DAY 39: REVIEW –PART I
Mechanical Tests and What They Tell Us.
(Mechanical Properties) (Ch 6 & 8)
 Crystallinity in Metals, Dislocations, Plasticity in
Metals.
 Multi-phase Alloys. Phase Diagrams (Start)

STRESS AND STRAIN

Definition of Engineering Stress – Uniaxial
P
force being transmitted


A0
original cs area

Definition of Engineering Strain -- Uniaxial

change in length


L0
original length
TENSION TEST

Standard Specimen pulled to breaking in
uniaxial tension.
BASIC BEHAVIORS
Brittle Material – No
plastic strain leftover
Ductile Material –
Significant leftover strain
after break.
DUCTILE AND BRITTLE FRACTURE
APPEARANCE
Dull appearance
of fracture
surface;
Lots of residual
deformation;
Shear lips at 45o
to max tension
Shiny or sparkly
fracture surface;
Little or no residual
deformation;
FS normal to max
tension;
Chevrons
STRAIN RATE & TEMPERATURE EFFECTS
(FAR MORE NOTICEABLE IN POLYMERS)
High strain rate, cold temperature
Low strain rate, high
temperature
Note how both stiffness and strength can be effected
BASIC PROPERTIES
UTS. Ultimate tensile
strength (Necking starts
in metals)
YS-0. 2% offset
E= Modulus of
Elasticity;
(Stiffness)
=0.002
%EL = plastic x 100% (Give Gauge
length
THE AREAS UNDER THE CURVE MEAN
SOMETHING TOO.
Toughness
Modulus of Resilience
PROBLEMS WITH THE TENSION TEST
1.
2.
3.
Destructive
Costly in time and machinery
Often does not give the full picture of what will
happen to a material in service, especially
under harsh conditions.
HARDNESS TEST
Hardness = Resistence to indentation.
 Cheap, non-destructive evaluation of a material
 Several scales
 Many correlations, but hardness correlates to
UTS numerically in most hard steels.
 Scales to remember
1. Rockwell
2. Brinell
3. Knoop / Vickers

NOTCH TOUGHNESS (IMPACT) TESTS
Unfavorable environment; i.e. cold temp
 High Strain rate
 Presence of a notch
 Energy absorbed in breaking specimen measured.

Good for finding minimum use
temperatures. (DBTT)
Good for categorizing materials in
severe conditions
FATIGUE

Failure after cyclical loads, with tension
component.
Fatigue is a very common problem facing
designers.
HOW TO RECOGNIZE FATIGUE IN A BROKEN
PIECE

Beach marks on the fracture surface x120
Indications of loading
changes
Striations
X700 (Show indiv.
Cycles)

IMPORTANCE OF FATIGUE
Fatigue is a major killer. It is an automatic
suspect in almost any failure.
 Fatigue appears in subtle ways, eg. Thermal
cycling.
 The use of rational, accepted design procedures
against fatigue is absolutely essential. (Subject
of a later course.)

FATIGUE TESTING
We need something that does cycles. Here is the rotating beam
test. (There are other tests as well.)
We get cycles to failure (N) at a corresponding stress amplitude, S.
We plot these on a curve.
THE S-N CURVES
Curves are based on
widely scattered data!
Here is SN curve for a
typical steel. Note:
There is an endurance
limit.
To the right is SN curve
for typical aluminum alloy.
Sorry! No endurance
limit.
WHAT’S DONE WITH THE CURVES
The curves provide a starting point for rational
fatigue design. In particular they are useful
where “high-cycle” fatigue failure is possible.
 If the cyclical stress is superimposed on a mean
stress, this mean stress is also important and
should be accounted for.
 You will be introduced to the methodology in a
later course.
 Be aware of the statistical scatter on these
curves. You CAN get failure at a stress below the
curve. There is always a probability of failure,
but there are ways of making that probability
acceptably small.

WAYS TO REDUCE DANGER OF FATIGUE

1.
2.
3.
4.
Basically, we want to reduce tension on and near
the surface. (Where cracks are most common.)
Avoid stress concentrations. They may not hurt
much in the static loading case, but are deadly
in the cyclic loading case.
Use surface treatments. Carburizing or
Nitriding makes the steel harder (i.e. stronger)
on the surface plus it introduces residual
compressive surface stresses.
Another method: shot peening.
Another method: polishing
FRACTURE
When a body has a notch, re-entrant corner, fillet
or other geometric discontinuity, there is said to
be a stress raiser, or stress concentration factor
present. K.  max  K  no min al
 BUT
 A sharp crack in the material might not be
visible, or easily detectable. A material that is
ductile in the tension test may fail in a brittle
manner due to an unstable crack.
 The science of fracture mechanics addresses this
problem.

