engr 151: materials of engineering midterm 2 review material · pdf filemidterm 2 review...
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2
POLYCRYSTALLINE MATERIALS
Grain Boundaries
regions between crystals
transition from lattice of
one region to that of the
other
slightly disordered
low density in grain
boundaries
high mobility
high diffusivity
high chemical reactivity Adapted from Fig. 4.7,
Callister & Rethwisch 8e.
• Vacancy atoms
• Interstitial atoms
• Substitutional atoms Point defects
TYPES OF IMPERFECTIONS
• Dislocations Line defects
• Grain Boundaries Area defects
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• Vacancies: -vacant atomic sites in a structure.
• Self-Interstitials: -"extra" atoms positioned between atomic sites.
POINT DEFECTS IN METALS
Vacancy
distortion
of planes
self- interstitial
distortion of planes
IMPURITIES IN SOLIDS
Alloys: impurity atoms have been added intentionally to impart certain characteristics
Sterling Silver – 92.5% silver, 7.5% copper (copper enhances mechanical strength without highly sacrificing corrosion resistance)
Solid Solution: adding impurity atoms to a material forms a solid solution
Solvent: element or compound present in greatest amount
Solute: element or compound in minor concentration
SOLID SOLUTIONS
Impurity atoms are randomly and uniformly dispersed within the solid
Substitutional: solute atoms replace host atoms
Interstitial
Solvent/Solute compatibility depends on:
Atomic size factor: must be within ±15%
Crystal Structure: crystal structure must be the same
Electronegativity: the greater contrast the better for creation of inter-metallic compound
Valences: a metal will have more of a tendency to dissolve another metal of higher valence than lower.
SPECIFICATION OF COMPOSITION
Weight/mass percent:
m1 = mass of element 1
Atom percent:
nm1= number of moles in specified mass of element 1
nm1 = m1 / A1
A1 = atomic weight of element 1
CONVERSIONS
Weight percent to atom percent:
Multiply weight percents by atomic weights:
Atom percent to weight percent:
DENSITY & ATOMIC WEIGHT COMPUTATIONS
Density for a 2-element metal:
Atomic weight for a two-metal element:
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IMPERFECTIONS IN SOLIDS
Linear Defects (Dislocations)
Are one-dimensional defects around which atoms are misaligned
Edge dislocation:
extra half-plane of atoms inserted in a crystal structure
b perpendicular () to dislocation line
Screw dislocation:
spiral planar ramp resulting from shear deformation
b parallel () to dislocation line
Burger’s vector, b: measure of lattice distortion
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EDGE, SCREW, AND MIXED DISLOCATIONS
Adapted from Fig. 4.5, Callister & Rethwisch 8e.
Edge
Screw
Mixed
BURGERS VECTOR
The magnitude and direction of the lattice
distortion associated with a dislocation
Perpendicular for edge
Parallel for screw
Neither for mixed
TENSION TESTS
Output is recorded as load or force versus
elongation
Engineering stress:
For problems keep in mind nature of cross-
section (e.g. rectangle, cylinder etc.)
COMPRESSION TESTS
Specimen contracts along the direction of the
stress
Use σ & ε equations to compute compressive
stress and strain (they will be negative)
ELASTIC DEFORMATION
The degree to which a structure deforms or
strains depends on the magnitude of stress (in
proportion):
PLASTIC DEFORMATION
Most metals have elastic deformation only to
strains of about 0.005
After this amount of strain, plastic deformation
occurs (non-recoverable)
Curvature will occur at the onset of plastic
deformation
PLASTIC DEFORMATION
From atomic perspective, plastic deformation corresponds to the breaking of atomic bonds and the reforming of bonds with neighbors
Yielding: stress level at which plastic deformation occurs
Mark point P (proportional limit) at initial departure from linearity
Yield Strength:
0.002 offset intersection with curve (σy)
PLASTIC DEFORMATION
From atomic perspective, plastic deformation corresponds to the breaking of atomic bonds and the reforming of bonds with neighbors
Yielding: stress level at which
plastic deformation occurs
Mark point P (proportional limit) at initial departure from linearity
Yield Strength:
0.002 offset intersection with curve (σy)
RESILIENCE
Capacity of a material to absorb
energy when it is deformed
elastically and then, to have energy
recovered
Modulus of resilience (Ur): the strain
per unit volume required to stress a
material from unloaded state to
yielding
Area under the engineering stress-
strain curve
RESILIENCE
Assuming linear stress-strain relationship (linear elastic region)
Resilient materials have high yield strengths and low moduli of
elasticity (used for spring applications)
Stress increases relatively slowly with strain
Can tolerate relatively high stress levels
TRUE STRESS
Must take into account the thinning of cross-sectional
area in plastic deformation
True stress: defined as the load F divided by the
instantaneous cross-sectional area Ai over which
deformation is occurring:
TRUE STRESS AND STRAIN
Only valid to the onset of necking
You can approximate the true stress-strain
curve from onset of plastic deformation to the
point at which necking begins:
K and n are constants that are material-
dependent.
STRENGTHENING BY GRAIN SIZE REDUCTION
Finer-grained material is harder and stronger
than coarse-grained material
Greater total grain boundary area to impede
dislocation motion
HALL-PETCH EQUATION
Yield strength vs. grain size:
σo , ky = constants for particular material
d: grain size
What does equation tell us?
STRAIN HARDENING
Occurs when a ductile metal becomes harder
and stronger as it is plastically deformed (work
hardening, cold working)
Percent Cold Work (degree of plastic
deformation) :
STRAIN HARDENING
Figure 6.17, pg 173
The metal with yield
strength σyo is plastically
deformed to point D
The stress is released,
then reapplied with a
new yield strength σyi.
The metal has become
stronger since σyi > σyo
UNDERSTANDING STRAIN HARDENING
Dislocation density in a metal increases with
deformation or cold work (dislocation
multiplication, formation of new dislocations)
Average distance of separation between
dislocations decreases
Strains between dislocations are repulsive
Motion of dislocation is hindered by the presence of
other dislocations
As strength and hardness increase ductility
decreases.
FATIGUE
Form of failure that occurs in structures
subjected to dynamic and fluctuating stresses.
Failure can occur at stress level considerably
lower than tensile of yield strength
Occurs after repeated stress/strain cycling
Single largest cause of failure in metals
CYCLIC STRESSES
Axial, flexural, or torsional
Three modes
Symmetrical
Asymmetrical
Random
Mean stress:
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