Engineering Science 1021A/B Lecture Notes - Lecture 12: Burgers Vector, Work Hardening, Tensile Testing
17 May 2018
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Department
Professor
Dislocation: linear imperfections in the crystal lattice
•
Dislocations move on close packed planes and in close packed lines
•
Materials deform by the sliding of planes of atoms over each other
•
Consider the force required to move an atom from position A to B
○
We must break the bond(s) associated with position A and make the bond(s) at B
○
Binding energy and force curves shows us how hard it is to break an atomic bond
○
It is mathematically more difficult because there are many more atoms involved, but
the basic principle remains the same
○
•
Extend that to a whole plane of atoms
○
Force would equal the force required to move one atom multiplied by the number of
atoms on the slip plane
○
•
Instead of breaking and remaking bonds everywhere on the slip plane, they are broken
only along the dislocation line
•
When a dislocation (edge or screw) moves through a crystal, the two halves of the crystal
are displaced by a distance equal to the Burger’s vector
•
Dislocations describe mechanical properties of metallic materials
Yield strength & work hardening rate
○
•
Two types of pure dislocations:
Edge dislocation
○
Screw dislocation
○
•
Slip
The tensile test applied a normal force to a sample that caused elongation
○
In order to move a dislocation there must be a shear force
○
•
Dislocations allow planes to move relative to each other (slip) at much lower stresses•
Slip: the process of moving dislocations by a sufficiently large shear stress acting parallel
to the Burgers vector
•
•
•
There is a minimum or threshold shear stress that must be applied before a dislocation
will move (slip)
Critical resolved shear stress: 𝜏"#$$
○
○
•
Edge Dislocation
An extra half-plane of atoms in a crystal
Are not created this way
○
•
Dislocation line is defined by the gap that is formed at the end of the "extra" plane
Represented by the symbols ⊥& ⊺indicating the location of the extra half-plane
○
•
•
Screw Dislocation
•
•
Burger's Vector
Burger's circuit: a path formed by making an equal number of steps in orthogonal
directions around a dislocation line
•
Burger’s vector: The vector required to close the Burger’s circuit•
Edge Type: Burger’s vector perpendicular to the dislocation line
○
Screw Type: Burger’s vector parallel to the dislocation line
○
•
Dislocation Loops
Dislocation lines are not straight but found as circular loops•
Burger's vector of a single dislocation does not change•
Dislocation Motion & Strain
Each dislocation results in a slip-step when it reaches the edge of the grain.•
The Burger’s vector is equal to one atom spacing (about 0.2nm)•
An extension of 1mm requires more than 7,000,000 dislocations to move through the
crystal
•
Strain Fields Around Dislocations
An edge dislocation has regions of compressive and tensile stress associated with it due to
the distortion in the lattice
Regions of compression (dark) and tension (red) located around an edge
dislocation
§
○
•
Depending on the sense of dislocation (+𝑣𝑒 or −𝑣𝑒) neighbouring dislocations will be
attracted or repelled
Two edge dislocations of the same sign and lying on the same slip plane exert
a repulsive force in each other
§
C & T denote compression and tension
§
○
•
If 2 dislocations of opposite sense are on the same slip plane, they will come together and
annihilate, leaving a perfect crystal
Edge dislocations of opposite sign and lying on the same slip plane exert an
attractive force on each other
§
Upon meeting they annihilate each other and leave a region of a perfect
crystal
§
○
•
Dislocations
Dislocation: linear imperfections in the crystal lattice
•
Dislocations move on close packed planes and in close packed lines
•
Materials deform by the sliding of planes of atoms over each other
•
Consider the force required to move an atom from position A to B
○
We must break the bond(s) associated with position A and make the bond(s) at B
○
Binding energy and force curves shows us how hard it is to break an atomic bond
○
It is mathematically more difficult because there are many more atoms involved, but
the basic principle remains the same
○
•
Extend that to a whole plane of atoms
○
Force would equal the force required to move one atom multiplied by the number of
atoms on the slip plane
○
•
Instead of breaking and remaking bonds everywhere on the slip plane, they are broken
only along the dislocation line
•
When a dislocation (edge or screw) moves through a crystal, the two halves of the crystal
are displaced by a distance equal to the Burger’s vector
•
Dislocations describe mechanical properties of metallic materials
Yield strength & work hardening rate
○
•
Two types of pure dislocations:
Edge dislocation
○
Screw dislocation
○
•
Slip
The tensile test applied a normal force to a sample that caused elongation
○
In order to move a dislocation there must be a shear force
○
•
Dislocations allow planes to move relative to each other (slip) at much lower stresses•
Slip: the process of moving dislocations by a sufficiently large shear stress acting parallel
to the Burgers vector
•
•
•
There is a minimum or threshold shear stress that must be applied before a dislocation
will move (slip)
Critical resolved shear stress: 𝜏"#$$
○
○
•
Edge Dislocation
An extra half-plane of atoms in a crystal
Are not created this way
○
•
Dislocation line is defined by the gap that is formed at the end of the "extra" plane
Represented by the symbols ⊥& ⊺indicating the location of the extra half-plane
○
•
•
Screw Dislocation
•
•
Burger's Vector
Burger's circuit: a path formed by making an equal number of steps in orthogonal
directions around a dislocation line
•
Burger’s vector: The vector required to close the Burger’s circuit•
