Chap 1- Plastic Deformation Dislocation
Transcript of 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
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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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