Post on 31-Mar-2021
LECTURE #12-13: DISLOCATIONS AND
STRENGTHENING MECHANISMS
ENGR 151: Materials of Engineering
RECOVERY, RECRYSTALLIZATION, AND GRAIN
GROWTH
Plastically deforming metal at low temperatures
affects physical properties of metal
Elevated temperature treatment
Recovery
Recrystallization
RECOVERY
Stored internal energy is relieved by dislocation
motion as a result of atomic diffusion
Physical properties restored (electrical, thermal)
Grains are still in a relatively high strain energy
state
RECRYSTALLIZATION
The formation of a
new set of strain-
free and
approximately
equal-sized grains
after recovery
period
Low dislocation
densities
RECRYSTALLIZATION
Difference between dislocation boundaries
(cold-worked) and grain boundaries
(recrystallized)
RECRYSTALLIZATION
Small nuclei grow till they completely consume
the parent material
Recrystallized metal is usually softer, weaker
yet more ductile that cold-worked version
RECRYSTALLIZATION
RECRYSTALLIZATION
Recrystallization Temperature
Temp at which recrystallization reaches completion in one
hour.
GRAIN GROWTH
After recrystallization, grains continue to grow if
elevated temperatures are maintained
For grain growth, dependence of grain size on
time
d0 = initial grain diameter at t = 0
K = time-independent constant
n= time-independent constant
GRAIN GROWTH
FAILURE (CHAPTER 8)
FAILURE (CHAPTER 8)
Lockheed cargo plane example
FAILURE (CHAPTER 8)
Simple fracture is the separation of a body into
two or more pieces in response to an imposed
static stress (constant or slowly changing with
time) and at temperatures relatively low as
compared to the material’s melting point
FRACTURE
Stress can be tensile, compressive, shear, or
torsional
For uniaxial tensile loads:
Ductile fracture mode (high plastic deformation)
Brittle fracture mode (little or no plastic
deformation)
FRACTURE
“Ductile” and “brittle” are relative (ductility is based on percent elongation and percent reduction in area)
Fracture process involves two steps:
Crack formation & propagation in response to applied stress
Ductile fracture characterized by extensive plastic deformation in the vicinity of an advancing crack
Process proceeds slowly as crack length is extended.
FRACTURE
Stable crack: resists further extension unless there is
increase in applied stress
Brittle fracture: cracks spread extremely rapidly with
little accompanying plastic deformation (unstable)
Ductile fracture preferred over brittle fracture
Brittle fracture occurs suddenly and catastrophically without
any warning
Ductile fracture gives preemptive “warning” that fracture is
imminent
Brittle (ceramics), ductile (metals)
DUCTILE FRACTURE
Figure 8.1 (differences between highly ductile,
moderately ductile, and brittle fracture)
DUCTILE FRACTURE
Common type of fracture
occurs after a moderate
amount of necking
After necking commences,
microvoids form
Crack forms perpendicular
to stress direction
Fracture ensues by rapid
propagation of crack
around the outer
perimeter of the neck (45°
angle)
Cup-and-cone fracture
DUCTILE VS. BRITTLE FRACTURE – EXAMPLE
BRITTLE FRACTURE
Takes place without much deformation (rapid crack
propagation)
Crack motion is nearly perpendicular to direction of tensile
stress
Fracture surfaces differ:
V-shaped “chevron” markings
Lines/ridges that radiate from origin in fan-like pattern
Ceramics: relatively shiny and smooth surface
BRITTLE FRACTURE
BRITTLE FRACTURE
Crack propagation corresponds to the successive and repeated breaking of atomic bonds along specific crystallographic planes (cleavage)
Transgranular: fracture cracks pass through grains
Intergranular: crack propagation is along grain boundaries (only for processed materials)
PRINCIPLES OF FRACTURE MECHANICS
Quantification of the relationships between
material properties, stress level, crack-
producing flaws, and propagation mechanisms
STRESS CONCENTRATION
Fracture strengths for most brittle materials are
significantly lower than those predicted by
theoretical calculations based on atomic
bonding energies.
Due to microscopic flaws that exist at surface and
within the material (stress raisers)
STRESS CONCENTRATION
MAXIMUM STRESS AT CRACK TIP
Assume that a crack is similar to an elliptical
hole through a plate, oriented perpendicular to
applied stress, then the maximum stress:
σo = applied tensile stress
ρt = radius of curvature of crack tip
a = represents the length of a surface crack
STRESS CONCENTRATION FACTOR (KT)
Measure of the degree to which an external
stress is amplified at the tip of a crack
Stress amplification can also take place:
Voids, sharp corners, notches
Not just at fracture onset
BRITTLE MATERIAL
Effect of a stress raiser is more significant (stronger) in brittle than ductile materials.
In ductile materials, there is a uniform distribution of stress in the vicinity of the stress raiser
This phenomenon does not occur in brittle materials
BRITTLE MATERIAL
Critical stress required for crack propagation in a brittle material:
E = modulus of elasticity
γs = specific surface energy
a = one half the length of an internal crack
When magnitude of tensile stress at tip of flaw exceeds critical stress, fracture results
EXAMPLE PROBLEM 8.1 (PG. 244):
IMPACT FRACTURE TESTING
Charpy V-notch (CVN) technique:
Measure impact energy (notch toughness)
Specimen is bar-shaped (square cross section) with
a V-notch
High-velocity pendulum impacts specimen
Original height is compared with height reached
after impact (energy absorption)
Izod Test
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:
THE S-N CURVE
Fatigue testing apparatus
Simultaneous axial, flex, and twisting forces
S-N curve (stress vs. number of cycles)
Fatigue limit
Fatigue strength
Fatigue life
CREEP
Deformation occurring at elevated
temperatures and exposed static mechanical
HW (DUE MONDAY, APRIL 10)
Chapters 7 & 8
7.23, 7.30, 7.38, 8.1, 8.3, 8.22