Chapter 10: Strengthening Mechanisms

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Chapter 10 Strengthening Mechanisms
ISSUES TO ADDRESS...
How do we increase strength? e.g.,
Strain-hardening, grain-boundary and solute
hardening, and solid-solution strengthening.
How can heating change strength and other
properties? e.g., recrystallization and grain
growth.
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Strengthening Mechanisms

• Increase Grain Boundaries
• barriers to slip/dislocation motion.
• Solid-Solution Strengthening
• pinning (opposing stress fields) or impeding
• dislocation motion (obstacles).
• Work-hardening (or Cold-Working)
• Increased dislocation density, more interactions
  interactions (increased stress fields and
  entanglements).

3
Plastic Deformation to Fracture Engineering is
in between
Stress-strain and microscopic factors can be used
to engineer materials.
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Work-hardening Mechanisms in Metals (mostly)

• Relaxation times in molecular processes in gases
  and most liquids are so short that they are
  almost always in a state of well-defined
  equilibrium.
• Consequently, structure of a gas or liquid does
  not depend on history.
• In contrast, relaxation times for some of the
  significant atomic processes in crystals are so
  long that a state of equilibrium is rarely, if
  ever, achieved.
• For this reason, metals show the generally
  desirable characteristic of work-hardening with
  strain, or strain-hardening.
• Various work-hardening effects
• dislocation interaction
• solute hardening (dislocation-solute)
• precipitation and dispersion hardening
• grain boundary hardening
• Hardening by plastic deformation (rolling,
  drawing, etc.) is one of the most important
  methods of strengthening metals, for example.

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Mechanism Cold-Working (CW)
Room temperature deformation. Forming
operations change the cross sectional area
-Forging
-Rolling
Adapted from Fig. 11.7, Callister 6e.
-Extrusion
-Drawing
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Critical Resolved Shear Stress vs Dislocation
Density

• tensile test single xtal oriented so that
  different values (cos? sin ?)max are generated in
  most -favored slip system.
• Measure ?ys are different. But, ?ys/m are
  invariant!

CRSS increases with dislocation density higher
YS
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Anisotropy in ?YS
Can be induced by rolling a polycrystalline
metal
-before rolling
-after rolling
Adapted from Fig. 7.11, Callister 6e.
rolling direction
235 mm
-anisotropic since rolling affects grain
orientation and shape.
-isotropic grains are spherical randomly
oriented.
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Dislocations during Cold-Working
Mo - single crystal
Ni
Ti
Dislocations entangle with one another during
cold working, so motion is inhibited.
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Results of Cold-Working
Dislocation density (rd) goes up Carefully
prepared sample rd 103 mm/mm3 Heavily
deformed sample rd 1010 mm/mm3
Ways of measuring dislocation density
40mm
OR
Micrograph adapted from Fig. 7.0, Callister 6e.
Yield stress increases as rd increases
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Dislocation-Dislocation Trapping
Dislocation have stress fields associated with
them. This traps (or inhibits motion of) other
dislocations.
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Effect of Cold-Working
Yield strength (?YS ) increases. Tensile
strength (TS) increases. Ductility (EL or
AR) decreases.
2nd drawn
1st drawn
Undrawn wire
Adapted from Fig. 7.18, Callister 6e.
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Cold-Working Analysis
What is the tensile strength ductility
after cold working?
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Stress-Strain vs. Temperature
Results for polycrystalline iron
Adapted from Fig. 6.14, Callister 6e.
sy and TS decrease with increasing test
temperature. EL increases with increasing
test temperature. Why? Vacancies help
dislocations past obstacles.
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14
Effect of Heating after CW
1 hour heating at Tanneal reduces TS and
increases EL. Effects of cold work are
reversed!
3 Annealing stages
Adapted from Fig. 7.20, Callister 6e.
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15
Recovery
Annihilation reduces dislocation density.
Scenario 1
diffusion (T dependent) plus dislocations
annihilating (density dependent).
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Recovery by Edge Climb Process
Dislocations can avoid obstacles.
Scenario 2 -- Dislocation is block by obstacle
(precipitate or another dislocation). -- Edge
moves to another slip plane by vacancy-assisted
climb, which is temperature-dependent process. --
Climbed dislocation can now move on parallel slip
plane and annihilate, like in scenario 1. (Also
important for creep process.)
Inclusion, Precipitate.
t ?t1
t0
t ?t2
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17
Screws Can Avoid Obstacles by Cross-Slip
Screw dislocations cannot CLIMB like edges.
Dir. of screw motion
(111)
Line of screw dislocation
(111)

• Not T-dependent like Climb, as there is no
  diffusion.
• Screw segments stays always on 111 planes, but
  avoid the obstacle.
• Edges successively must move from one plane to
  another by vacancy diffusion.

