Chap 1- Plastic Deformation Dislocation

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    Chap. 1 Plastic Deformation-

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    Strength

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    Average Linear strain

    Stress Derived from

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    Stress is not uniform: the stress equation isan average stress

    Anisotropy between grains in a

    polycrystalline metal rules out uniformity ofstress

    Presence of more than one phase gives rise

    Nonuniformity occurs if the bar is notstraight , not centrally loaded, with the

    presence of stress raisers or stressconcentration.

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    Below the elastic limit, Hooks Law can beconsidered valid so that the average

    stress is proportional to the averagestrain:

    The constant E is the modulus of elasticity

    or Young Modulus

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    Tensile deformation of ductile metal

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    Ductile versus Brittle behaviour

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    Brittleness is not an absolute metalproperty

    Tungsten is brittle at room temperaturebut ductile at an elevated temp.

    ductile under hydrostatic compression

    A metal which is ductile in tension at RTcan become brittle in the presence of

    notches, low temperature, high rates ofloading or embrittling agents (hydrogen)

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    What constitutes failure?

    Structural members and machines can failfor perform their intended function in threegeneral ways:

    Excessive elastic deformation

    Fracture

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    Two general types of excessive elasticdeformation

    Excessive deflection

    Sudden deflection or buckling Yield occurs when the elastic limit of the material

    has been exceeded

    Permanent change of shapeIn a ductile metal, yielding rarely results in

    fracture under static loading at RT because the

    metal strain hardens as it deforms and anincreased stress is required to produce furtherdeformation

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    Failure by excessive plastic deformation is

    controlled by the yield strength of the metalfor a uniaxial loading condition

    For complex loading conditions, the YT is the

    significant parameter but use a suitablefailure criterion

    constant stress in a time dependant yieldingknown as CREEP

    Failure criterion under creep conditions is

    complicated by:

    Stress and strain are proportional

    Mechanical properties may change10

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    Metal fail by fracture in three ways

    Sudden Brittle fracture (DTBT)

    Fatigue (failure under cyclic loading)

    Delayed fracture (stress-rupture in

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    All engineering materials show avariability in mechanical properties

    Mechanical properties can be influencedby change in heat treatment or fabrication

    again failure from unpredictable cause

    Safe stress or Working stress

    For static applications, the working stressof ductile metals is based on the yieldstrength and for brittle materials on theultimate tensile strength

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    Concept of Stress and type of Stress

    Stress: force per unit area

    Surface forces: Hydrostatic pressure

    Centrifugal forces due to high speedrotation

    differential over the body

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    Stress at the point O on plane mmOf body 2

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    The total stress can be resolved in:

    Normal stress

    Shear stress

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    Concept of Strain and type of Strain

    Linear strain

    True strain

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    Elastic deformation may result in a changeof any initial angle between 2 lines

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    Shear strain: angular change

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    Example

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    ex: hardness vs structure of steel Properties depend on structure

    Structure, Processing, & Properties

    BHN)

    500

    600

    (d)

    30m(c)

    ex: structure vs cooling rate of steel Processing can change structure

    Hardness

    (

    Cooling Rate (C/s)100

    200

    300

    0.01 0.1 1 10 100 1000

    4m

    30m

    (a)

    30m

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    1. Pick Application Determine required Properties

    2. Properties Identify candidate Material(s)

    The Materials Selection Process

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    3. Material Identify required Processing

    Processing: changes structureand overall shape

    ex: casting, sintering, vapor deposition, dopingforming, joining, annealing.

    Material: structure, composition.

