Failure

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Failure

• Chapter 9

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• Simple fracture is separation of a body into two
  or more pieces in response to stress at T lower
  than melting point.
• Our discussion is confined to fractures resulting
  from uniaxial tensile loads.
• There are two types of fracture for engineering
  materials

cup-cone (ductile) fracture in Al
brittle fracture in a mild steel
In ductile fracture, materials experience
plastic deformation before fracture.
In brittle fracture, materials experience little
or no plastic deformation.
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• A typical fracture process has two steps
• 1)crack formation
• 2)propagation-this is the step determining the
  mode of the fracture.
• For example ductile fracture proceeds slowly as
  the crack length is extended. This type of crack
  is called stable. On the other hand, cracks
  spread rapidly with very little accompanying
  plastic deformation. This type of cracks are
  called unstable.

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Ductile fracture is generally preferred since the
plastic deformation prior to fracture can be
accepted as a warning so that preventive measures
can be taken. Most of the metal alloys are
ductile and they experience ductile frature under
stress. But ceramics are brittle. Polymers
exhibits the two types of fracture. DUCTILE
FRACTURE For extremely soft metals
There is about 100 reduction in area. pure gold
or lead at RT or some metals polymers and
inorganic glasses at high T.
Most common tensile fracture profile
Necking is followed by frature.
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• More detailed progress of the fracture is
  illustrated here

This type of fracture is also called cup and cone
fracture since one of the mating surfaces is in
the form of a cup and the other like a cone.
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• BRITTLE FRACTURE
• Propagation of the crack is fast.

The motion of the crack is perpendicular to
applied stress.
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• Brittle crystalline materials have successive and
  repeated breaking of
• atomic bonds along specific crystalline plane and
  fracture cracks pass
• through grains. The process is called cleavage
  and type of fracture is
• called transgranular.

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• Crack propagation is sometimes along the grain
  boundaries and this fracture is called
  intergranular.

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• Fracture Mechanics This research area is about
  the relationships
• between material properties, stress level, the
  presence of crack
• producing flaws and crack propagation mechanisms.
  
• The measured fracture strengths for brittle
  materials are lower than those predicted by
  theoretical calculations. This difference is
  mainly
• due to presence of very small microscopic flaws
  or cracks already existing within the material.
  The applied stress is amplified around the flaws
  as shown below

The flaws are sometimes called stress raisers due
to their ability to amplify the applied stress in
their locale.
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• If the crack has an elliptical shape and is
  oriented perpendicular to the applied stress,
  then the maximum stress at the crack tip is
  calculated using the equation of

where sm is the maximum stress at the crack tip
s0 is the magnitude of the nominal
applied tensile stress ?t is the radius
of curvature of the crack tip a is the
length of a surface crack or half of the length
of an internal crack
The ratio of sm/ s0 is denoted as the stress
concentration factor Kt
This factor shows the degree to which an external
stress is amplified at the tip of a crack.
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• The effect of stress raiser in brittle fracture
  is more significant than in ductile fracture of
  the materials. In ductile material, the plastic
  deformation indicates the point when maximum
  stress exceeds the yield strength. This causes a
  more uniform distribution of stress in the
  vicinity of the stress raiser. But this does not
  occur in brittle materials.
• The critical stress (sc) required for crack
  propagation in a brittle material can be
  calculated using the equation below

If the magnitude of a tensile stress at the tip
of a flaw exceeds the value of this critical
stress, then acrack forms and then propagates,
which results in fracture
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• Fracture Toughness (Kc) is a measure of materials
  resistance to brittle fracture when a crack is
  present.

sc is the critical stress for crack propagation a
is the crack length Y is a dimensionless
parameter and its value depends on both crack
adn specimen sizes and geometries, and load
application.
Y1
Y1.1
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• For relatively thin specimens, the value of Kc
  depends on the thickness. However, if the
  thickness is much greater than the crack
  dimensions, Kc becomes independent of thickness
  and under these conditions plain strain
  condition exists.
• This means that when a load operates on a crack
  in the manner shown in Figure 9-11a (previous
  slight) , there is no strain component
  perpendicular to the front and back faces.
• Plain strain fracture toughness is calculated by

The subscript of K denotes the plain strain
fracture toughness for mode I crack displacement.
Plain strain fracture toughness is lower for
brittle materials while it is higher for ductile
materials.
KIC is a fundamental material property depending
on many factors, such as, T, strain rate, and
microstructure.
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• The magnitude of KIC decreases with increasing
  strain rate and decreasing T.
• KIC decreases as yield strength is improved by
  solid solution or dispersion additions or by
  strain hardening.
• KIC increases with reduction in grain size.
• DESIGN USING FRACTURE MECHANICS
• There are three variables that must be considered
  for fracture of a component
• The fracture toughness (KC) or plain strain
  fracture toughness (KIC)
• The imposed stress (s)
• The flaw size (a)
• When designing a component first decide which of
  these variables are
• constrained and which are subject to design
  control.

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• Once a combination of two factors is fixed, then
  the third factor is automatically fixed.
• If KIC and a are fixed, then

If stress level and plain strain fracture
toughness are fixed, then the maximum allowable
flaw size is
Sizes of the flaws are measured by nondestructive
tests (NDT).
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Impact Fracture Testing

• There are two standardized tests Charpy and Izod
• The tests are used to measure the impact energy,
  which is also called notch toughness.
• For both of the tests, the specimen is in the
  shape of a bar with square X-section and a
  V-notch is machined.