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CREEP Processes
CREEP deformation of a material placed
in-service at elevated temperatures and exposed
to static stress, such as turbine rotors under
centrifugal stress or high-P steam lines
Primary or transient creep ??/?t decreases with
time indicating increase in strain-hardening. Sec
ondary (steady-state) creep ??/?t continually
decreasing indicating increase in
strain-hardening. ??/?t is a constant indicating
a balance between strain-hardening and
recovery. Rupture lifetime, tR Is dominant
design consideration for, e.g., turbine blades
and rocket motor nozzles.
Recovery some stored strain energy is relieved
by dislocation motion due to enhanced atomic
diffusion at elevated temperature (e.g., reduced
disl. density and formation of tilt boundaries).
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Ex thermally-activated secondary creep process
Secondary (steady-state) creep ??/?t continually
decreasing indicating increase in
strain-hardening. ??/?t is a constant indicating
a balance between strain-hardening and recovery.
At high-T obstacles are avoided by dislocations
climb, a vacancy-assisted process, and stress is
relieved. Note this mechanism does not explain
annihilation and multiplication of dislocation
such that dislocation density is
constant. Possible mechanism emission-climb/annih
ilate-new-emission, see text.
Recovery some stored strain energy is relieved
by dislocation motion due to enhanced atomic
diffusion at elevated temperature (e.g., reduced
disl. density and formation of tilt boundaries).
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Grain-Boundary and Deformations
Plastic deformation, recovery and
recrystallization

• The dislocation array formed by plastic
  deformation is dependent on
• crystal structure
• test temperature
• strain
• strain-rate
• crystal features
• As is now clear, hardening of crystals during
  plastic deformation is due to increase in
  dislocation density and the mutual interaction
  between disls.
• Work done by external load is dissipated as
  HEAT, but a small portion is retained in
  materials as stored energy (e.g., increased
  dislocation density).
• Energy remains stored provided that the T is low
  enough for atoms to be immobile T lt 0.3 Tmelt.
• Stored energy reduced if disls arrange
  themselves into low-angle (lt 50) G.B. (called
  polygonization), or into tangles.
• Rearrangement involves glide and climb and
  requires thermal assist.

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Mechanism reduce grain size
Adapted from Fig. 7.12, Callister 6e. (Fig. 7.12
is from A Textbook of Materials Technology, by
Van Vlack, Pearson Education, Inc., Upper Saddle
River, NJ.)
Grain boundaries are barriers to
slip. Barrier "strength" increases
with misorientation. Smaller grain
size more barriers to slip.
Hall-Petch Equation
From Ian Robertson, UIUC
Why?
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Example Grain-Size Strengthening
70wtCu-30wtZn brass alloy
Data
0.75mm
Fig. 4.11(c), Callister 6e.
Adapted from Fig. 7.13, Callister 6e.
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Bicrystals and Compatibility
Each bicrystal must have six strain components 3
tensile and 3 shear ?ii, (tensile) and ?ij
(shear) with i1,3 and j1,3. To have
compatibility of strains at interface (grain
boundary) must have ?11A ?11B , ?33A ?33B
, and ?13A ?13B . Because one grain has a
larger value of cos ? cos ? smaller Schmidt
factor (1/m), the above constraints restrict the
deformation of this more favorably oriented grain
and result in a higher YS (greater work-hardening
response) of the bicrystal.
For poly-xtals, more restrictive constraint are
required than those above. While each grain has 3
tensile and 3 shear components, plastic
deformation has volume constraint, or ?11 ?22
?330. Thus, 5 independent slip systems are
needed in vicinity of g.b. to have compatibility!
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Grain-Boundary Strengthening and Cracking

• Dislocation-G.B. Interactions
• G.B. impede motion of dislocations along entire
  length of disl. Line.
• Expect G.B. to be more efficient at pinning than
  dislocation obstacles.
• See discussion in text!
• Stress to activate dislocation motion for a given
  grain increases with number of dislocations
  pile-up at the GB due to stress concentration.

