Presentation on theme: "Plastic deformation and creep in crystalline materials"— Presentation transcript:
1Plastic deformation and creep in crystalline materials Chap. 11
2Mechanical Properties of Materials StiffnessResistance to elastic deformationYoung’s modulusStrengthResistance to plastic deformationYield stressToughnessResistance to fractureEnergy to fractureductilityAbility to deform plasticallyStrain to fracture
3Uniaxial Tensile Test (Experiment 6) Gauge lengthspecimen
4Result of a uniaxial tensile test STRENGTH (Engineering stress)neckingUltimate tensile strengthUTSYield pointplasticYield strengthybreakelasticArea = ToughnessSTIFFNESSSlope = Young’s modulus (Y)DUCTILITYf (strain to fracture) (engineering strain)
5If there is a smooth transition from elastic to plastic region (no distinct yield point) then 0.2 % offset proof stress is used
6Ai = instantaneous area During 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 stressAi = instantaneous areaEqn. 11.3True incremental strainTrue strainEqn. 11.4
7Eqn. 11.5K Strength coefficientn work hardening exponent
8What happens during plastic deformation? Externally, permanent shape change begins at syInternally, what happens?
9What happens to crystal structure after plastic deformation?
10Some Possible answers Becomes random Remains the Changes to or same anothercrystalstructureBecomes randomoramorphous
11How Do We Decide? X-ray diffraction No change in crystal structure! No change in internal crystal structure but change in external shape!!
12How does the microstructure of polycrystal changes during plastic deformation? EXPERIMENT 5Comparison of undeformed Cu and deformed Cu
13Before Deformation After Deformation Slip LinesBefore Deformation After Deformation
14Slip lines in the microstructure of plastically deformed Cu CallisterSlip lines in the microstructure of plastically deformed CuExperiment 5
20Tensile vs Shear Stress Plastic deformation takes place by slipSlip requires shear stressThen, how does plastic deformation take place during a tensile test?
21s s s: Applied tensile stress N: Slip plane normal D: Slip direction N 1D2F1: 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?s
22F F Resolved Shear stress = F/ A Area=A FD = F cos 2 N As = A cos 1f1D2Area = AsF
23FFNo resolved shear stress on planes parallel or perpendicular to the stress axisFFcos 2 = 0cos 1 = 0
24Plastic deformation recap No 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 STRESS
26Schmid’s Law: CRSS is a material constant. If we change the direction of stress with respect to theslip plane and the slip direction cos 1 cos 2 will change.To maintain the equality which of the following changes takes place?1. CRSS changes.2. y changesSchmid’s Law: CRSS is a material constant.
27Anisotropy of Yield Stress Yield stress of a single crystal depends upon the direction of application of loadcos 1 cos 2 is called the Schmid factor
28Active slip systemSlip system with highest Schmid factor is the active slip system
29Magnitude of Critical Resolved Shear Stress Theory (Frenkel 1926)Experiment
49Movement of an Edge Dislocation A unit slip takes place only when the dislocation comes out of the crystal
50During plastic deformation dislocation density of a crystal should go down Experimental ResultDislocation Density of a crystal actually goes upWell-annealed crystal: 1010 m-2?Lightly cold-worked: 1012 m-2Heavily cold-worked: 1016 m-2
51Dislocation SourcesF.C. Frank and W.T. ReadSymposium on Plastic Deformation of Crystalline Solids Pittsburgh, 1950
55Strain Hardening or Work hardening sysyStress, s=Force/Initial AreaStrain, e=change in length/initial lengthStrength ParametersYield Stress, sY= Stress at yield pointUltimate tensile strength, sUTS= stress at maximumDuctility Parameter% Elongation= 100 X Strain at fracture, efStrain, e
56? During 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?
