Dislocations can be prevented from moving in several ways:

1. Pinning: Dislocations can be pinned or obstructed by impurities, precipitates, or other dislocations. This prevents their movement and increases the material's strength.

2. Work Hardening: During plastic deformation, more dislocations are generated which interact with each other and create a 'forest' of dislocations. This makes it harder for individual dislocations to move.

3. Grain Size Reduction: Smaller grain sizes result in more grain boundaries, which act as barriers to dislocation movement.

(i) When dislocation bowing around precipitate particles is the dominant contribution to yield strength, the Orowan equation can be used:

τy = αGb/L

where τy is the yield strength, α is a constant, G is the shear modulus, b is the Burgers vector, and L is the mean spacing of precipitate particles.

(ii) When dislocations cutting through a forest of dislocations is the dominant contribution, the yield strength can be given by:

τy = αGb√ρd

where ρd is the dislocation density.

Additional dislocations can be generated during plastic flow through a process called multiplication or the Frank-Read source. When a dislocation line is pinned at two points and an external stress is applied, a loop of dislocation can be formed and detached. This new loop can then act as a source of more dislocations. This increase in dislocation density leads to strain-hardening of the material, as the increased number of dislocations interact and obstruct each other's movement, making further deformation more difficult.

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Dislocations can be prevented from moving in several ways:

1. Pinning: Dislocations can be pinned or obstructed by impurities, precipitates, or other dislocations. This prevents their movement and increases the material's strength.

2. Work Hardening: During plastic deformation, more dislocations are generated which interact with each other and create a 'forest' of dislocations. This makes it harder for individual dislocations to move.

3. Grain Size Reduction: Smaller grain sizes result in more grain boundaries, which act as barriers to dislocation movement.

(i) When dislocation bowing around precipitate particles is the dominant contribution to yield strength, the Orowan equation can be used:

τy = αGb/L

where τy is the yield strength, α is a constant, G is the shear modulus, b is the Burgers vector, and L is the mean spacing of precipitate particles.

(ii) When dislocations cutting through a forest of dislocations is the dominant contribution, the yield strength can be given by:

τy = αGb√ρd

where ρd is the dislocation density.

Additional dislocations can be generated during plastic flow through a process called multiplication or the Frank-Read source. When a dislocation line is pinned at two points and an external stress is applied, a loop of dislocation can be formed and detached. This new loop can then act as a source of more dislocations. This increase in dislocation density leads to strain-hardening of the material, as the increased number of dislocations interact and obstruct each other's movement, making further deformation more difficult.

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Dislocations can be prevented from moving in several ways:

1. Pinning: Dislocations can be pinned or obstructed by impurities, precipitates, or other dislocations. This prevents their movement and increases the material's strength.

2. Work Hardening: During plastic deformation, more dislocations are generated which interact with each other and create a 'forest' of dislocations. This makes it harder for individual dislocations to move.

3. Grain Size Reduction: Smaller grain sizes result in more grain boundaries, which act as barriers to dislocation movement.

(i) When dislocation bowing around precipitate particles is the dominant contribution to yield strength, the Orowan equation can be used:

τy = αGb/L

where τy is the yield strength, α is a constant, G is the shear modulus, b is the Burgers vector, and L is the mean spacing of precipitate particles.

(ii) When dislocations cutting through a forest of dislocations is the dominant contribution, the yield strength can be given by:

τy = αGb√ρd

where ρd is the dislocation density.

Additional dislocations can be generated during plastic flow through a process called multiplication or the Frank-Read source. When a dislocation line is pinned at two points and an external stress is applied, a loop of dislocation can be formed and detached. This new loop can then act as a source of more dislocations. This increase in dislocation density leads to strain-hardening of the material, as the increased number of dislocations interact and obstruct each other's movement, making further deformation more difficult.

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