Hall-Petch relation
For infinite grain, YS is intrinsic value of
single crystal slip. For finite and decreasing
grain size, YS increases.
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Grain-Boundary Strengthening and Cracking
Cracking may originate at the intersection of
slip plane with G.B., if ?crack lt
?disl. Response of G.B. will be affected by test
conditions, i.e. environment and distribution of
solutes at G.B.
Ni-24Al 1-3 intergranular Ni-24Al-0.5B
35-54 trans-granular Ni-24Al-0.5B H
mixed-mode fracture
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Movement of Dislocation via Thermal Activation

• Divide stress required for deformation into
  Thermal and Shear (T-indep.) components, i.e. ?Th
  and ?G, where ?G is the stress to move
  dislocation.
• Without barrier from long-ragen stress fields
  from other dislocations.
• Relative important of ?Th and ?G can be studied
  by determining T and/or strain-rate dependence of
  flow-stress (YS).
• Stage I ?Th /?G 1 gives easy glide.
• Stage II ?Th /?G lt 1 gives strain-rate
  increases (linear hardening).
• With applied ?, extra force is required to free
  dislocations Fx (? ?G )b L
• U0 ?0d Fx dx
• If Fx is not big enough, slip cannot occur!
• e.g. Peierls-Nabarro barrier is example.

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Stage II Work-hardening with Hard Obstacles
Stage II ?disl higher, much dislocation-dislocati
on interaction Strain-hardening high (hard
obstacles Lomer-Cottrell locks, jogs) For hard
obstacles ?max Gb/L, therefore, ?max
?Gb?? assuming all dislocations represent
obstacles L2?disl constant (Homework)
Intrinsic Strength ?0 of material having low
dislocation density so that dislocation
interactions are inconsequential. For bcc, ?
0.4, whereas for fcc, ? 0.2.
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3 Main Stages of Work-hardening
Stage I ?disl low, little disl-disl
interaction Strain-hardening low (soft obstacles,
2 disls same type and slip system) Stage II
?disl higher, much dislocation-dislocation
interaction Strain-hardening high (hard
obstacles Lormer-Cottrell locks, jogs) Stage
III Re-arrangement processes Load -gt heat
stored energy (say, in dislocation).
(thermally-assisted tilt and grain boundary)
See Disl. Interactions Last lectures
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Critical Resolved Shear Stress versus Temperature
?
I
II
III
T

• For T lt 0.7 Tmelt, ?CRSS ?a ?,
• with athermal and thermal dependent
  contributions.
• Athermal arises from dislocation-dislocation
  interaction (stress fields).
• Thermal arises from Peierls stress involving
  impurities, kinks and jogs.
• Small impurities are more mobile at intermediate
  T and can catch up to dislocations, repinning,
  etc. Impurity atoms increase CRSS.

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Temperature Variation of Yield-Strength in
Polycrystals
Temperature variation of YS in polycrystals
parallels that of CRSS in single-crystals. BCC
metals, e.g., V, have intrinsically higher YS
than that of FCC metals, e.g., Cu. YS is more
temperature sensitive in BCC metals than FCC ones.
High YS of MgO is related to strong
polar-covalently bonds, and explains why MgO is
stronger than ionically bonds NaCl, even though
they have the same crystal structure.
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Recrystallization
New crystals are formed that (1) have a
small dislocation density (2) are small and
(3) consume cold-worked crystals.
0.6 mm
0.6 mm
Adapted from Fig. 7.19 (a),(b), Callister 6e.
33 cold worked brass
New crystals nucleate after 3 sec. at 580C.
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Further Recrystallization
All cold-worked crystals are consumed.
0.6 mm
0.6 mm
Adapted from Fig. 7.19 (c),(d), Callister 6e.
After 8 seconds
After 4 seconds
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Grain Growth
At longer times, larger grains consume smaller
ones. Why? Grain boundary area (thus energy)
reduced.
0.6 mm
0.6 mm
Adapted from Fig. 7.19 (d),(e), Callister 6e.
(Fig. 7.19 (d),(e) are courtesy of J.E. Burke,
General Electric Company.)
After 8 s, 580C
After 15 min, 580C
coefficient dependent on material and T.
Empirical Relation
exponent typ. 2
elapsed time
grain diam. at time t.
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Mechanism - solid solutions
Impurity atoms distort the lattice generate
stress. Stress can produce a barrier to
dislocation motion.
Larger substitutional impurity
Smaller substitutional impurity
Impurity generates local shear at A and B that
opposes dislocation.
Impurity generates local shear at C and D that
opposes dislocation.
How?
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Ex solid solution strengthening in Cu
Tensile strength yield strength increase
w/wt Ni.
Adapted from Fig. 7.14 (a) and (b), Callister 6e.
Why?
Empirical relation
Alloying increases sy and TS.
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Solid-Solution Strengthening Size- and Modulus-
effect
Cu modulus effect
Tetragonal distortion for Cu
R. Flescher, Acta Metall. 11, 203 (1963)
e.g. Tetragonal distortion ?TET ?Gb(?c/b)
?G ?c In local-force model, spacing between
solute is L b/?(2c) due to solute atoms in the
2 planes immediately adjacent to slip plane
giving 2(c/b2) atoms/area.
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Mechanism precipitation strengthening
Hard precipitates are difficult to shear.
Ex Ceramics in metals (SiC in Iron or Aluminum).
Why?
Result
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Particle Cutting
For particle, surface areas is created and
Stacking Faults For chemically ordered particle,
also creates APBs.
Meyers and Chawla, Mechanical Metallurgy
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Particle Hardening bowing versus cutting
If the particle is harder than matrix,
dislocation can avoid cutting by bowing around
particle, or traversing around particle at
interphase boundary (a complex process).
Harder to cut stiffer, larger particles. Easy to
bow around stiffer, larger particles. Crossover
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Particle Strengthening
Effects Particle size and volume fraction.
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Strain accommodation for a non-deforming particle
by shear loops and bypassing (edge and screws).
Shear loop
Edge I loop V
Screw I V loop
b
b
Cross-slip
Leave behind atoms
interstitial
b
vacancies
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Particle Hardening coherent, incoherent, and
intermediate