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    Relationship between atomic structure andplastic behavior of materials

    Much of the fundamental work on theplastic deformation of metals are performedwith sin le cr stal to eliminate the effect of

    Atomic Structure

    grain boundary and restrains imposed byneighboring grains and second phaseparticles

    Plastic deformation and dislocation theory

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    Crystal Geometry

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    Simple Cubic Structure

    Found in ionic crystals (NaCl) but not in metal

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    Metals have either BCC (body centered

    cubic), FCC (face centered cubic) crystalstructure or HCP (Hexagonal closed

    acked structure

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    FCC and HCP are closed packed structure

    74% of the volume is occupied by atoms

    n con ras or:

    BCC ( 68 % Volume occupied by atoms)

    Simple Cubic Cell (52%)

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    Plastic deformation is generally confined to thelow index planes, which have a higher densityof atoms than the high-index plane

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    Deformation by Slip

    The usual method of plastic deformation ofmetals is by sliding of block of crystal over

    one another along defined crystallographicplanes

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    Slip occurs in specific direction on certainplanes

    The slip plane is the plane of greatest

    closest packed direction within the slipplane

    Slip system is together the slip plane andthe slip direction

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    In HCP structure, there are 3 slip systems

    Limited number of slip systems is the

    raison for the extreme orientationdependence and low ductility in hcpcr stals

    In FCC structure, { 1 1 1} and are theclosed packed systems. 4 sets of { 1 1 1}planes each contains three

    directions. Therefore, 12 possible slipsystems

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    BCC is not a closed packed structure likeFCC or HCP

    There is no one plane of predominantatomic density

    {112}, {123} planes and always in theclosed packed which is common toeach of these planes

    Dislocation can readily move from onetype of plane to another by cross sipgiving rise to the irregular wavy slip bands

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    Certain metals show additional slipsystems with increased temperature

    Al deform on {110} plane at elevatedtemperature while in magnesium

    above 225 Celcius.

    In all cases, the slip direction remains the

    same when the slip planes changes withtemperature

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    Slip in perfect lattice

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    Shear stress and displacement can beestimated by:

    Hooks law at small value of displacement

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    With a = b (approximation)

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    Shear modulus for metals is in the range 20 to 150 Gpa

    Therefore this equation predict theoretical shear stress

    in the range (3 to 30 Gpa)

    Actual values of shear stress required to produce plasticdeformation in metal single crystals are in the range of

    0.5 to 10 MPa.

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    Even if more refined calculations are used

    to correct the sine wave assumptions, thevalue of the maximum shear stress cannotbe made equal to the observed shear

    stress

    times greater that the observed shearstrength, it must be concluded that amechanism other than bodily shearing of

    planes of atoms is responsible for slip.

    Dislocations provide such mechanism40

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    Slip begins when shearing stress in theslip plane and the slip direction reaches a

    threshold value called Critical resolvedshear stress

    Critical Resolved shear stress

    This value is really the single crystalequivalent of the yield stress of anordinary stress-strain curve

    The value of CRSS depends oncomposition and temperature

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    Example

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    Deformation of single crystals

    Since plastic flow occurs by slip on certainplanes along particular directions

    The increase in length of a specimen (subjecte

    depend on the orientation of the slip planes andirection with the specimen axis

    Plastic strain is measured by crystallographicglide strain

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    Important differences between metals

    Typically FCC metals exhibit greater strainhardening than HCP metals

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    D f ti b t i i

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    Deformation by twinning

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    Stacking Faults

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    Stacking Faults Atomic arrangement of {111} plane in fcc

    structure and {0001} in hcp could be achievedby stacking the closed-packed planes

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    The lower Stacking Fault Energy (SFE) thegreater the separation between partial

    dislocations and the wider the stackingfault

    SFE for stainless steel is very sensitive tochemical composition

    Stacking faults influence the plasticdeformation in several ways

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    Metals with wide stacking fault (low SFE):

    strain harden more rapidly

    twin easily on annealingShow a different temperature

    with narrow stacking faults

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    Lattice Defects

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    Lattice Defects

    Lattice defects help explain mechanicalproperties of materials such as:

    Yield strengthFracture strength

    Practically all mechanical properties arestructure-sensitive properties

    Defect or imperfection is used to describe

    any deviation from an orderly array orlattice point

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    Point Defect

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    Point Defect

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    In pure metals, small numbers of vacanciesare created by thermal activation and these

    are thermodynamically stable at temperaturegreater that absolute zero

    A equilibrium

    n is the number of vacant sites in N sites Es isthe energy required to move an atom from theinterior of a crystal to its surface

