MIDTERM 2 REVIEW MATERIAL

ENGR 151: Materials of Engineering

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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:

DENSITY & ATOMIC WEIGHT COMPUTATIONS

DENSITY & ATOMIC WEIGHT COMPUTATIONS

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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

MECHANICAL PROPERTIES OF METALS

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.)

TENSION TESTS

Engineering Strain:

COMPRESSION TESTS

Specimen contracts along the direction of the

stress

Use σ & ε equations to compute compressive

stress and strain (they will be negative)

SHEAR AND TORSIONAL TESTS

Shear stress:

Shear strain:

ELASTIC DEFORMATION

The degree to which a structure deforms or

strains depends on the magnitude of stress (in

proportion):

ELASTIC DEFORMATION

ELASTIC PROPERTIES OF MATERIALS

ELASTIC PROPERTIES OF MATERIALS

ELASTIC PROPERTIES OF MATERIALS

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)

EXAMPLE PROBLEM 6.3

EXAMPLE PROBLEM 6.3 CONTD.

EXAMPLE PROBLEM 6.3 CONTD.

DUCTILITY

Percent Elongation:

Percent Reduction:

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.

EXAMPLE PROBLEMS

SLIP IN SINGLE CRYSTALS

EXAMPLE 7.1

EXAMPLE 7.1 – SOLUTION

EXAMPLE 7.1 – SOLUTION

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.

STRAIN HARDENING

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:

CYCLIC STRESSES

Range of stress:

Stress amplitude:

Stress ratio: