Exercice 6

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Exercice 6
1. Elactic interactions between defects
2. Strain hardening mechanisms Single crystal
stress strain curve
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1.1 Interactions between dislocations
Long-range interaction
1. Determine the force acting on (2) due to the
stress field of dislocation (1)
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1.1 Interactions between dislocations
Long-range interaction
Solution
Pure Copper
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1.2 Interactions between dislocations and solute
atoms

• A. Calculate the additional strain energy due to
  the presence of an oversized solute atom in the
  stress field due to a screw dislocation

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1.2 Interactions between dislocations and solute
atoms
Solution
The simplest model to represent a solute atom
(point defect) is a sphere of radius Ra. The
size of the hole. The size of the occupied site.
Oversized defects
Undersized defects
Total volume change of a finite body
Octahedral interstitial site in a BCC crystal
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1.2 Interactions between dislocations and solute
atoms
Stress field due to a screw dislocation
Solution
Stress field in the crystal
Additional strain energy due to the presence of
the point defect
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1.2 Interactions between dislocations and solute
atoms
B. Calculate the additional strain energy due to
the presence of an oversized solute atom in the
stress field due to an edge dislocation
Stress field due to an edge dislocation
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1.2 Interactions between dislocations and solute
atoms
Stress field due to an edge dislocation
Solution
Additional strain energy due to the presence of
the point defect
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2. Strain hardening mechanismsSingle crystal
stress-strain curve
Dislocation cells
Multiple slip
Cross slip
Single slip
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2. Strain hardening mechanismsSingle crystal
rotation
Single slip
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2. Strain hardening mechanisms
How to describe the stage II ?
Approach from continuum mechanics
Have to be identified from experimental curves
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2. Strain hardening mechanisms
How to describe the stage II ?
Approach from physics
Strain hardening is due to forest dislocations
Montreras tu cette loi dans le cours 7 ? Si non
voir T14
Mean free path
?Grain size
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2. Strain hardening mechanisms
How to describe the stage II ?
Approach from physics
Strain hardening is due to forest dislocations
But multislip
And saturation of the strain hardening
Annihilation distance
Grain size
Cell size
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2. Strain hardening mechanisms
One Dislocation
Effect on the crystal deformation
N Dislocations
Orowan relation
Mean glide distance per dislocation mean free
path