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Plastic deformation and creep in crystalline materials Chap. 11

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CreepPlastic DeformationMetallurgy

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  • Plastic deformation and

    creep in

    crystalline materialsChap. 11

  • Mechanical Properties of Materials

    Stiffness

    Strength

    ductility

    Toughness

    Resistance to elastic deformation

    Youngs modulus

    Resistance to plasticdeformation

    Yield stress

    Resistance to fracture Energy to fracture

    Ability to deform plastically

    Strain to fracture

  • Uniaxial Tensile Test

    Gaugelength

    specimen

  • Result of a uniaxial tensile test

    Slope = Youngs modulus (Y)

    UTSUltimate tensile strength

    yYield strength

    (Engineering stress)

    (engineering strain)

    f (strain to fracture)

    necking

    Area = Toughness

    elas

    tic

    plastic

    break

    Yield point

    STIFFNESS

    STRENGTH

    DUCTILITY

  • If there is a smooth transition from elastic to plastic region (no distinct yield point)

    then 0.2 % offset proof stress is used

  • 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 stress i

    T AP

    = Ai = instantaneous area

    True incremental strain L

    dLd T =

    0

    ln0

    LL

    LdLL

    LT == True strain

    Eqn. 11.3

    Eqn. 11.4

  • nTT K =

    K Strength coefficientn work hardening exponent

    Eqn. 11.5

  • What happens during plastic deformation?

    Externally, permanent shape change begins at y

    Internally, what happens?

  • What happens to crystal structure after plastic deformation?

    ?Plastic

    Deformation

  • Some Possible answers

    Remains the

    same

    Changes to

    another

    crystal

    structure

    Becomes random

    or

    amorphous

  • How Do We Decide?

    X-ray diffraction

    No change in crystal structure!

    No change in internal crystal structure but change in external shape!!

  • How does the microstructure of polycrystalchanges during plastic deformation?

    EXPERIMENT 5

    Comparison of undeformed Cu and deformed Cu

  • Slip Lines

    Before Deformation After Deformation

  • Slip lines in the microstructure of

    plastically deformed Cu

    Callister

  • Slip

  • Slip Planes, Slip Directions, Slip Systems

    Slip Plane: Crystallographic planes

    Slip Direction: Crystallographic direction

    Slip System: A combination of a slip plane and a slip direction

  • Slip Systems in Metallic Crystals

    Crystal Slip Slip Slip Plane Direction Systems

    FCC {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)

  • Why slip planes are usually close packed planes?

    Why slip directions are close-packed directions?

  • Slip Systems in FCC Crystal

    x

    y

    z(111)

  • Tensile vs Shear Stress

    Plastic deformation takes place by slip

    Slip requires shear stress

    Then, how does plastic deformation take place during a tensile test?

  • ND21

    : Applied tensile stress

    N: Slip plane normal

    D: Slip direction

    1: angle between and N

    2 =angle between and D

    Is there any shear stress on the slip plane in the slip direction due to the applied tensile stress?

  • FND21

    F

    Area=A = F/ A

    FD = F cos 2

    Area = As

    As = A cos 1

    S

    DRSS A

    F=

    1

    2

    cos

    cos

    A

    F=

    21 coscos AF

    =

    21 coscos =RSS

    Resolved Shear stress

  • FF

    F

    F

    No resolved shear stress on planes parallel or perpendicular to the stress axis

    cos 2 = 0 cos 1 = 0

  • Plastic deformation recap

    No change in crystal structure:sliptwinning

    Slip takes place on slip systems (plane + direction)Slip planes usually close-packed planesSlip directions usually close-packed direction

    Slip requires shear stressIn uniaxial tension there is a shear component of tensile stress on the slip plane in the slip direction:

    RESOLVED SHEAR STRESS

  • Extra ClassesThursdays 10-11

    MS 702

  • 21 coscos =RSSRSS

    21 coscos y

    CRSS

    CRITICAL RESOVED SHEAR STRESS

    21 coscos yCRSS =

    ND21

  • 21 coscos yCRSS =

    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 changes

    Schmids Law: CRSS is a material constant.

  • Anisotropy of Yield Stress

    21coscos

    crssy =

    Yield stress of a single crystal depends upon the direction of application of load

    cos 1 cos 2 is called the Schmid factor

  • RSS

    bb2

    coscos 1

    y

    CRSS

    Active slip system

    21 coscos yCRSS =

    aa

    2coscos 1

    Slip system with highest Schmidfactor is the active slip system

  • Magnitude of

    Critical Resolved Shear StressTheory (Frenkel 1926)

    Experiment

  • bd

    CRSS

    Shear stress

    b/2 b

    Potential energy

  • Fe (BCC)

    Cu (FCC)

    Zn (HCP)

    Theory

    (GPa)12

    7

    5

    Experiment

    (MPa)15

    0.5

    0.3

    Ratio

    Theory/Exp

    800

    14,000

    17,000

    Critical Resolved Shear Stress

  • ?

  • 19341934

    E. OrowanMichael Polanyi

    Geoffrey Ingram Taylor

    Solution

  • Solution

    Not a rigid body slip

    Part slip/ part unslipped

  • Slip Not-yet-slipped

    Boundary between slipped and unslipped parts

    on the slip plane

    Dislocation Line (One-Dimensional Defect)

  • Movement of an Edge Dislocation

    From

    W.D. Callister

    Materials Science

    and Engineering

  • Minor Answer Scripts

    10-11 am and 4-5 pm from Lab

    Extra ClassThursday 2nd. Nov. 10-11 am MS 702

    I never did a day's work in my life. It was all fun. Thomas A. Edison

  • Plastic Deformation Summary Plastic deformation slip

    Slip dislocations

    Plastic deformation requires movement of dislocations on the slip plane

  • Recipe for strength?

