Materials Science

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Week 5Fracture, Toughness, Fatigue, and Creep

• Materials Science

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Mechanical Failure
ISSUES TO ADDRESS...
How do flaws in a material initiate failure?
How is fracture resistance quantified how do
different material classes compare?
How do we estimate the stress to fracture?
How do loading rate, loading history, and
temperature affect the failure stress?
Computer chip-cyclic thermal loading.
Hip implant-cyclic loading from walking.
Ship-cyclic loading from waves.
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What is a Fracture?

• Fracture is the separation of a body into two or
  more pieces in response to an imposed stress that
  is static and at temperatures that are low
  relative to the melting temperature of the
  material.
• The applied stress may be tensile, compressive,
  shear, or torsional
• Any fracture process involves two stepscrack
  formation and propagationin response to an
  imposed stress.

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Fracture mechanisms

• Ductile fracture
• Occurs with plastic deformation

• Brittle fracture
• Little or no plastic deformation
• Catastrophic

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Ductile vs Brittle Failure
Classification
Ductile fracture is usually desirable!
Ductile warning before fracture
Brittle No warning
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Example Failure of a Pipe
Ductile failure --one/two piece(s)
--large deformation
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Moderately Ductile Failure
Evolution to failure
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Ductile vs. Brittle Failure
cup-and-cone fracture
brittle fracture
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Transgranular vs Intergranular Fracture
Intergranular Fracture
Transgranular Fracture
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Brittle Fracture Surfaces
Transgranular (within grains)
Intergranular (between grains)
304 S. Steel (metal)
316 S. Steel (metal)
160 mm
4 mm
Polypropylene (polymer)
Al Oxide (ceramic)
3 mm
1 mm
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Ideal vs Real Materials
Stress-strain behavior (Room T)
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Flaws are Stress Concentrators!

• Results from crack propagation
• Griffith Crack
• where ?t radius of curvature
• so applied stress
• sm stress at crack tip
• Kt Stress concentration factor

?t
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Concentration of Stress at Crack Tip
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Engineering Fracture Design
Avoid sharp corners!
s
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Crack Propagation

• Cracks propagate due to sharpness of crack tip
• A plastic material deforms at the tip, blunting
  the crack.
• deformed region
• brittle
• Energy balance on the crack
• Elastic strain energy-
• energy stored in material as it is elastically
  deformed
• this energy is released when the crack propagates
• creation of new surfaces requires energy

plastic
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When Does a Crack Propagate?

• Crack propagates if above critical stress
• where
• E modulus of elasticity
• ?s specific surface energy (J/m2)
• a one half length of internal crack
• For ductile gt replace gs by gs gp
• where gp is plastic deformation energy

i.e., sm gt sc
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Fracture Toughness Design Against Crack Growth
Crack growth condition
Largest, most stressed cracks grow first!
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Fracture Toughness

• For relatively thin specimens, the value of Kc
  will depend on specimen thickness. However, when
  specimen thickness is much greater than the crack
  dimensions, Kc becomes independent of thickness.
• The Kc value for this thick-specimen situation is
  known as the plane strain fracture toughness KIC

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Fracture Toughness
Kc
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Design Example Aircraft Wing
Material has Kc 26 MPa-m0.5
Two designs to consider...
Design B --use same material --largest flaw
is 4 mm --failure stress ?
Design A --largest flaw is 9 mm --failure
stress 112 MPa
Key point Y and Kc are the same in both
designs.
Reducing flaw size pays off!
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Loading Rate
Increased loading rate... -- increases sy
and TS -- decreases EL
Why? An increased rate gives less time
for dislocations to move past obstacles
and form into a crack.
s
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Impact Testing
Impact loading -- severe testing case
-- makes material more brittle -- decreases
toughness
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Impact Tests

• A material may have a high tensile strength and
  yet be unsuitable for shock loading conditions
• Impact testing is testing an object's ability to
  resist high-rate loading.
• An impact test is a test for determining the
  energy absorbed in fracturing a test piece at
  high velocity
• Types of Impact Tests -gt Izod test and Charpy
  Impact test
• In these tests a load swings from a given height
  to strike the specimen, and the energy dissipated
  in the fracture is measured

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A. Izod Test

• The Izod test is most commonly used to evaluate
  the relative toughness or impact toughness of
  materials
• Izod test sample usually have a V-notch cut into
  them
• Metallic samples tend to be square in cross
  section, while polymeric test specimens are often
  rectangular

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Izod Test - Method

• It involves striking a suitable test piece with a
  striker, mounted at the end of a pendulum
• The test piece is clamped vertically with the
  notch facing the striker.
• The striker swings downwards impacting the test
  piece at the bottom of its swing.

