture mechanics, Equivalence between SIF and G, Various methods forevaluating Stress Intensity Factors, Modeling plastic zone at the crack-tip, Irwinand Dugdale models, Fracture toughness testing, Fedderson’s residual strengthdiagram, Paris law, J- integral, HRR field, Mixed-mode fracture, Crack arrestmethodologies.

COURSE ORGANISATION

Modules Title Lectures

Module - 1 Overview of Engineering Fracture Mechanics 7

Module - 2 Energy Release Rate 5

Module - 3 Review of Theory of Elasticity 2

Module - 4 Crack-tip Stress and Displacement Fields 9

Module - 5 Discussion Session - I 1

Module - 6 SIF’s, Plastic Zone Modeling, Fracture ToughnessTesting 9

Module - 7 Crack Initiation and Life Estimation 3

Module - 8 Advanced Topics 4

NPTELhttp://nptel.iitm.ac.in

MechanicalEngineering

Pre-requisites:

Strength ofMaterials

Theory of Elasticity(Desirable).

Additional Reading:

Articles from thejournals:

EngineeringFracture Mechanics

International Journalof Fracture

ExperimentalMechanics

Journal ofMechanics andPhysics of Solids

Journal of AppliedMechanics

Strain

Journal of StrainAnalysis forEngineeringAnalysis and

Design, Engineering

Module - 9 Discussion Session - II 1

Module - 1 Overview of Engineering Fracture Mechanics

Lecture Concepts Covered

1 - EFM Course Outline

List of chapters and the concepts that would becovered in the course. Review of tension test,bending and torsion. Method of handling combinedstresses, principal stresses. Definition of failure, yieldcriteria, buckling as a failure mode. Need for fatiguetest and focus on what data being collected.

2 - Spectacular Failures

Further details on Fatigue test, Review onconventional design methodologies. List ofspectacular failures. Discussion on Boston molassesfailure, Liberty ship failure, Ductile-brittle transitiontemperature and its relevance.

3 - Lessons fromSpectacular Failures

Comet disaster, Aloha Airline failure. Lessons fromspectacular failures. Fracture – Bane or boon?Common applications of fracture/fracture prevention,Brief introduction to photoelasticity, Photoelasticappreciation of severity of a crack.

4 - LEFM and EPFM

Historical development, Contributions of Inglis, Griffithand Irwin. Extremum cases of an elliptical hole,Various results of fracture in glass, Classification ofLEFM and EPFM – based on plastic deformation,materials and applications. Modes of Loading –Mode-I, Mode-II and Mode-III.

5 - Fracture Mechanicsis Holistic

New test for fracture mechanics, Crack-growthcurves, Residual strength diagram, Summary offracture parameters. Practical examples of fracture,Typical photoelastic fringes for Mode-I, Mode-II andMixed mode loadings.

6 - Fatigue CrackGrowth Model

Geometric features of photoelastic fringes observednear the crack-tip. Multiple radial cracks in annularplates – its engineering relevance. Books andreferences. Crack growth and fracture mechanisms.Shear-lip in necking. Fatigue crack growth model.Striations and Beachmarks.

7 - Crack Growth andFracture Mechanisms

Clarifications on fatigue crack growth model. Stresscorrosion cracking (SCC) – Active path dissolution,Hydrogen embrittlement, Film induced cleavage.Creep, Corrosion fatigue, Liquid metal embrittlement.

Failure Analysis etc.

Coordinators:

Prof. K. RameshDepartment of AppliedMechanicsIIT Madras

Fracture mechanisms – Brittle fracture, Ductilefracture.

Module - 2 Energy Release Rate

Lecture Concepts Covered

8 - Elastic Strain Energy

Surface energy, Elastic strain energy stored in termsof stress components, in terms of axial, torsion andbending loads for slender members. Strain energychange in the presence of a crack under constantloading and constant displacement.

9 - Fracture Strength byGriffith

Strain energy in the presence of a crack by relaxationanalogy, Fracture strength, Validation of Griffith’sapproach, Estimation of Theoretical strength basedon lattice properties, Size effect, Crack-size effect.

10 - Energy ReleaseRate

Definition of energy release rate (G) and Resistance(R) , G as a function of Potential energy by energybalance. Expression of G in terms of compliance,Design of constant G specimen, Evaluation of G fortwo examples.

11 - Utility of EnergyRelease Rate

Difficulties in Griffith’s theory, Necessary and sufficientconditions for fracture, Crack branching in brittlematerials, Irwin and Orowan extension of Griffth’stheory to ductile solids, R-curve in plane strain andp l a n e stress. Specimen specification for classexperiment.

12 - Pop-inPhenomenon

Need for energy release rate being non-linear, Pop-inphenomenon, Class experiment demonstrating theinfluence of crack configuration on fracture behavior,Review of Strength of Materials, Deformation of aplane section due to constant shear in a beam,Definition of a free surface and its utility.

Module - 3 Review of Theory of Elasticity

Lecture Concepts Covered

13 - Displacement andStress Formulations

Simply connected and multiply connected domains,Displacement and stress formulations, Compatibilityconditions, Plane stress and plane strain situations,Airy’s stress function, Semi-inverse method, Forms ofstress functions in Cartesian co-ordinates.

