Title: STRUCTURE PROPERTY RELATIONS
1STRUCTURE PROPERTY RELATIONS
2Hexagonal Arrangement of Atoms
Close Packed ABABAB...
Not close packed.
Note that there are continuous space along three
holes even for the hexagonal close packed
structure.
3Cubic Close Packed Arrangement of Atoms
More commonly designated as face centered cubic
(fcc) structure. Materials like Cu, Ni, Al, etc.
C site
ABCABC packing
4Designation of Planes Miller Index
Cubic unit cell with the designated sides.
Z
b
a
c
The plane ABC is designated as (hkl), where a/h
is the intersection of the plane with the X-axis,
b/k is the intersection with the Y axis, and c/l
is the intersection with the Z axis. Similarly
directions are designated as hkl. Note the
different symbols for the brackets.
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6DISLOCATION IS THE LINE BOUNDING THE SLIPPED AND
UNSLIPPED REGIONS OF THE CRYSTAL
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1012 independent slip systems in the fcc lattice.
In general, 5 independent slip systems are
necessary to make a polycrystalline material
ductile.
11DEFORMATION OF POLYCRYSTAL
At yielding, the applied stress in different
grains will be different, depending on the local
Schmid Factor. However, they will all have the
same CRSS. See previous formula. On the average,
sapplied Taylor FactorCRSS In fcc and bcc
materials, Taylor factor is around 3.1.
12STRENGTHENING MECHANISMS
Solid Solution Strengthening Dislocation-dislocati
on interactions and strengthening Precipitate
Strengthening Cutting Bowing Grain boundary
strengthening
13Dislocation Strengthening tCRSS Gb/l Gbr 1/2
Typically, r 1012 to 1014 /m2
Precipitate Strengthening The effect of
precipitates is to block dislocations. However,
dislocations can either cut precipitates or bow
around precipitates. One gets
Here gAPB is an anti-phase-boundary energy
(typically 50 - 300 mJ/m2), vf is the volume
fraction of precipitates (0.02-0.7), r is the
precipitate radius, and l is the center distance
between precipitates.
14PRECIPITATE STRENGTHENING
r
Process of overcoming precipitates by cutting
them.
Process of overcoming precipitates by Orowan
bowing.
The process that requires least applied shear
stress will operate.
15- Precipitate size (r) is controlled by the heat
treatment. - The volume fraction (vf) of ppt. is controlled
by the alloying additions.
16Al-Cu PHASE DIAGRAM
Window of compositions for vf control
2xxx Al-alloys
From Ashby Jones
17AGING TREATMENT IN Al-Cu ALLOYS
TTT Diagram
Age
Quench
From Ashby Jones
18Grain Boundary Strengthening in Polycrystals
Strengthening comes about because dislocation
motion is hampered by slip having to change
direction. There is also the barrier caused by
different strains in different grains.
Typically, d ranges between 1 to 250
microns. Note that strength increases with lower
grain size. Thus, nanometer sized grains can
give very high strength.
19Total Strength
For fcc or bcc polycrystal, sy 3.1 tCRSS
20CRYSTAL ROTATION CRYSTALLOGRAPHIC TEXTURE
Rotation of crystals in center region. Rotation
is reduced if other slip systems operate
simultaneously.
Lateral grip motion
No lateral motion
If many grains remain in single slip mode, then
the final orientation of all grains is no longer
random. We say that it has crystallographic
texture. Thus, in an fcc material, the Taylor
factor is no longer 3.1.
21During crystallographic rotation, the slip
direction under tension loading approaches the
loading direction. Thus, if the loading
direction of the crystal is such that the -101
slip direction on the -111 plane is activated
(due to highest resolved shear stress, recall
formula), then the -101 direction of the
crystal will like to line up with the loading
axis. Such crystal rotations give rise to
non-random orientation of crystals. The effects
are many-fold (1) The yield strength is
anisotropic. (Why?). When slip direction
approaches loading direction, q simultaneously
increases. Then sy for that grain increases for
a given CRSS (sytCRSS/CosqCosf). Large strength
in rolling/extrusion direction. (2) The
elongation will be different in different
directions, because often a major problem in
hexagonal metals. (3) The Young's modulus will
be anisotropic a severe case is that of Be.
