ME 350 Lecture 2 Chapter 2

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ME 350 Lecture 2 Chapter 2 3

• Macroscopic Structures of Matter
• When materials solidify from the molten state,
  they tend to close ranks and pack tightly,
  arranging themselves into one of two structures
• Crystalline
• Noncrystalline

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Crystalline Structure

• Structure in which atoms are located at regular
  and recurring positions in three dimensions
• - basic geometric grouping of
  atoms that is repeated
• Pattern may be replicated millions of times
  within a given crystal
• Characteristic structure of virtually all metals,
  as well as many ceramics and some polymers

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Three Crystal Structures in Metals

• Body-centered cubic (BCC)
• e.g. Chromium, Iron, Molybdenum, Tungsten
• Face centered cubic (FCC)
• e.g. Aluminum, Copper, Gold, Lead, Silver, Nickel
• Hexagonal close-packed (HCP)
• e.g. Magnesium, Titanium, Zinc

Figure 2.8 Three types of crystal structure in
metals.
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Imperfections (Defects) in Crystals

• Imperfections often arise due to inability of
  solidifying material to continue replication of
  unit cell, e.g., in
  metals
• Imperfections can also be introduced purposely
  e.g., addition of alloying ingredient in metal
• Types of defects
• Point defects
• Line defects
• Surface defects

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Point Defects

• Imperfections in crystal structure involving
  either a single atom or a few number of atoms

Figure 2.9 Point defects (a) vacancy, (b)
ion-pair vacancy, (c) interstitialcy, (d)
displaced ion (Frenkel Defect).
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Line Defects

• Connected group of point defects that forms a
  line in the lattice structure. Examples
• dislocation extra plane of atoms
• dislocation spiral within the
  lattice

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Surface Defects

• Imperfections that extend in two directions to
  form a boundary
• Examples
• External the of a crystalline
  object is an interruption in the lattice
  structure
• Internal are
  internal surface interruptions

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Elastic Strain

• When a crystal experiences a gradually
  increasing stress, it first deforms
• If force is removed lattice structure returns to
  its original shape

Figure 2.11 Deformation of a crystal structure
(a) original lattice (b) elastic deformation,
with no permanent change in positions of atoms.
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Plastic Strain

• If stress is higher than forces holding atoms in
  their lattice positions, a
  shape change occurs

Figure 2.11 Deformation of a crystal structure
(c) plastic deformation (slip), in which atoms in
the lattice are forced to move to new "homes.
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Effect of Dislocations on Strain

• In the series of diagrams, the movement of the
  dislocation allows deformation to occur under a
  stress than in a perfect lattice
  

Figure 2.12 Effect of dislocations in the
lattice structure under stress
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Slip on a Macroscopic Scale

• Slip occurs many times over throughout the metal
  when subjected to a deforming load, thus causing
  it to exhibit its macroscopic behavior in the
  stress-strain relationship
• Dislocations are a good-news-bad-news situation
• Good news in manufacturing the metal is easier
  to form
• Bad news in design the metal is not as strong
  as the designer would like
• HCP has the fewest slip directions (thus usually
  has ductility), then FCC, and BCC
  has the most.

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Twinning

• Type of plastic deformation in which atoms are
  shifted to form a mirror image of the crystal
  structure of the other side
• An important phenomena with metals
  e.g. Zn Mg
• When it occurs it occurs nearly instantaneously.
  when it is subjected to high strain
  rates will twin, but at moderate rates will
  deform by slip.

Figure 2.13 Twinning, involving the formation of
an atomic mirror image on the opposite side of
the twinning plane (a) before, and (b) after
twinning.
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Polycrystalline Nature of Metals

• A block of metal may contain millions of
  individual crystals, called
• Such a structure is called polycrystalline
• Each grain has its own unique lattice
  orientation but collectively, the grains are
  randomly oriented in the block

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Grains and Grain Boundaries in Metals

• As molten metal cools and begins to solidify,
  individual crystals nucleate at random positions
  and orientations throughout the liquid
• These crystals grow and finally interfere with
  each other, forming at their interface a surface
  defect - a
• are transition zones (not part of either
  crystal grain), perhaps only a few atoms thick
• Faster cooling promotes smaller grain sizes
• Smaller grain size generally means
  strength, hardness, and ductility
• Metals regions that are cool too fast can be
  not polycrystalline

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Noncrystalline (Amorphous) Structures

• Many materials are noncrystalline
• Water and air have noncrystalline structures
• A metal loses its crystalline structure when
  melted
• Important engineering materials have
  noncrystalline forms in their solid state
• Rubber

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Crystalline versus Noncrystalline

• Figure 2.14 (a) crystalline and (b)
  noncrystalline materials. The crystal structure
  is regular, repeating, and denser the
  noncrystalline structure is less tightly packed
  and random.

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Volumetric Effects
Tm Tg Amorphous
and Crystalline structures differ in both melting
and thermal expansion characteristics

• Figure 2.15 Characteristic change in volume for
  a pure metal (a crystalline structure), compared
  to the same volumetric changes in glass (a
  noncrystalline structure).

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Summary Characteristics of Metals

• structures in the solid state, almost
  without exception
• , or unit cells
• Properties high strength and hardness, high
  electrical and thermal conductivity
• metals are generally the most ductile,
  the least (also fewest slip planes), and
  has the most slip planes.