14 - Forms of Stress Solution to the problem of a beam under uniformly

Functions distributed loading, Forms of stress function in polarco-ordinates, List of problems that could be solved,Illustration of principle of superposition, Analyticfunctions.

Module - 4 Crack-tip Stress and Displacement Field Equations

Lecture Concepts Covered

15 - Airy’s StressFunction for Mode-I

Cauchy-Riemann conditions, Airy’s stress function forMode-I, Satisfaction of bi-harmonic equation,Boundary conditions.

16 - WestergaardSolution of Stress Field

for Mode-I

Westergaard stress function for Mode-I, Originshifting, Very-near tip stress field, Definition of SIF,Comparison of photoelastic fringes with Westergaardsolution, Irwin’s modification of Westergaard’ssolution, T-stress, Work of Tada, Paris and Irwin.

17 - Displacement Fieldfor Mode-I

Review of Westergaard and modified Westergaardstress field equations, Stress field near a bluntedcrack-tip by Creager and Paris, Displacement field inplane stress and plane strain in the form of stressfunctions as well as in terms of polar co-ordinates,Definition of COD.

18 - Relation betweenKI and GI

Evaluation of COD from displacement field referredwith crack centre as origin, Crack opens like anellipse, Evaluation o f G from displacement of crackfaces, Interrelationship between KI and GI by closingan incremental crack extension.

19 - Stress Field inMode-II

Westergaard solution for near-tip stress field inMode-II, Photoelastic fringes in Mode-II, Comparisonof fringes plotted from Westergaard’s solution,Discussion on influence of T-stress on fringe patternsin Mode-I, Mixed Mode (Mode-I+ Mode-II),Displacement formulation for Mode-III.

20 - GeneralisedWestergaard Approach

Stress and displacement field in Mode-III, Need forimprovement to Westergaard solution for Mode-I,Kolosov-Muskhelishvili approach, Forms of stressfunctions in complex potentials, ComprehensiveA i r y ’ s stress function for Mode-I, GeneralisedWestergaard equations.

21 - William’s EigenFunction Approach

Generalised Westergaard equations, Forms of Z andY, Series stress field, Variation of maximum shearalong crack axis, William’s eigen function approach,Boundary conditions, Characteristic equation,

Discussion on admissible roots.

22 - Multi-parameterStress Field Equations

Stress function Φ as a series solution, William’ssingular solution and six term series solution of stressfield, Airy’s stress function for GeneralisedWestergaard Mode-II situation, Series solution ofstress field by Atluri and Kobayashi, Photoelastic andholographic fringe patterns for Mode-I.

23 - Validation of Multi-parameter Field

Equations

Multi-parameter stress field equations, Equivalence ofthem, Photoelastic and holographic fringe patterns forMode-I and combination of Mode-I and Mode-II, Multi-parameter displacement field equations, Multi-parameter displacement fringe field, Evaluation of SIFfor various geometries.

Module - 5 Discussion Session - I

Lecture Concepts Covered

24 - DiscussionSession-I

A few questions from the course raised by thestudents were answered. The list of questions isavailable as a .pdf file from the Downloadable section.

Module - 6 SIF's, Modeling of Plastic Zone, Fracture Toughness Testing

Lecture Concepts Covered

25 - Evaluation of SIF forVarious Geometries

Evaluation of SIF from stress functions using themathematical definition: Crack faces loaded withconcentrated load, Symmetric load and asymmetricload, SIF for collinear cracks evenly spaced, SIF forfinite strips.

26 - SIF for EmbeddedCracks

Verification of class experiment on multiple cracks,SIF by method of superposition, SIF for embeddedcircular flaw, SIF for embedded elliptical flaw,Parametric representation, Extension of the result tonon-elliptical embedded flaws, Modeling of surfaceflaws.

28 - Modeling of PlasticDeformation

Empirical relations of Newman and Raju – continued,Triaxiality at the crack-tip – pictorial explanation,Selection of fracture toughness for various types ofcracks, Insights of SIF for various cracks, Principalstresses at the crack-tip, Triaxiality – mathematicaldefinition, Simplistic model to get plastic zone lengthand shape for Mode-I using Tresca and von Misesyield criteria.

29 - Irwin’s Model Approximate plastic zone shapes in plane strain andplane stress for Mode-I and Mode-II loadings, plasticzone shape in Mode-III, Accounting for redistributionof load, Irwin’s model, Plastic zone length in planestress and plane strain, Small scale yieldingapproximations, Motivation of Dugdale model.

30 - Dugdale Model Dugdale model, Experimental result of Hahn andRosenfield, Plastic zone lengths and correction tocrack lengths – summary, Plasticity corrected SIF,Variation of plastic zone shape over the thickness ofthe specimen, Slip planes in plane strain and planestress, Transition of plane strain to plane stress alongthe length of the specimen.

