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Fatigue of Materials

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Fatigue of Materials Dr. Richard Chung Department of Chemical and Materials Engineering San Jose State University – PowerPoint PPT presentation

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Title: Fatigue of Materials


1
Fatigue of Materials
  • Dr. Richard Chung
  • Department of Chemical and Materials Engineering
  • San Jose State University

2
Learning Objectives
  • Explain why the fatigue problems are more
    profound in polymers and metals than ceramics and
    composites
  • Describe three stages of a fatigue process in a
    material (crack nucleation, crack growth and
    crack propagation)
  • Discuss how the fatigue crack propagation is
    determined by the relationship between dC/dN
    (crack advance rate) and ?K (cyclic stress
    intensity factor)
  • Design and use a material having ?K is less than
    ?Kth (fail-safe failure mode)
  • Examine and discuss the physical meaning of
    striation formed on the fractured surface and
    determine the crack advance between cycles
  • Determine the conditions of the slow crack growth
    region and fast crack growth region of the
    fractured surface
  • Find the relationship between cyclic stress (or
    strain) amplitude and number of cycles to help
    design fatigue resistant material or applications

3
What is fatigue?
  • An engineering structure is often subjected to
    the repeated application of a stress below its
    yield strength of the material.
  • This cyclical stress may occur in the form of
    rotation, bending, or vibration.

4
Fatigue Testing
  • A common test to measure a materials fatigue
    properties is to use a rotating cantilever beam.
  • A cylindrical beam is mounted in a motor-driven
    chuck with a load applied from the opposite end.
  • A fatigue mode (a sinusoidal cycle) of C-0-T-0 is
    repeatedly applied to the beam.
  • The maximum stress acting on the beam is governed
    by the following equation
  • where l is the length of the beam, P is the
    load, and d is the diameter of the beam.

5
Example 1 A solid tool-steel shaft must be 96
inch long and must survive continuous operation
for one year with an applied force of 12,500
pounds. The shaft is rotating one revolution per
minute during operation. Design a shaft that will
meet these requirements.
  • Solution
  • No. of cycles (1 cycle/min)(60 x 24 x 365min)
    5.256 x 105 cycles/yr.
  • From figure 6-19, the applied stress is around
    72,000psi

6
72,000 psi
7
Example 1 A solid tool-steel shaft must be 96
inch long and must survive continuous operation
for one year with an applied force of 12,500
pounds. The shaft is rotating one revolution per
minute during operation. Design a shaft that will
meet these requirements.
  • Solution
  • No. of cycles (1 cycle/min)(60 x 24 x 365min)
    5.256 x 105 cycles/yr.
  • From figure 6-19, the applied stress is around
    72,000psi
  • d 5.54 inches
  • Add a safety factor to the system
  • d 5.54 x1.05 5.82 inches

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9
Terminology
  • Endurance limit is the stress below which that
    failure by fatigue will never occur, this is a
    preferred design criterion.
  • Fatigue life indicates how long (no. of cycles)
    a component survives a particular stress.
  • Fatigue strength is applicable to a component
    has No endurance limit. It is the maximum stress
    for which fatigue will not occur at a particular
    number of cycles, in general, 500 million cycles.
  • Endurance ratio the endurance limit is
    approximately ½ the tensile strength.

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11
Definitions
12
The difference between Point Stresses (?) and
Nominal Stresses (S)
  • For simple axial loading, ? S 
  • For bending, ? ? S
  • SMc/I where M bending moment, c the
    distance from neutral axis to edge, and I the
    area moment of inertia about the axis.
  • For notched specimen (No yielding), ? Kt?S
  • where Kt elastic stress concentration factor.

13
Stress vs. Life (S-N) Curves
  • An equation can be derived to represent an S-N
    curve

14
A 2b ?f B b
15
Plotting in Linear vs. Logarithmic scales
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20
Three factors are necessary to cause fatigue
failure
  • A maximum tensile stress of sufficiently high
    value
  • A large enough variation or fluctuation in the
    applied stress
  • A sufficiently large number of cycles of the
    applied stress

21
Variables Affecting Fatigue In A Material
  • Stress concentration
  • Corrosion (Environment)
  • Temperature
  • Overload
  • Metallurgical structure (Microstructure)
  • Residual stress (shot peening, presetting)
  • Combined stress
  • Surface condition

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23
Stress Amplitude versus Mean Stress
  • Mean stress effects can be plotted in a diagram
    using stress amplitude versus mean stress.
  • Estimates of mean stress effects for un-notched
    specimens can be determined by Morrow equation or
    SWT equation (Smith, Watson, and Topper)
  • where ?ar equivalent completely reversed stress

24
The Palmgren-Miner Rule
The fatigue failure of a material under a
variable (multiple) amplitude loading is expected
when such life fractions sum to unity. In the
case of creep-fatigue, a fracture criterion will
be defined as
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29
Initiation of Fatigue Cracks
Design based on strength
Fracture Toughness (KIC)
Design based on toughness
Yield Strength (?y)
30
Crack Initiation and Propagation
Nt Ni Np
Ni
Ni of cycles for initiation Np of cycles
for propagation
Maximum Cycle Stress
Ni
Np
Number of Cycles
31
Crack Rate As A Function of The Stress-Intensity
Range (?K)
  • When the length of the crack is small, the growth
    rate of the crack (?a/?N)is also small
  • As the the length of the crack increases, the
    growth rate of the crack (?a/?N) also increases
  • Under identical cyclic loading, larger initial
    cracks propagate to failure in short cycles

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Example A metal strip (4 inch wide and 0.2 inch
thick) is loaded in a cyclic loading ranging from
6,000 to 43,000 lbs. A crack is found located in
the center of the strip that extends through the
thickness. For c 0.1 and 0.4 inch , calculate
?K.
  • Answer
  • Assume the geometry factor F 1

34
The Walker Equation
35
The Forman Equation
  • The R ratio has strong effects on the behavior of
    slow growth rate

36
Fatigue Life
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39
Summary
  • Fatigue failures are often focused on metals and
    polymers.
  • Endurance limit and fatigue life can be used to
    help prevent fatigue in materials
  • When applied stress magnitude increases, the
    number of cycles decreases
  • Materials can fail by fatigue even when they
    contain no cracks
  • A fatigue failure is based on the accumulation of
    fatigue cycles used at low and high cyclic
    stresses
  • A final fractured surface resembles a ductile
    failure pattern which includes three distinct
    stages crack nucleation, crack growth and crack
    propagation.
  • The spacing between the beach marks corresponds
    to the crack advance per cycle in materials.

40
Summary (contd)
  • As long as ?K is less than ?Kth , the crack
    growth rate is not going to increase
  • Using a material at ?K value (less than ?Kth), a
    fail safe fatigue design can be achieved.
  • The slow-crack growth surface in metals is
    generally smooth, unless oxidation or abrasion
    have already developed.
  • The fast-crack region on a fractured surface is
    observed as dull and fibrous resembling a tensile
    ductile failure.
  • Polymers can develop eDCG (shear band cracking
    accompanied by crazing) prior to DCG
    (discontinuous crack growth)
  • Temperature will have great effects on polymer
    and metal fatigue. High frequency of loading
    could yield hysteric heating and thermal
    softening which could significantly reduce the
    fatigue life/endurance limit in a material.
    Creep-fatigue could be a complicated process for
    material failure prediction.
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