57Dislocation against Dislocation Strain HardeningDislocation against DislocationA dislocation in the path of other dislocation can act as an obstacle to the motion of the latter
58Sessile dislocation in an FCC crystal ]110[2Energetically favourable reaction]1[2(001) not a favourable slip plane (CRSS is high).The dislocation immobile or sessile.Eqn]1[2)1(]110[2)111()001(Fig
59Sessile dislocation a barrier to other dislocations creating a dislocation pile-up Sessile dislocation (barrier))1()111(FigPiled up dislocations
60Empirical relation for strain hardening or work hardening Eq Is the shear stress to move a dislocation in a crystal with dislocation density o and A : empirical constants
642-D Defect: Grain Boundaries Single Crystal PolycrystalGrains of different orientationsseparated by grain boundariesNo Grain Boundaries
65Discontinuity of a slip plane across a grain boundary Disloca-tionGrain Boundary
66Grain Boundary Strengthening Slip plane discontinuity at grain boundaryA dislocation cannot glide across a grain boundaryHigher stresses required for deformationFiner the grains, greater the strength
69I 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:The 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.Science 5 April 2002: Vol. 296 no pp POLYCRYSTALLINE MATERIALSGrain Boundaries and Dislocations
70Solid Solutions Mixture of two or more metals Solute atoms: a zero dimensional defect or a point defectTwo types:1. Interstitial solid solution2. Substitutional solid solution
71Interstitial Solid Solution Distortion caused by alarge interstitial atomPerfect Crystal
72Substitutional Solid Solution Small solute atomLarge solute atomSolute atom: a zero-dimensional point defect
73Solid Solution Strengthening Strains in the surrounding crystalSoluteatomsObstacle to dislocation motionStrong crystalAlloys stronger than pure metals
74Figure: Anandh Subramaniam 200Sn (1.51)Be (1.12)Matrix = Cu (r = 1.28 Å)150Si (1.18)Al (1.43)(Values in parenthesis are atomic radius values in Å)100Ni (1.25)Zn (1.31)5010203040Solute Concentration (Atom %) →Figure: Anandh SubramaniamFig 11.13
77Alfred Wilm’s Laboratory 1906-1909 Steels harden by quenchingWhy not harden Al alloys also by quenching?
78Eureka ! Hardness has Increased !! TWilm’s Plan for hardening Al-4%Cu alloyHold550ºCHeatQuenchCheck hardnesstimeSorry! No increase in hardness.Eureka ! Hardness has Increased !!One of the greatest technological achievements of 20th century
79Hardness increases as a function of time: AGE HARDENING Property = f (microstructure)Wilm checked the microstructure of his age-hardened alloys.Result: NO CHANGE in the microstructure !!
80Hardness initially increases: age hardening Peak hardnessHardnessOveragingAs- quenched hardnesstimeHardness initially increases: age hardeningAttains a peak valueDecreases subsequently: Overaging
81: solid solution of Cu in FCC Al + Tsolvus: solid solution of Cu in FCC Al+: intermetallic compound CuAl24supersaturatedsaturated Precipitation of in FCCFCCTetragonal4 wt%Cu0.5 wt%Cu54 wt%Cu
82TTT diagram of precipitation of in Stable Tsolvus startunstable finsh+As-quenched AgingA fine distribution of precipitates in matrix causes hardeningCompletion of precipitation corresponds to peak hardness
83-grainsAs quenched-grains + AgedPeak agedDense distribution of fine overagedSparse distribution of coarse Driving force for coarsening/ interfacial energy
84Aging temperaturehardness100ºC20ºC180ºCFig. 9.15Aging time0.1110100(days)Peak hardness is less at higher aging temperaturePeak hardness is obtained in shorter time at higher aging temperature
86Hardness increases as as a function of time As-quenched hardnessNo change in microstructure - Wilm!
