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Plastic deformation and creep in crystalline materials Chap. 11

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Plastic deformation and creep in crystalline materials Chap. 11. Mechanical Properties of Materials. Stiffness. Resistance to elastic deformation . Young’s modulus. Strength. Resistance to plastic deformation. Yield stress. Toughness. Resistance to fracture. Energy to fracture. - PowerPoint PPT Presentation

Text of Plastic deformation and creep in crystalline materials Chap. 11

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Plastic deformation and creep in crystalline materialsChap. 111Mechanical Properties of MaterialsStiffnessStrengthductilityToughnessResistance to elastic deformation Youngs modulusResistance to plastic deformationYield stressResistance to fractureEnergy to fractureAbility to deform plasticallyStrain to fracture2

Uniaxial Tensile Test (Experiment 6)Gaugelengthspecimen3Result of a uniaxial tensile testSlope = Youngs modulus (Y)UTSUltimate tensile strengthyYield strength (Engineering stress) (engineering strain)f (strain to fracture)neckingArea = ToughnesselasticplasticbreakYield pointSTIFFNESSSTRENGTHDUCTILITY4

If there is a smooth transition from elastic to plastic region (no distinct yield point) then 0.2 % offset proof stress is used5During uniaxial tensile test the length of the specimen is continually increasing and the cross-sectional area is decreasing.True stress Engineering stress (=F/A0)True strain Engineering strain (=L/L0)True stress

Ai = instantaneous areaTrue incremental strain

True strainEqn. 11.3Eqn. 11.46

KStrength coefficientnwork hardening exponentEqn. 11.5


What happens during plastic deformation?Externally, permanent shape change begins at syInternally, what happens?8What happens to crystal structure after plastic deformation??PlasticDeformation9Some Possible answersRemains thesameChanges to another crystalstructureBecomes randomoramorphous10How Do We Decide?X-ray diffractionNo change in crystal structure!No change in internal crystal structure but change in external shape!!11How does the microstructure of polycrystal changes during plastic deformation?EXPERIMENT 5Comparison of undeformed Cu and deformed Cu12Slip LinesBefore Deformation After Deformation13

Slip lines in the microstructure of plastically deformed CuCallisterExperiment 514 Slip15Slip Planes, Slip Directions, Slip SystemsSlip Plane: Crystallographic planesSlip Direction: Crystallographic directionSlip System: A combination of a slip plane and a slip direction16Slip Systems in Metallic CrystalsCrystalSlipSlipSlip PlaneDirectionSystemsFCC{111}4x3=12(4 planes)(3 per plane)BCC{110}6x2=12(6 planes)(2 per plane)HCP{001}3x1=3(1 plane)(3 per plane)17Why slip planes are usually close packed planes?Why slip directions are close-packed directions?18Slip Systems in FCC Crystalxyz(111)19Tensile vs Shear StressPlastic deformation takes place by slip

Slip requires shear stress

Then, how does plastic deformation take place during a tensile test?20sND21ss: Applied tensile stressN: Slip plane normalD: Slip directionF1: angle between s and NF2 =angle between s and DIs there any shear stress on the slip plane in the slip direction due to the applied tensile stress?21FND2f1FArea=A = F/ AFD = F cos 2Area = AsAs = A cos 1

Resolved Shear stress22FFFFNo resolved shear stress on planes parallel or perpendicular to the stress axiscos 2 = 0cos 1 = 023Plastic deformation recapNo change in crystal structure:sliptwinningSlip takes place on slip systems (plane + direction)Slip planes usually close-packed planesSlip directions usually close-packed directionSlip requires shear stressIn uniaxial tension there is a shear component of tensile stress on the slip plane in the slip direction:RESOLVED SHEAR STRESS24



If we change the direction of stress with respect to the slip plane and the slip direction cos 1 cos 2 will change. 1. CRSS changes.To maintain the equality which of the following changes takes place?2. y changesSchmids Law: CRSS is a material constant.26Anisotropy of Yield Stress

Yield stress of a single crystal depends upon the direction of application of loadcos 1 cos 2 is called the Schmid factor27

Active slip system

Slip system with highest Schmid factor is the active slip system28Magnitude of Critical Resolved Shear StressTheory (Frenkel 1926)Experiment29bd CRSSShear stress b/2bPotential energy30Fe (BCC)

Cu (FCC)

Zn (HCP)Theory(GPa)12






17,000Critical Resolved Shear Stress31?321934E. Orowan Michael Polanyi Geoffrey Ingram TaylorSolution33 SolutionNot a rigid body slip

Part slip/ part unslipped

34SlipNot-yet-slippedBoundary between slipped and unslipped parts on the slip planeDislocation Line (One-Dimensional Defect)35






Movement of an Edge DislocationFromW.D. CallisterMaterials Scienceand Engineering41