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Summary Ceramics Polymers

• Most ceramics have structures, while glass
  (SiO2) is
• Ceramic properties high hardness and stiffness,
  electrically insulating, refractory, and
  chemically inert
• Most polymers are amorphous, but can be a mixture
  of amorphous and crystalline
• Polymer properties low density, high electrical
  resistivity, and low thermal conductivity,
  strength and stiffness vary widely

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MECHANICAL PROPERTIES OF MATERIALS

• Chapter 3
• Stress-Strain Relationships
• Hardness
• Effect of Temperature on Properties
• Fluid Properties
• Viscoelastic Behavior of Polymers

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Stress-Strain Relationships

• Three types of static stresses to which materials
  can be subjected
• Tensile - tend to stretch the material
• Compressive - tend to squeeze it
• Shear - tend to cause adjacent portions of
  material to slide against each other
• Stress-strain curve - basic relationship that
  describes mechanical properties for all three
  types

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Tensile Test

• Most common test for studying stress-strain
  relationship, especially metals
• In the test, a force pulls the material,
  elongating it and reducing its diameter
• Figure 3.1 Tensile test (a) tensile force
  applied in (1) and (2) resulting elongation of
  material

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Tensile Test Sequence

• Figure 3.2 Example tensile test (1) no load
  (2) uniform elongation and reduction of
  cross-sectional area (3) continued elongation,
  maximum load reached (4) necking begins, load
  begins to decrease and (5) fracture. If pieces
  are put back together as in (6), final length an
  be measured.

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Stress Strain

• Stress defined as force divided by area

where ? stress, F applied force, and A
instantaneous cross-sectional area

• Strain defined at any point in the test as

where e strain L length at any point during
elongation and Lo original gage length
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Typical Stress-Strain Plot
Ultimate tensile strength (or TS)
(or yield point or
yield stress, or elastic limit)
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Elastic Region in Stress-Strain Curve

• Relationship between stress and strain is linear
• Material returns to its original length when
  stress is removed
• Law ?e E e
• where E
• E is a measure of the inherent of
  a material

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Problem 3.3 in Text p63

• A tensile test specimen has a gage length of 2.0
  in and an area 0.5 in2. During the test the
  specimen yields under a load of 32,000 lb. The
  corresponding gage length 2.0083 in. This is
  the 0.2 percent yield point. The maximum load
  60,000 lb is reached at a gage length 2.60 in.
  Determine (a) yield strength, (b) modulus of
  elasticity, and (c) tensile strength if the
  smallest cross-sectional area was 0.4 in2.
• (a)
• (b)
• (c)

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Ductility in Tensile Test

• Ability of a material to plastically strain
  without fracture
• Elongation EL measures
• Area reduction AR measures

where Lf specimen final length, Lo original
specimen length, Ao original specimen area, Af
final specimen area
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Problem 3.4 in Text p63

• In Problem 3.3, if the fracture occurred instead
  at a gage length of 2.92 in. (a) Determine the
  percent elongation. (b) If the specimen necked to
  an area 0.27 in2, determine the percent
  reduction in area.
• (a) EL
• (b) AR

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Conservation of Volume

• Before necking or barreling in an ideal test
• If Lf/L0 1.5 what does Af / A0 ?

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True Stress-Strain in Log-Log Plot
Flow Curve
where K strength coefficient n exponent
Experimentally, a higher value of n means that
the metal can be strained further before the
onset of necking
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Problem 3.7 in Text p64

• In a tensile test on a metal specimen, strain
  0.08 at a stress 265 MPa. When the stress 325
  MPa, the strain 0.27. Determine the strength
  coefficient and the strain-hardening exponent in
  the flow curve equation.
• (a)
• (b)

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Categories of Stress-Strain Relationship

• Perfectly (fractures rather than
  yields)
• Elastic and perfectly (Flow curve K
  and n heated metals can behave like
  this)
• Elastic and (K
  and n )

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Compression Test

• Applies a load that squeezes the ends of a
  cylindrical specimen between two platens

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Stress-Strain Curve in Compression

• Shape of plastic region is different from tensile
  test because cross section increases
• Instead of necking point ?
  wider in middle than top or bottom
• K, n, Y, and E values should be

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Shear Properties

• Application of stresses in opposite directions on
  either side of a thin element

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Shear Stress and Strain

• Shear stress defined as
• where F applied force and A area over which
  deflection occurs. And T applied torque, R
  radius of the tube, and t tube wall thickness
• Shear strain defined as
• where ? deflection element
• and b distance over which
• deflection occurs. And a the
• angular deflection, L the
• gauge length of the tube

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Torsion Stress-Strain Curve

• In the elastic region

where G For most materials, G ? 0.4E, where
E elastic modulus
In the plastic region,
where S coefficient For most materials S ?
0.7 TS (tensile strength) n strain hardening
exponent
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Problem 3.28 in Text p65

• In a torsion test, a torque of 5000 ft-lb is
  applied which causes an angular deflection 1
  on a thin-walled tubular specimen whose radius
  1.5 in, wall thickness 0.10 in, and gage length
  2.0 in. Determine (a) the shear stress, (b)
  shear strain, and (c) shear modulus, assuming the
  specimen had not yet yielded.
• (a)

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Problem 3.29 in Text p65

• In Problem 3.28, the specimen fails at a torque
  8000 ft-lb and an angular deflection 23.
  Calculate the shear strength of the metal.