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    By rapidly quenching from close to themelting point it is possible to trap high

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    melting point, it is possible to trap highnumber of vacancies

    High number of vacancies that equilibriumcan be achieved by:

    Extensive lastic deformation (cold

    work)Bombardment with high energy nuclear

    particles

    When densities of vacancies become largeit is possible for them to cluster to form

    voids 66

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    If the defect extends through microscopicregions of the crystal it is called Lattice

    imperfections Line defects

    Surface or place defects

    Low angle boundaries and grainboundaries are surface defects

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    Important to realize that no metal iscompletely pure

    Most commercially pure materials

    In alloys, foreign atoms are added in 1 to50 % to obtain special mechanical

    properties

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    Dislocation

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    The most important defect

    Dislocation is a line defect responsible forthe phenomenon of Slip by which most

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    In the absence of an obstacle, a Disl.Moves freely in the application of a small

    force

    Strain hardening, yield point, creep,fatigue and brittle failure

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    Basic types of Disl. are:

    Edge dislocationScrew dislocation

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    Edge dislocation

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    The lattice is distorted in the region of thedislocation

    There is one more vertical rows of atoms

    Compressive stress above the slip plane

    Tensile stress below the slip plane

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    A pure dislocation can glide or slip in directionperpendicular to its edge

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    perpendicular to its edge

    May move vertically by a process known byclimb if diffusion of atoms or vacancies cantake place at an appreciable rate

    For the edge dislo. to move Upward, it isnecessary to remove the extra atom above thesymbol or to add a vacancy on this spot

    Conversely, if the dislo. moves down, atomswould have to be added

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    Disl. Width determines the force requiredto move the disl. through the crystal

    lattice. This force is called the Peierles-Nabarro force

    The Peierless stress is the stress requiredto move the disl.

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    Screw dislocation

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    Observation of dislocations

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    Experimental techniques for detectingdislocations utilize the strain field around thedislocation to increase its effective size

    Physical changes

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    Burgers vectors and dislocationloop

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    p

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    Stress field and energy of dislocation

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    Dislocation is surrounded by a stress field

    Approximation of the stress field bymathematical theory of elasticity for

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    For screw disl., no tensile or compressivenormal stress (no half plane)

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    Strain energy in edge disl.

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    Strain energy of a disl. Is about 8eV for

    each atom plane threaded by the disl

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    each atom plane threaded by the disl.

    Core energy in the order of .5 eV

    Large positive strain energy means thatt e ree energy o t e crysta s ncrease

    by the presence of the disl.

    Since nature tries to minimize the energy,

    crystals will try to lower its energy by theelimination of disl. Example: annealing

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    Forces on dislocations

    Wh t l f i li d th di l

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    When external force is applied, the disl.Move and produce slip

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    Forces between dislocation

    Di l f th i ith b

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    Disl. of the same sign with same bugersvector will repel each other

    Disl. of opposite sign with same burgersvector would eliminate the disl.

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    2 parallel screw dislo.

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    Force of attraction on a dislocation at the free

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    Force of attraction on a dislocation at the freesurface since escape from the surface wouldreduce its strain energy

    When disl. approach a surface with a coating

    of an elastically harder material, repulsiveforce is observed. This is the case in metalsurfaces generally coated with thin oxide films

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    Intersection of dislocations

    Intersection of disl creates a sharp break

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    Intersection of disl. creates a sharp breakin the dislo. Line

    Jog is a break is a sharp break in the disl.

    Kink is a sharp break in the disl. Whichremain in the slip plane

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    Dislocation Sources

    All metals contain disl as the result of the

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    All metals contain disl. as the result of thegrowth of the crystal from melt or vaporphase (exception whiskers)

    density of

    Heavy cold worked:

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    Emission from grain boundaries is an

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    Emission from grain boundaries is animportant source of disl. In the early stages ofplastic deformation

    vacancies to form a disk or prismatic loop

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    Multiplication of dislocations

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    Dislocations pile up

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