Edge Type: Burger’s vector perpendicular to the dislocation line
○
Screw Type: Burger’s vector parallel to the dislocation line
○
•
Dislocation Loops
Dislocation lines are not straight but found as circular loops•
Burger's vector of a single dislocation does not change•
Dislocation Motion & Strain
Each dislocation results in a slip-step when it reaches the edge of the grain.•
The Burger’s vector is equal to one atom spacing (about 0.2nm)•
An extension of 1mm requires more than 7,000,000 dislocations to move through the
crystal
•
Strain Fields Around Dislocations
An edge dislocation has regions of compressive and tensile stress associated with it due to
the distortion in the lattice
Regions of compression (dark) and tension (red) located around an edge
dislocation
§
○
•
Depending on the sense of dislocation (+𝑣𝑒 or −𝑣𝑒) neighbouring dislocations will be
attracted or repelled
Two edge dislocations of the same sign and lying on the same slip plane exert
a repulsive force in each other
§
C & T denote compression and tension
§
○
•
If 2 dislocations of opposite sense are on the same slip plane, they will come together and
annihilate, leaving a perfect crystal
Edge dislocations of opposite sign and lying on the same slip plane exert an
attractive force on each other
§
Upon meeting they annihilate each other and leave a region of a perfect
crystal
§
○
•
Dislocations
Dislocation: linear imperfections in the crystal lattice•
Dislocations move on close packed planes and in close packed lines•
Materials deform by the sliding of planes of atoms over each other•
Consider the force required to move an atom from position A to B
○
We must break the bond(s) associated with position A and make the bond(s) at B
○
Binding energy and force curves shows us how hard it is to break an atomic bond
○
It is mathematically more difficult because there are many more atoms involved, but
the basic principle remains the same
○
•
Extend that to a whole plane of atoms
○
Force would equal the force required to move one atom multiplied by the number of
atoms on the slip plane
○
•
Instead of breaking and remaking bonds everywhere on the slip plane, they are broken
only along the dislocation line
•
When a dislocation (edge or screw) moves through a crystal, the two halves of the crystal
are displaced by a distance equal to the Burger’s vector
•
Dislocations describe mechanical properties of metallic materials
Yield strength & work hardening rate
○
•
Two types of pure dislocations:
Edge dislocation
○
Screw dislocation
○
•
Slip
The tensile test applied a normal force to a sample that caused elongation
○
In order to move a dislocation there must be a shear force
○
•
Dislocations allow planes to move relative to each other (slip) at much lower stresses
•
Slip: the process of moving dislocations by a sufficiently large shear stress acting parallel
to the Burgers vector
•
•
•
There is a minimum or threshold shear stress that must be applied before a dislocation
will move (slip)
Critical resolved shear stress: 𝜏"#$$
○
○
•
Edge Dislocation
An extra half-plane of atoms in a crystal
Are not created this way
○
•
Dislocation line is defined by the gap that is formed at the end of the "extra" plane
Represented by the symbols ⊥& ⊺indicating the location of the extra half-plane
○
•
•
Screw Dislocation
•
•
Burger's Vector
Burger's circuit: a path formed by making an equal number of steps in orthogonal
directions around a dislocation line
•
Burger’s vector: The vector required to close the Burger’s circuit•
Edge Type: Burger’s vector perpendicular to the dislocation line
○
Screw Type: Burger’s vector parallel to the dislocation line
○
•
Dislocation Loops
Dislocation lines are not straight but found as circular loops•
Burger's vector of a single dislocation does not change•
Dislocation Motion & Strain
Each dislocation results in a slip-step when it reaches the edge of the grain.•
The Burger’s vector is equal to one atom spacing (about 0.2nm)•
An extension of 1mm requires more than 7,000,000 dislocations to move through the
crystal
•
Strain Fields Around Dislocations
An edge dislocation has regions of compressive and tensile stress associated with it due to
the distortion in the lattice
Regions of compression (dark) and tension (red) located around an edge
dislocation
§
○
•
Depending on the sense of dislocation (+𝑣𝑒 or −𝑣𝑒) neighbouring dislocations will be
attracted or repelled
Two edge dislocations of the same sign and lying on the same slip plane exert
a repulsive force in each other
§
C & T denote compression and tension
§
○
•
If 2 dislocations of opposite sense are on the same slip plane, they will come together and
annihilate, leaving a perfect crystal
Edge dislocations of opposite sign and lying on the same slip plane exert an
attractive force on each other
§
Upon meeting they annihilate each other and leave a region of a perfect
crystal
§
○
•
Dislocations
Document Summary
Dislocations move on close packed planes and in close packed lines. Materials deform by the sliding of planes of atoms over each other. Consider the force required to move an atom from position a to b. We must break the bond(s) associated with position a and make the bond(s) at b. Binding energy and force curves shows us how hard it is to break an atomic bond. It is mathematically more difficult because there are many more atoms involved, bu the basic principle remains the same. Extend that to a whole plane of atoms. Force would equal the force required to move one atom multiplied by the number of atoms on the slip plane. Instead of breaking and remaking bonds everywhere on the slip plane, they are broken only along the dislocation line. When a dislocation (edge or screw) moves through a crystal, the two halves of the crystal are displaced by a distance equal to the burger"s vector.