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Determination of Izod Impact Energy

• At the point of impact, the striker has a known
  amount of kinetic energy.
• The impact energy is calculated based on the
  height to which the striker would have risen, if
  no test specimen was in place, and this compared
  to the height to which the striker actually
  rises.
• Tough materials absorb a lot of energy, whilst
  brittle materials tend to absorb very little
  energy prior to fracture

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B. Charpy Test

• Charpy test specimens normally measure 55 x 10 x
  10mm and have a notch machined across one of the
  larger faces
• The Charpy test involves striking a suitable test
  piece with a striker, mounted at the end of a
  pendulum.
• The test piece is fixed in place at both ends and
  the striker impacts the test piece immediately
  behind a machined notch.

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Factors Affecting Impact Energy

1. For a given material the impact energy will be
   seen to decrease if the yield strength is
   increased
2. The notch serves as a stress concentration zone
   and some materials are more sensitive towards
   notches than others
3. Most of the impact energy is absorbed by means of
   plastic deformation during the yielding.
   Therefore, factors that affect the yield behavior
   (and hence ductility) of the material such as
   temperature and strain rate will affect the
   impact energy

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Effect of Temperature on Toughness
Increasing temperature... --increases EL
and Kc
Ductile-to-Brittle Transition Temperature
(DBTT)...

FCC metals (e.g., Cu, Ni)


BCC metals (e.g., iron at T lt 914C)
polymers

Impact Energy
More Ductile

Brittle

s

High strength materials (
gt E/150)
y
Temperature
Ductile-to-brittle
transition temperature
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Fatigue Test

• Fatigue is concerned with the premature fracture
  of metals under repeatedly applied low stresses
• A specified mean load (which may be zero) and an
  alternating load are applied to a specimen and
  the number of cycles required to produce failure
  (fatigue life) is recorded.
• Generally, the test is repeated with identical
  specimens and various fluctuating loads.
• Data from fatigue testing often are presented in
  an S-N diagram which is a plot of the number of
  cycles required to cause failure in a specimen
  against the amplitude of the cyclical stress
  developed

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Fatigue Testing Equipment
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Fatigue Loading
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Fatigue Test - S-N Curve

• This SN diagram indicates that some metals can
  withstand indefinitely the application of a large
  number of stress reversals, provided the applied
  stress is below a limiting stress known as the
  endurance limit

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Fatigue Mechanism
Crack grows incrementally
typ. 1 to 6
increase in crack length per loading cycle
Failed rotating shaft --crack grew even
though Kmax lt Kc --crack grows
faster as Ds increases
crack gets longer loading freq.
increases.
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Improving Fatigue Life
1. Impose a compressive surface stress
(to suppress surface cracks from
growing)
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4. Creep Test

• Creep is defined as plastic (or irrevresible)
  flow under constant stress
• Creep is high temperature progressive deformation
  at constant stress
• A creep test involves a tensile specimen under a
  constant load maintained at a constant
  temperature.
• At relatively high temperatures creep appears to
  occur at all stress levels, but the creep rate
  increases with increasing stress at a given
  temperature.

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Creep Test

• Creep occurs in three stages Primary, or Stage
  I Secondary, or Stage II, and Tertiary, or Stage
  III

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Creep Test

• Stage I occurs at the beginning of the tests, and
  creep is mostly transient, not at a steady rate.
• In Stage II, the rate of creep becomes roughly
  steady
• In Stage III, the creep rate begins to accelerate
  as the cross sectional area of the specimen
  decreases due to necking decreases the effective
  area of the specimen

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Creep
Occurs at elevated temperature, T gt 0.4 Tm
tertiary
primary
secondary
elastic
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Secondary Creep
Strain rate is constant at a given T, s
stress exponent (material parameter)
activation energy for creep (material parameter)
strain rate
applied stress
material const.
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Creep Failure
Estimate rupture time S-590 Iron, T
800C, s 20 ksi
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Numerical Problems

• Problems 8.1 8.10 8.14 8.23 and 8.27