lecture #13: dislocations and strengthening mechanisms...lecture #13: dislocations and strengthening...

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