Plastic Deformation in Single or Polycrystalline Materials

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Plastic Deformation in Single or Polycrystalline
Materials

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

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Learning Objectives

• Explain the deformation mechanisms of plastic
  flow in single and polycrystalline materials
• List factors affecting the plastic deformation
  process in single and polycrystalline materials
• Calculate and interpret the effects of critical
  resolved shear stress in single and poly crystals
• Identify geometrically necessary dislocations
  developed along grain boundaries (in
  polycrystalline)
• Examine slip systems of a material and determine
  most favorable slip system
• Compare the stress-strain relationships between
  single and polycrystalline material

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Plastic deformation in Single Crystals

• Critical resolved shear stress is the driving
  force.
• This stress depends on temperature, strain rate,
  and impurity in material.
• Plastic straining (such as work hardening)
  enables multiple slip ? increases strain rate
• Slip Dislocation interactions may immobilize
  dislocations in a single crystal ? reduces strain
  rate

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Critical Resolved Shear Stress

• m is determined by the slip plane w.r.t. the
  tensile axis

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Schmids Law

• This formula is used to determine the
  relationship between tensile yield strength and
  critical resolved shear stress. (?y gt ?CRSS )
• Except for BCC transition metals, for most of
  the material, ?CRSS is independent of ?y and m

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CRITICAL RESOLVED SHEAR STRESS
Condition for dislocation motion
Crystal orientation can make it easy or
hard to move disl.
?CRSS is the minimum shear stress required to
initiate slip.
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CALCULATE RESOLVED SHEAR STRESS

• Example Compute the resolved shear stress along
  a (110) plane and in a i11 direction when a
  tensile stress of 52 MPa is applied in the 010
  direction of a BCC single crystal iron.
• Answer
• First, we need to calculate the angle ? (between
  110 and 010 ) and the angle ? (i11 and
  010)

Normal to the (110) plane
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The resolved shear stress is 21.3 MPa. Also, if
a critical resolved shear stress is given, then
the yield stress could be calculated accordingly.
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DISLATION MOTION IN POLYCRYSTALS
Slip planes directions (l, f) change from
one crystal to another. tR will vary from
one crystal to another. The crystal with
the largest tR yields first. Other (less
favorably oriented) crystals yield
later.
Adapted from Fig. 7.10, Callister 7e. (Fig. 7.10
is courtesy of C. Brady, National Bureau of
Standards now the National Institute of
Standards and Technology, Gaithersburg, MD.)
300 mm
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If the Slip plane is perpendicular to the Tensile
Stress

• 0o , and ?90o
• cos ? 1 and cos ?0 ? ?CRSS 0
• This means even if the applied tensile stress is
  enormous, the critical resolved shear stress is
  simply zero.
• The dislocations cant move (slip cant occur).

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?CRSS vs. Strain Rate and Temperature
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Factors Affecting ?CRSS

• Increasing temperature decrease ?CRSS
• Increasing strain Rate increase ?CRSS
• In region II, the ?CRSS is not a function of
  temperature and strain rate.
• Increasing impurity increase ?CRSS
• Increasing dislocation density increase ?CRSS

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• For temperature lt 0.77 Tm (Region I and II), the
  critical resolved shear stress can be expressed
  using two terms.
• ?a is the athermal component of stress (long
  range internal stress field) ? is the thermal
  stress (short range inter-atomic spacing)

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Three Stages of Work Hardening in A Shear
Stress-Shear Strain Curve

• Stage I Stage II Stage III
• (no work (linear (exhaustion
• hardening) hardening) hardening)
• ?CRSS
• ?

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Wavy Slip Steps in BCC Iron
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• Why 45o?

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Plastic Flow in Polycrystalline Materials

• Plastic Deformation Mechanisms
• The stress required for plastic flow increases
  with the increase of dislocation density
• Geometrically necessary dislocations help
  transfer stress to the flow stress of plastic
  flow

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Slip Mechanisms

• Slip mechanisms are similar in single and
  polycrystals. The stress-strain behavior differ
  somewhat.
• The slip processes occur within individual
  crystals of polycrystal aggregate
• The strain displacements across grain boundaries
  must match the spacing between individual grains

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Plastic Deformation Mechanisms

• The stress required for plastic flow increases
  with the increase of dislocation density
• Geometrically necessary dislocations help
  transfer stress to the flow stress of plastic
  flow

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Conclusion

• When tRSS (resolved shear stress) reaches a
  critical value the slip system will occur.
• tCRSS is a function of temperature, material
  purity and strain rate
• At region I, the tCRSS increases with decreases
  in temperature and increase in strain rate
• At region II, the tCRSS is independent of
  temperature and strain rate
• At high temperature region (region III) the tCRSS
  decreases when temperature increases and strain
  rate decreases
• Work hardening in single crystals can be divided
  into 3 stages glide and plastic strain,
  dislocation density increases resulting in
  immobilization, strain rate decreases.

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Conclusion (continued)

• Comparing to single crystals, polycrystalline
  requires higher stresses in order to be
  plastically deformed.
• Yielding in BCC metals is temperature dependent,
  whereas FCC metals are not temperature sensitive
• Number of grains and grain size play important
  roles in metal strengthening