    Remove the dislocation

  • 700

    50

    Stress, MPa

    strainCu Whiskers tested in tension

    Fig. 11.6

  • The critical resolved shear stress to move the dislocation depends upon

    1.The width of dislocation2.The Burgers vector

  • WIDTH of a DISLOCATION

    Narrow dislocation Wide Dislocation

    Wide dislocations are easier to move than narrow dislocations

  • Width of a dislocation in crystal of different types of bonding:1. Covalent crystal:

    Strong and directional bond: narrow dislocation

    brittle2. Metallic crystal:

    Weak and non directional bondswide dislocation

    ductile3. Ionic Crystal

    Weak and non-directional bond but large bbrittle

    Eqn. 11.13

    Not in course

  • Effect of temperature on dislocation motionHigher temperature makes the dislocation motion easier

    WFe S

    i

    Al2O3

    Ni

    Cu

    18-8 ssYi

    e

    l

    d

    s

    t

    r

    e

    s

    s

    T/Tm0 0.7

    Fig. 11.8

    Eqn. 11.1411.15

    11.1611.17

    11.18

  • Recipe for strength

    Remove the dislocation: Possible but Impractical

    Alternative:Make the dislocation motion DIFFICULT

  • Strengthening Mechanisms Strain hardening

    Grain refinement

    Solid solution hardening

    Precipitation hardening

  • Movement of an Edge DislocationA unit slip takesplace only whenthe dislocation

    comes out of thecrystal

  • During plastic deformation dislocation density

    of a crystal should go down

    Experimental Result

    Dislocation Density of a crystal actually goes up

    Well-annealed crystal: 1010 m-2

    Lightly cold-worked: 1012 m-2

    Heavily cold-worked: 1016 m-2?

  • Dislocation Sources

    F.C. Frank and W.T. Read

    Symposium on

    Plastic Deformation of Crystalline SolidsPittsburgh, 1950

  • AB

    P

    Q

    b

    b

    b

  • http://zig.onera.fr/~douin/index.html

    b

  • http://zig.onera.fr/~douin/index.html

    bb

    Fig. 11.9

    Problem 11.11

  • Strain Hardening or Work hardening

    Strain,

    y

    y

  • During plastic deformation dislocation density increases.

    Dislocations are the cause of weakness of real crystals

    Thus 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

    ?

  • Dislocation against Dislocation

    A dislocation in the path of other dislocation can act as an obstacle to the motion

    of the latter

    Strain Hardening

  • ]110[21

    )111(

    ]110[21

    )111(

    )001(

    ]011[21

    ]110[21

    ]011[21

    Sessile dislocation in an FCC crystal

    Eqn. 11.20

    222

    222 aaa+Tm is the m.p. in K.

  • CREEP

  • Fig. 11.15

  • CreepDislocation climb

    Vacancy diffusion

    Cross-slip

    Grain boundary sliding

    Creep Mechanisms of crystalline materials

  • 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)]

  • Dislocation climb

    Edge dislocations piled up against an obstacle can climb to another slipplane and cause plastic deformation [as f(t), in response to stress]

    Rate controlling step is the diffusion of vacancies

  • Diffusional creep

    In response to the applied stress vacancies preferentially move from surfaces/interfaces (GB) of specimen transverse to the stress axis tosurfaces/interfaces parallel to the stress axis causing elongation

    This process like dislocation creep is controlled by the diffusion ofvacancies but diffusional does not require dislocations to operate

    Flow of vacancies

    Coble creep low T Due to GB diffusion

    Nabarro-Herring creep high T lattice diffusion

  • Grain boundary sliding

    At low temperatures the grain boundaries are stronger than the crystalinterior and impede the motion of dislocations

    Being a higher energy region, the grain boundaries melt before the crystalinterior

    Above the equicohesive temperature grain boundaries are weaker thangrain and slide past one another to cause plastic deformation

  • Creep Resistant Materials

    Higher operating temperatures gives better efficiency for a heat engine

    Creepresistance

    Dispersion hardening ThO2 dispersed Ni (~0.9 Tm)

    Solid solution strengthening

    High melting point E.g. Ceramics

    Single crystal / aligned (oriented) grains

  • Cost, fabrication ease, density etc. are other factors which determine the final choice of a material

    Commonly used materials Fe, Ni, Co base alloys Precipitation hardening (instead of dispersion hardening) is not a good

    method as particles coarsen (smaller particles dissolve and largerparticles grow interparticle separation )

    Ni-base superalloys have Ni3(Ti,Al) precipitates which form a lowenergy interface with the matrix low driving force for coarsening

    Cold work cannot be used for increasing creep resistance as recrystallization can occur which will produced strain free crystals

    Fine 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

  • No Dislocations

    Ultra Strong Crystals

    Whiskers

    Composite Materials

  • Various Crystal Defects

    Disloca-tions

    Grain Boundary

    G-P zone

    Substitu-tionalsolute

    Interstitial solute

    Stacking fault

    Vacancy (Diffusion)

  • Moral of the Story

    Strength depends upon defects

  • Microstructure

    Structural features observed under a microscope Phases and their distribution Grains and grain boundaries Twin boundaries Stacking faults Dislocations

  • Hierarchy of Structures

    engineering structure

    macrostructure

    microstructure

    crystal structure

    atomic structure

    nuclear structure

    Physics and chemistry

    Metallurgy and Materials Science

    Engineering: Civil, Mechanical, etc. 1m

    1mm

    1m1nm

    1A0

  • Real Moral of the Story

    Structure Sensitive vs

    Structure Insensitive Properties

  • 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(1613-1680)