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The main difference b/w Izod and Charpy is
the manner of specimen support as shown here.
The load is applied as an impact blow from a
weighted pendulum hammer. It is released from a
fixed height (h). Pendulum strikes and fractures
the specimen at the notch. The
pendulum continues its swing rising to maximum
height h. The energy absorption, computed from
the difference between h and h is a measure of
the impact energy.
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• Fracture properties of the materials are defined
  by plane strain fracture toughness and impact
  energy. The later is easier to measure than
  former and there is no correlation between them.
• Ductile to Brittle Transition
• One of the most commonly used areas of Charpy and
  Izod tests is determination of ductile-to-brittle
  transition that a material experiences with
  decreasing temperature.

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• Appearance of the fracture surface is also
  indicative of the transition.

ductile (fibrous)
brittle (shiny)
Transition has both types of surfaces and
corresponds to a temperature range. Metal alloys
with FCC structures (Al and Cu) remain ductile
even at extremely low T. BCC and HCP alloys
experience this transition. The grain size and
microstructure of the materials controls
transition T. Decreasing the grain size lowers
the transition T and increasing C content raises
the CVN transition of the steels.
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• Fatigue
• It is a form of failure occurred when the
  structures are exposed to dynamic and fluctuating
  stresses. Failure as a result of fatigue can
  occur at a stress level lower than the tensile or
  yield strength.
• 90 of the fractures in metallic materials is due
  to fatigue.
• Cyclic stresses Applied stress may be axial
  (tension or compression), flexural (bending) or
  torsional (twisting).
• There are three modes of stress-time
• Regular sinusoidal time dependence and amplitude
  is symmetrical about a mean zero stress level,
  alternating from max. tensile stress to max.
  compressive stress.

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• 2) Repeated stress cycle maxima and minima are
  asymmetrical relative to zero stress level.

3) Random stress cycle
Mean stress Range of stress Amplitude Stress
ratio
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• The S-N Curve
• For testing fatigue, a rotating bending test is
  employed.

The compression and tensile stresses are imposed
on the specimen by bending and rotating
simultaneously. A series of tests is made by
subjecting the specimen to the stress cycles
(cycle between max. and min. stress) and number
of cycles until the failure is counted. Based on
the data obtained S-N curve is plotted.
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• Important observations are made using S-N curves.

The higher the magnitude of the stress, the
smaller the number of cycles before the failure.
For some ferrous and titanium alloys, the S-N
curve becomes horizontal at higher N values and
this is called as fatigue or endurance limit.
Below this limit fatigue failure does not occur.
For many steels, the fatigue limit is between
35 to 60 of the tensile strength. For most
nonferrous alloys, there is no fatigue limit and
there is a continuous decrease in strength for
increasing number of cycles.
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• There is a significant scatter in fatigue data
  leading to significant design
• uncertainities. This is why fatigue data are
  shown on constant
• probability curves. The P value of the curve is
  the probability of failure.

At a stress of 200 MPa, 1 of the specimens to
fail at about 106 cycles and 50 to fail at
about 2x107 cycles. There are two domains in
fatigue behavior. For the short fatigue lives
with high loads, not only elastic but plastic
deformation of the material is observed also.
This domain is called low-cycle fatigue
(N104-105). For long-cycle fatigue, deformations
are totally elastic and longer lives result.
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• Factors Affecting Fatigue Life
• 1)mean stress S-N plot shows the dependence of
  fatigue life to stress amplitude. However mean
  stress also affects the fatigue life.
• As seen, increasing the mean stress level
  decreases the fatigue life.

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• 2) Surface effects In general, the maximum
  stress within a component occurs at the surface
  of the material. Therefore, most cracks originate
  at the surface.
• Fatigue life has been found to be sensitive to
  surface conditions. Many factors influence
  fatigue resistance including design criteria and
  surface treatments.
• Design factors Any notch or geometrical
  discontinuity acts as a stress raiser and fatigue
  crack initiation site. The probability of
  fatigue failure can be reduced by avoiding
  structural irregularities in the design.

Surface treatments Surface markings during
machining can increase the probability of
fatigue failure. The surface finish by polishing
improves fatigue life significantly. One of the
techniques is imposing residual compressive
stresses within a thin outer surface layer to
nullify the syrface tensile stress. Case
hardening is a technique increasing the hardness
and fatigue life of steel alloys. this is
accomplished by carburizing and nitriding process.
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Creep Materials exposed to static mechanical
stresses and high temperatures deform, which is
specifically called as creep. Creep limits the
lifetime of a part and undesirable. It is
observed in all of the materials. For metals, it
becomes important at T greater than about 0.4Tm.
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• A typical creep test consists of subjecting a
  specimen to a constant load or stress while
  maintaining the temperature constant.
• Typical constant load creep behavior of metals

Instantenous deformation is usually elastic.
After this deformation, there are three
stages Primary or transient creep creep rate
diminishes with time. Material resistance to
creep increases and this is same strain
hardening. Secondary or steady state creep rate
of creep is constant. Tertiary creep
acceleration in rate and ultimate failure.
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• The slope of the secondary portion of the creep
  curve is an important parameter. It is called as
  minimum or steady state creep rate (es).
• Time to rupture is also anothe rdesign parameter
  used.
• Stress and Temperature Effects on Creep

• With increasing stress or temperature
• instantenous strain at the time of stress
  application increases
• steady state creep rate is increased
• the rupture lifetime is diminished.

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Creep characteristics of the metals are affected
by melting T, elastic modulus, and grain size.
The higher the melting temperature, the greater
the elastic modulus and the larger the grain
size, the better is a materials resistance to
creep. Smaller grains permit more grain boundary
sliding.