• Small particles of second phase (1-10) resist
  dislocation penetration, especially more so than
  single solute particles.
• Degree of strengthening depends on size, volume
  fraction, shape, nature of boundary (coherency
  hardening).

interphase boundaries that is incoherent, which
has no coherency strains.
Intermediate interphase boundaries coherency
strain are relieved by edge dislocation (not
quite1-1 match)
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Particle Hardening coherent, incoherent,
modulus,
Stress fields from coherent solute particle
coherency hardening
Dislocations cutting particle modulus hardening
As dislocation cuts particle and goes halfway
G
Gp
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Particle Hardening chemical, ordering
For particle, surface areas is created and
Stacking Faults For chemically ordered particle,
also creates APBs.
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Precipitation Strengthening Application
Internal wing structure on Boeing 767
Adapted from Fig. 11.0, Callister 5e.
Aluminum is strengthened with precipitates
formed by alloying.
Adapted from Fig. 11.24, Callister 6e.
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Precipitation Strengthening Application
Aluminum is strengthened by ordered metastable
Al3Li precipitates formed by alloying.
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Precipitation Hardening Alloys
Cu and temperature of quench and anneal
determines microstructure. Subsequent heat
treatment will affect type of particles, e.g.
coherent and incoherent. Anneal too long and
particles will try to remove coherency strain by
going incoherent. GP I (GP II) coherent,
chemically disordered (ordered). ? is
incoherent particle of Al2Cu.
Similar to L12 Al3Li, but different structure
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Temperature Aged Precipitation Hardening Alloys
Strength drops if aged to long into ? is
incoherent particle of Al2Cu
Strong, stop here
GP I (GP II) coherent, chemically disordered
(ordered) particles. ? is incoherent particle of
Al2Cu.
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Controlling Microstructures Controls Strengthening
fcc Fe
Eutectoid formation of bcc Fe (ferrite, soft)
Fe3C (cementite, hard) like pearl under
microscope.
Cool and warm-work
Recall Fe-C Snoek effect and tetragonal
distortion
Martensite bct Fe w/C interstitials
Mechanical properties reflect hardness of phases
and inhibiting of dislocation motion
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Summary of Mechanisms

• Increase Grain Boundaries barriers to
  dislocation motion.
• Solid-Solution/Precipitation Strengthening
  impedes disl. motion.
• Work-hardening (or Cold-Working) Increase disl.
  Density
• T-Dependent Recovery and Recrystallization
  oppose these. Heating can reduce dislocation
  density and increase grain size.
• Controlling microstructure, particle phases and
  stiffness, ageing, etc., impacts mechanical
  response.
• Each effect has specific functional dependence
  on disl. density, solute concentration, modulus
  difference, grain size, annealing time, etc.
  Do you know and understand them? Can you explain?