Such different E will generate high internal
stresses, and is a major concern in design.
22MECHANICAL TEXTURE/FIBERING
The inclusions tend to flatten in rolling or
extrusion direction. These flattened inclusions
are potential cracks. Thus, although elongation
to failure can be enhanced along the longitudinal
axis of the inclusions, ductility can be severely
reduced perpendicular to their elongated axis.
This is a major concern when working with sheet
metal forming operations, such as bending,
tubular extrusions, pressure forming of domes,
etc.
23TEXTURE SUMMARY
- There are two types of textures
- 1) Mechanical Texture
- 2) Crystallographic Texture
- Both types of texture induce anisotropic
mechanical properties (strength, elongation,
elastic modulus). - The mechanical forming process influences the
type of texture. - Annealing, following forming operation can
produce new crystals. This can reduce texturing
effects. Nevertheless, textures are major
concerns in metal forming, and need to be
considered seriously. - In polymer forming operation, such as tube
drawing, pre-existing textures have similar
effects as in metal forming
24RECOVERY RECRYSTALLIZATION
From Kalpakjian and Smith
25RECOVERY RECRYSTALLIZATION
- Recovery and recrystallization involve
diffusion. - During recovery, dislocations are annihilated,
and that reduces strength. However, ductility is
improved. - During recrystallization, new grains are
nucleated and then they grow. Ideally one would
like to get recrytallized structure with fine
grain size t1/sqrt(d), to get the best of both
strength and ductility. - Recrystallization involves time and temperature
- The following rules generally apply
- 1. For given prior work, time for recryst.
decreases with temperature - 2.The more cold work, the lower the temperature
for start of recryst. - 3. The higher the cold work, the finer the grain
size.
26RECRYSTALLIZATION
From Kalpakjian and Smith
- One has to watch out for abnormal grain
growth.
27GRAIN GROWTH
The growth of new grains is controlled by time
and temperature. In order to control grain size,
for improved strength and ductility, various
techniques are utilized 1. Use of dispersoids,
such as sub-micron sized intermetallic or ceramic
particles. Grain boundaries get pinned. 2. Grow
the grains in the two-phase field of the phase
diagram. Then each competing phase restricts the
other phase.
Used in alloys of Ti, Fe, etc.
28FRACTURE
Bridgman Correction
Void Nucleation Growth
29FRACTURE SURFACES MECHANISMS
Ductile Dimple
Intergranular
Cleavage
30DUCTILE DIMPLE FAILURE
Ductile failure involves (1) Void Nucleation
(2) Void Growth, and (3) Void Coalescence
- Void nucleation occurs at inclusions, such as
coarse intermetallic particles (eg. Fe3Si),
oxides, sulfides (MnS in steels), etc. The
nucleation (decohesion or particle fracture) is
stress driven, and is influenced by plastic flow
of matrix past the elastic inclusions. - Void growth is controlled by both the plastic
strain (ep) and mean stress (sm(s1s2s3)/3).
The plastic flow increases local stress at
interface and in particle
The mean stress effect is exponential. Thus,
regions of high mean stress enhance void growth.
This is present at the center of necked region,
or ahead of a notch or crack tip. Also applies
for polymers.
31DUCTILE DIMPLE FAILURE
Void coalescence is largely strain driven.
Neighboring dimples join together in a shear
localization, or they grow separately until their
surfaces touch.
32BRITTLE FRACTURE
Low energy fracture, without any significant
plastic energy dissipation. In ductile fracture,
cracks are blunted, and then failure must proceed
through void nucleation and growth. In brittle
fracture, plastic deformation is minimal.
Materials Ceramics, intermetallics, bcc metals
(steels) below the ductile-to-brittle transition
temperature (DBTT).
The transition in energy and fracture mode around
DBTT is sharp.
Energy
T
33BRITTLE FRACTURE
In bcc metals, brittle failure also depends
slightly on the rate of deformation. Brittle
failure also occurs when hydrogen is present in
the metal. The hydrogen in steels promotes
brittle failure. In Ti-alloys, the hydrogen
effect is primarily through the formation of
hydrides.
34PROPERTIES OF MATERIALS
Please read up on the properties of different
types of materials in chapter 3.
From Kalpakjian and Smith
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