Title: ME 350 Lecture 2 Chapter 2
1ME 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
2Crystalline 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
3Three 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.
4Imperfections (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
5Point 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).
6Line 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
7Surface 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
8Elastic 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.
9Plastic 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.
10Effect 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
11Slip 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.
12Twinning
- 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.
13Polycrystalline 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
14Grains 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
15Noncrystalline (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
16Crystalline 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.
17Volumetric 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).
18Summary 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.
19Summary 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
20MECHANICAL PROPERTIES OF MATERIALS
- Chapter 3
- Stress-Strain Relationships
- Hardness
- Effect of Temperature on Properties
- Fluid Properties
- Viscoelastic Behavior of Polymers
21Stress-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
22Tensile 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
23Tensile 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.
24Stress 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
25Typical Stress-Strain Plot
Ultimate tensile strength (or TS)
(or yield point or
yield stress, or elastic limit)
26Elastic 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
27Problem 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)
28Ductility 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
29Problem 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
30Conservation of Volume
- Before necking or barreling in an ideal test
- If Lf/L0 1.5 what does Af / A0 ?
-
-
-
-
31True 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
32Problem 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)
33Categories 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 )
34Compression Test
- Applies a load that squeezes the ends of a
cylindrical specimen between two platens
35Stress-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
36Shear Properties
- Application of stresses in opposite directions on
either side of a thin element
37Shear 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
38Torsion Stress-Strain Curve
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
39Problem 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)
-
-
-
40Problem 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. -
-
-