31 - FractureToughness Testing

Variation of plastic zone over the thickness, Slipplanes in plane strain and plane stress, Experimentalevidence, Minimum thickness for fracture toughnessspecimen based on plastic zone, Fracture testing –early attempts, Fracture toughness as a function ofspecimen thickness, Requirements of the test,Candidate fracture toughness, Compact tension andthree point bend specimens, Chevron notch –visualization exercise.

32 - Plane StrainFracture Toughness

Testing

Specimens for the test, Constraints on specimendimensions, Chevron notch, Fatigue pre-crackingrestrictions, Experimental procedure, Measurement ofload, Measurement and acceptance criteria of cracklength, Selection of specimen from stock, Someimportant standards and practices: E399-06, B 645-07, E 1820-99, and E 1823-96.

33 - Plane StressFracture Toughness

Testing

Material anisotropy in fracture toughness testing,Fracture toughness values for selected materials,Plane stress fracture toughness testing, Anti-bucklingguide, Influence of panel width, Stable fracturefollowed by catastrophic fracture, Residual strengthd i a g r a m , Apparent toughness, Feddersen’sapproach, Experimental validation, Conventionalfatigue test, Questions to be answered in fracturemechanics.

Module - 7 Crack Initiation and Life Estimation

Lecture Concepts Covered

34 - Paris Law andSigmoidal Curve

Lacuna of fatigue test, Crack growth curve, Paris law,Validation of Paris law, Threshold stress intensityfactor, Definition of stress ratio, Sigmoidal curve:Region I, Region II and Region III, Donahue Law,Forman Law, Complete Sigmoidal curve, Mean stressinfluence and environmental effects on crack growth

rate.

35 - Crack Closure Review of Paris law, Crack closure: Designer’sapproach, Empirical relations of ΔKeff, Current focus.Residual stress ahead of a crack in a cycle, Plasticityinduced crack closure, Plastic wake, Different crackclosure types: Phase deformation induced, Oxideinduced, Roughness induced. Influence of overloadon crack growth.

36 - Crack GrowthModels

Residual stress in a cycle, Influence of overload oncrack growth, Wheeler’s model, Issues on fatiguecrack growth calculations, NASGRO, AFGROW,Summary of empirical fatigue crack growth models,Crack initiation, Intrusion and extrusion, Evidence ofslip bands.

Module - 8 Advanced Topics

Lecture Concepts Covered

37 - J-Integral

Eshelby’s line integrals, J-integral, Path-integral, Analytical evaluation of J-

integral for the DCB specimen, Graphicalinterpretation of J, Importance of strain history inelasto-plastic analysis, Extension of NLEFM to EPFM,Proportional loading.

38 - HRR Field andCTOD

Review of elasto-plastic material behaviour, J asstress intensity parameter, Cherepanov-HRR field, J-Q approach, Limitation of HRR field, Work of Begleyand Landes, Application areas of EPFM, CTOD:Definition, Estimation of CTOD from: Irwin’s result;Dugdale’s work, J and CTOD, Interrelationshipbetween fracture parameters.

39 - FAD and MixedMode Fracture

Relationship between J and CTOD, COD designcurve, Failure Assessment Diagram (FAD): Motivation,Historical development, FAD curve definition,Definition of Kr and Lr. Mixed mode fracture: Self-similar crack growth, Crack growth direction in ModeII, Criteria based on energy release rate, Maximumtangential stress criterion, Calculation of crack growthangle, Condition for fracture instability.

40 - Crack Arrest andRepair Methodologies

Mixed-mode fracture continued, Strain energydensity criterion, Comparison of crack growth andcritical value of KII by MTS and SED, Experimentalwork of Wu, Empirical relations in mixed-modefracture, Crack arrest principle, Use of patches,Photoelastic demonstration of usefulness of a patch,Hole drilling to delay crack re-initiation, Self healing

polymers, Metallic stitching.

Module - 9 Discussion Session - II

Lecture Concepts Covered

41 - Discussion Session- II

A few questions raised by the students from thewhole course were discussed. The list of questions isavailable as a .pdf file from the Downloadable section.

Please Note The naming of each lecture indicates only the major thrust in thatlecture.Guideline to use the Lectures: Please note that these are lectures given in aregular class in which students were taking notes. They are not seminars - whereyou try to get the basic idea and one just listens to them may be take down someshort notes. The listeners are advised to take down their own notes from thelectures. If necessary use the pause option. The media player also allows one toeither increase the speed or decrease the speed of content delivery as well. Usethese features effectively to get the maximum benefit from the lectures.

References:

1. K. Ramesh, e-Book on Engineering Fracture Mechanics, IIT Madras, 2007.URL: http://apm.iitm.ac.in/smlab/kramesh/book_4.htm

2. Prashant Kumar, Elements of Fracture Mechanics, Tata McGraw Hill, NewDelhi, India, 2009.

3. K. R.Y. Simha, Fracture Mechanics for Modern Engineering Design,Universities Press (India) Limited, 2001

4. D. Broek, Elementary Engineering Fracture Mechanics, Kluwer AcademicPublishers, Dordrecht, 1986.

5. T.L. Anderson, Fracture Mechanics - Fundamentals and Applications, 3rdEdition, Taylor and Francis Group, 2005.

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