STRESS INTENSITY
The factor Y depends on crack length and
geometry.
 So, an alternate, and more useful way of talking
about crack stability is to frame the discussion in
terms of the stress intensity as opposed to the
critical strain energy release rate. A crack will
become unstable when K = Kc, a critical value
called fracture toughness.

a
Kc  Y   c  a
W 

The specimen geometry comes in through Y. See
Figure 8.13 in the text.
FRACTURE TOUGHNESS
Well, fracture toughness, Kc, depends on
specimen thickness. But it’s kind of
counterintuitive. Think of a plate.
 A thin plate is in a condition called plane stress.
When in-plane stress is applied, the plate can
easily contract in the out-of-plane direction. The
corresponding out of plane normal stress and
shear stresses are zero.
 But in a thick plate, the bulk of the material
inhibits this out of plane contraction. When it’s
thick enough we have plane strain, in which we
have three non-zero principal stresses, but zero
out of plane strain.

PLANE STRAIN FRACTURE TOUGHNESS
As the specimen gets thicker, fracture toughness
diminishes, until, in plane strain, it finally
becomes constant, that is geometry independent.
It can now be regarded as a material property.
 This material property is called plane strain
fracture toughness, KIc.
 Failure occurs by yielding takes place when

   YS

Failure occurs by fracture when
a
K  K Ic or Y   
W 
 a  K Ic
CRYSTALLINITY IN METALS
Three types of unit cells. List in order of slip
systems.
 Name a point defect, a line defect, and an area
defect.
 What is the relationship between slip and plastic
deformation?
 What is the relationship between dislocation
motion and slip?

WHAT’S HAPPENING?
The tin atoms dissolve in the matrix of copper.
There are many, many substitutional solute
atoms.
 These atoms interact with dislocations, impeding
their motion.

1.
2.
3.
The solute atoms are not quite the right size.
This produces stress and strain in the lattice.
The solute atoms’s stess field attracts or repels
the stress field around the dislocation.
The result is that the dislocation is pinned or
blocked – It’s motion is impeded!
RESULT
Here is the plot in the notes.
Strength
Effect depends
upon alloying
element
% alloy
Solid Solution Strengthening
ANOTHER DISLOCATION BLOCKER: THE
GRAIN BOUNDARY
A dislocation coming up
on the grain boundary will
not be able to cross easily
into the adjacent grain.
It will probably stop
waiting for more stress to
be applied. Other
dislocations will pile up
behind it.
THE HALL-PETCH RELATIONSHIP
Yield Strength
sys =so+kyd-1/2
d -1/2
Effect of Grain Size Reduction
ANOTHER BLOCKER: OTHER
DISLOCATIONS
Recall that as plastic deformation proceeds the
density of dislocations increases by several orders
of magnitude.
 So dislocations block themselves! This accounts for
the strengthening that occurs during plastic
deformation. (Done on purpose, we call it cold
work.
Yield Strength

Degree of
strengthening
depends on
material
%area reduction
Effect of Plastic Deformation
REVIEW OF THREE STRENGTHENING
MECHANISMS
1.
2.
3.
4.
Solute Atoms. (Alloying)
Grain boundaries. (Grain boundary refinement)
Dislocations. (Cold Work, i.e. plastic
deformation done on purpose. AND
Phase Boundary. What’s a phase?
LET’S LOOK AT SOME METALLOGRAPHS

An alloy of Cu in Aluminum
Al, surrounded by a mixture
of Al and CuAl2.
Al and CuAl2 mixture.
ANOTHER – A CLOSEUP OF A STEEL.
The darker area is Fe
with small amount of
interstitial carbon.
The lighter standout
areas are the
compound cementite,
Fe3C. (Iron carbide.)
WHAT HAVE WE SEEN?
Multiphase materials, or alloys. Phases are
separate, they are clearly different materials.
But they are mixed together, at times very finely.
 We do not always have multiphase alloys. There
are many useful single phase alloys. BUT
 The presence of the second phase is very
important to…

BLOCK DISLOCATIONS! INCREASE STRENGTH.
CONCEPT OF THE PHASE
Phase: “A distinct state of matter in a system;
matter that is identical in chemical composition
and physical state and separated.” (Google)
 Examples
1. Ice in water
2. Sugar and water
3. Alloys in metals can have a phase rich in each
metal component.

THE LEAD TIN SYSTEM PHASE DIAGRAM