Fracture Behavior of Bulk Crystalline Materials

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Fracture Behavior of Bulk Crystalline Materials

• Rices J-Integral
• As A Fracture Parameter
• Limitations
• Ductile-to-Brittle Transition
• Impact Fracture Testing
• Fatigue
• The S-N Curve
• Fatigue Strength
• Creep

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Rices J-Integral

• Parameter which characterizes fracture under
  elastic-plastic and fully plastic conditions
• Similar to the K parameter in fully elastic
  fracture
• Rice defined the J-integral for a cracked body as
  follows
• W elastic strain energy density
• T traction vector
• u displacement vector
• G counter clockwise contour beginning on the
  lower crack surface and ending on any point on
  the upper crack surface

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Rices J-Integral
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Rices J-Integral

• Relation between J and Potential Energy
• under linear elastic conditions, J becomes the
  Griffiths crack extension force.
• Relation is also critical because some
  derivations of J rely on this concept.
• For a body of thickness B

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The J-Integral as a Fracture Parameter

• JIc and J - Da curves
• relationship between J and Da, ductile crack
  length extension, was hypothesized.
• also proposed a physical ductile tearing process
  during different stages of fracture.
• J was only used to specify the onset of ductile
  tearing, point 3 in the figure.
• this point was defined as JIc, the critical J in
  mode I at the onset of ductile tearing.

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The J-Integral as a Fracture Parameter

• JIc is defined at the intersection of the crack
  blunting line and the line which defines the J-
  Da curve.
• crack blunting line is described by
• this construction is necessary because it is
  quite difficult to define this parameter with
  physical detection to a high degree of
  consistency.

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The J-Integral as a Fracture Parameter
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The J-Integral as a Fracture Parameter

• J-dominance
• crack tip conditions are equal for all geometries
  and they are all controlled by the magnitude of
  J.
• large deformation zone (zone of intense
  deformation) can be expected to extend one CTOD
  distance beyond the crack tip
• this zone is surrounded by a larger zone where J
  dominance applies.
• in order for J to be a valid fracture parameter,
  all pertinent length parameters (crack size,
  ligament size, and thickness) all exceed several
  times dt

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Example Calculation of the J-Parameter

• http//risc.mse.vt.edu/farkas/cmsms/public_html/j
  int/cav6.gif
• picture not on website!!

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Limitations of the J-Integral

• nonlinear elasticity or deformation theory of
  plasticity only applies to elastic-plastic
  materials under monotonic loading
• no unloading is permitted
• small deformation theory was used in developing
• path independence of J
• relationship of J with potential energy, crack
  tip stress fields and CTOD
• stresses cannot exceed 10 or ductility will
  occur.

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Ductile-to-Brittle Transition
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Ductile-to-Brittle Transition

• Materials may transition from ductile to brittle
  behavior
• This phenomenon most often occurs in BCC and HCP
  alloys due to a decrease in temperature.
• At low temperatures, materials which experience
  this transition become brittle. This can lead to
  rapid, catastrophic failure, with little or no
  warning.

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Ductile-to-Brittle Transition

• Curve A represents this transition in a steel
  specimen
• The range of temperatures over which this occurs
  as shown in the next slide is approximately 20 to
  80 C

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Impact Fracture Testing

• This temperature range is determined through two
  standardized testing methods
• Charpy impact testing
• Izod impact testing
• These tests measure impact energy through the
  mechanism shown on the next page
• The energy expended is computed from the
  difference between h and h, giving the impact
  energy

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Impact Fracture Testing
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Impact Fracture Testing
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Impact Fracture Testing

• Energy per unit length crack growth

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Fatigue

• Occurs when a material experiences lengthy
  periods of cyclic or repeated stresses which can
  lead to failure at stress levels much lower than
  the tensile or yield strength of the material.
• Fatigue is estimated to be responsible for
  approximately 90 of all metallic failures
• Failure occurs rapidly and without warning.
• The stresses acting repeatedly upon the material
  may be due to
• tension-compression type stresses
• bending or twisting type stresses

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Fatigue

• The average mean stress, or maximum and minimum
  stress values are given by
• Stress amplitude is given by
• sr being the range of stress.
• And the stress ratio of the maximum and minimum
  stress amplitudes
• Note that tensile stresses are positive while
  compressive stresses are always negative

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The S-N Curve

• Data from the tests are plotted as stress S
  versus the logarithm of the number of cycles to
  failure, N.
• When the curve becomes horizontal, the specimen
  has reached its fatigue limit
• This value is the maximum stress which can be
  applied over an infinite number of cycles
• The fatigue limit for steel is typically 35 to
  60 of the tensile strength of the material

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The S-N Curve

• Fatigue testing is performed using a
  rotating-bending testing apparatus shown below.
  Figure 8.18.
• Specimens are subjected to relatively high cyclic
  stresses up to about two thirds of the tensile
  strength of the material.
• Fatigue data contains considerable scatter, the
  S-N curves shown are best fit curves.

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Fatigue Strength

• Fatigue strength is a term applied for nonferrous
  alloys (Al, Cu, Mg) which do not have a fatigue
  limit.
• The fatigue strength is the stress level the
  material will fail at after a specified number of
  cycles (e.g. 107 cycles).
• In these cases, the S-N curve does not flatten
  out.
• Fatigue life Nf, is the number of cycles that
  will cause failure at a constant stress level.

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Creep

• Permanent deformation under a constant stress
  occurring over time
• Three stages of creep
• Primary
• Steady-state
• tertiary
• Testing performed at constant stress and
  temperature
• Deformation is plotted as a function of time

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Creep