87Numerous fine precipitates form with time Not visible in optical micrographX-Ray Diffraction (XRD) Transmission Electron Microscopy (TEM)Guinier-Preston Zones, 1938
88“It seems justifiable at the moment to conclude that the process of age hardening in this alloys is associated with the segregation of copper atoms on the (100) planes of the crystal as suggested by C.H. Desch in The Chemistry of Solids, 1934”Preston, 1938, “The Diffraction of X-rays by Age-Hardening Aluminium Copper Alloys
89Precipitation Hardening Precipitates are obstacles to the motion of dislocationSolute atoms PebblesPrecipitates bouldersCake with nutsAge-hardening = Precipitation hardening
90Dislocation-precipitate interaction Dislocation canEither cut through the precipitate particles (small precipitate)Or they can bypass the precipitates
92Dislocation bypassing the precipitate Fig b and d
93Obstacles to the movement of dislocations cause strengthening Movement of one-dimensional defects called dislocations causes plastic deformationObstacles to the movement of dislocations cause strengthening
105Creep Mechanisms of crystalline materials Cross-slipDislocation climbCreepVacancy diffusionGrain boundary sliding
106b 1 2 3 Slip plane 2 Slip plane 1 Cross-slip In the low temperature of creep → screw dislocations can cross-slip (by thermal activation) and can give rise to plastic strain [as f(t)]123bSlip plane 1Slip plane 2
107Dislocation climbEdge dislocations piled up against an obstacle can climb to another slip plane and cause plastic deformation [as f(t), in response to stress]Rate controlling step is the diffusion of vacancies
108Nabarro-Herring creep → high T → lattice diffusion Diffusional creepCoble creep → low T → Due to GB diffusionIn response to the applied stress vacancies preferentially move from surfaces/interfaces (GB) of specimen transverse to the stress axis to surfaces/interfaces parallel to the stress axis→ causing elongationThis process like dislocation creep is controlled by the diffusion of vacancies → but diffusional does not require dislocations to operateFlow of vacancies
109Grain boundary sliding At low temperatures the grain boundaries are ‘stronger’ than the crystal interior and impede the motion of dislocationsBeing a higher energy region, the grain boundaries melt before the crystal interiorAbove the equicohesive temperature grain boundaries are weaker than grain and slide past one another to cause plastic deformation
110Single crystal turbine blade Single crystal blade: best creep resistancePigtail: a helical channel which gradually eliminates most columnar grainsStarter: initiates columnar grains as in Directional Solidification (DS)
111Coarser grains. -> Less grain boundaries Coarser grains -> Less grain boundaries -> Better for creep applicationSingle Crystal -> No grain boundaries -> Best for creep applicationNanocrystalline materials > not good for creep applications!
112Improvements due to blade manufacturing technique: Show turbine blades
113Improvements due to engineering design: Blade cooling Engineering Materials 1: Ashby and Jones
114Thermal Barrier Coating (TBC) NiCrAlY or NiCoCrAlYCeramic top coat:Yittria stabilized Zirconia (YSZ)Low thermal conductivityHigh thermal expansionHigh M.PReduction in surface temp oCOperating temp > M.P. (~1300 oC)
115Creep Resistant Materials Higher operating temperatures gives better efficiency for a heat engineHigh melting point → E.g. CeramicsDispersion hardening → ThO2 dispersed Ni (~0.9 Tm)Creep resistanceSolid solution strengtheningSingle crystal / aligned (oriented) grains
116Cost, fabrication ease, density etc. are other factors which determine Cost, fabrication ease, density etc. are other factors which determine the final choice of a materialCommonly used materials → Fe, Ni, Co base alloysPrecipitation hardening (instead of dispersion hardening) is not a good method as particles coarsen (smaller particles dissolve and larger particles grow interparticle separation ↑)Ni-base superalloys have Ni3(Ti,Al) precipitates which form a low energy interface with the matrix low driving force for coarseningCold work cannot be used for increasing creep resistance as recrystallization can occur which will produced strain free crystalsFine grain size is not desirable for creep resistance → grain boundary sliding can cause creep elongation / cavitation ► Single crystals (single crystal Ti turbine blades in gas turbine engine have been used) ► Aligned / oriented polycrystals
119Strength depends upon defects Moral of the StoryStrength depends upon defects
120Microstructure Structural features observed under a microscope Phases and their distributionGrains and grain boundariesTwin boundariesStacking faultsDislocations
121Hierarchy of Structures Physics and chemistry1A01nmMetallurgy and Materials Science1mm1mmEngineering: Civil, Mechanical, etc.1m
122Properties depend upon microstructure Real Moral of the StoryProperties depend upon microstructureStructure Sensitive vs Structure Insensitive Properties
123Duc Franccois de la Rochefoucald (1613-1680) For true understanding comprehension of detail is imperative. Since such detail is well nigh infinite our knowledge is always superficial and imperfect.Duc Franccois de la Rochefoucald ( )