42Plastic Deformation SummaryPlastic deformation slip

Slip dislocations

Plastic deformation requires movement of dislocations on the slip plane43Recipe for strength?Remove the dislocation4470050Stress, MPastrainCu Whiskers tested in tensionFig. 11.645Effect of temperature on dislocation motionHigher temperature makes the dislocation motion easierWFeSiAl2O3NiCu18-8 ssYield stressT/Tm00.7Fig. 11.8Eqn. 11.1411.1511.1611.1711.1846Recipe for strengthRemove the dislocation: Possible but ImpracticalAlternative:Make the dislocation motion DIFFICULT47Strengthening MechanismsStrain hardening

Grain refinement

Solid solution hardening

Precipitation hardening


Movement of an Edge DislocationA unit slip takesplace only whenthe dislocationcomes out of thecrystal49During plastic deformation dislocation density of a crystal should go downExperimental ResultDislocation Density of a crystal actually goes upWell-annealed crystal: 1010 m-2Lightly cold-worked: 1012 m-2Heavily cold-worked: 1016 m-2?50Dislocation SourcesF.C. Frank and W.T. ReadSymposium onPlastic Deformation of Crystalline SolidsPittsburgh, 195051ABPQbbb52 11.9Problem 11.1154Strain Hardening or Work hardeningStrain, esysy55Stress, s=Force/Initial AreaStrain, e=change in length/initial lengthStrength Parameters Yield Stress, sY= Stress at yield point Ultimate tensile strength, sUTS= stress at maximumDuctility Parameter % Elongation= 100 X Strain at fracture, efDuring plastic deformation dislocation density increases.Dislocations are the cause of weakness of real crystalsThus as a result of plastic deformation the crystal should weaken.However, plastic deformation increases the yield strength of the crystal: strain hardening or work hardening?56Dislocation against DislocationA dislocation in the path of other dislocation can act as an obstacle to the motion of the latterStrain Hardening57]110[21)111(]110[21)111()001(


Sessile dislocation in an FCC crystalEqn. 11.20

]110[21(001) not a favourable slip plane (CRSS is high). The dislocation immobile or sessile.Energetically favourable reactionFig. 11.1058)111()111(Sessile dislocation a barrier to other dislocations creating a dislocation pile-upPiled up dislocationsSessile dislocation (barrier)Fig. 11.1059Empirical relation for strain hardening or work hardening

Is the shear stress to move a dislocation in a crystal with dislocation density o and A : empirical constantsEq. 11.2160

Fig. 11.1161Dislocation MotionPlastic DeformationDifficult Dislocation MotionDifficult Plastic DeformationStrong CrystalEasy Dislocation MotionEasy Plastic DeformationWeak Crystal62Grain Boundary Grain1Grain 2Grain boundary632-D Defect: Grain BoundariesSingle Crystal PolycrystalNo Grain BoundariesGrains of different orientations separated by grain boundaries64Discontinuity of a slip plane across a grain boundaryDisloca-tionSlip planeGrain Boundary65Grain Boundary StrengtheningSlip plane discontinuity at grain boundaryA dislocation cannot glide across a grain boundaryHigher stresses required for deformationFiner the grains, greater the strength66Coarse GrainsFine Grains67Grain Size StrengtheningHall-Petch Relation

sy: yield strengthD: average grain diameters0, k: constants 68Science 5 April 2002: Vol. 296 no. 5565 pp. 66-67 POLYCRYSTALLINE MATERIALSGrain Boundaries and DislocationsThe hardness of coarse-grained materials is inversely proportional to the square root of the grain size. But as Van Swygenhoven explains in her Perspective, at nanometer scale grain sizes this relation no longer holds. Atomistic simulations are providing key insights into the structural and mechanical properties of nanocrystalline metals, shedding light on the distinct mechanism by which these materials deform. I did not mention this in the class but in the interest of recent developments of nanotechnology I feel you should at least be aware of this:Mixture of two or more metalsSolute atoms: a zero dimensional defect or a point defectTwo types:1. Interstitial solid solution2. Substitutional solid solutionSolid Solutions70Interstitial Solid SolutionPerfect CrystalDistortion caused by a large interstitial atom71Substitutional Solid SolutionSmall solute atomLarge solute atom Solute atom: a zero-dimensional point defect72Solid Solution StrengtheningStrains in the surrounding crystalSolute atomsObstacle to dislocationmotionStrongcrystalAlloys stronger than pure metals73Fig 11.13Solute Concentration (Atom %) 50100150102030402000Matrix = Cu (r = 1.28 )Be (1.12)Si (1.18)Sn (1.51)Ni (1.25)Zn (1.31)Al (1.43)(Values in parenthesis are atomic radius values in )Figure: Anandh Subramaniam74

Airbus A380 to be launched on October 200775

A shop inside Airbus A38076Alfred Wilms Laboratory 1906-1909Steels harden by quenchingWhy not harden Al alloys also by quenching?

77timeWilms Plan for hardening Al-4%Cu alloySorry! No increase in hardness.550CTHeatQuenchHoldCheck hardnessEureka ! Hardness has

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