MSE 3300-Lecture Note 11-Chapter 07 Dislocation and Strengthening Mechanisms

8/18/2019 MSE 3300-Lecture Note 11-Chapter 07 Dislocation and Strengthening Mechanisms

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MSE 3300 / 5300 UTA Spring 2015 Lecture 11 -

Lecture 11. Dislocations andStrengthening Mechanisms (1)Learning Objectives

After this lecture, you should be able to do the following:

1. Understand how plastic deformation occurs by the motion of

dislocations in response to applied shear stresses.

2. Understand slip systems: slip plane and slip direction

3. Describe slip in single crystals: resolved shear stresses

Reading

• Chapter 7: Dislocations and Strengthening Mechanisms (7.1–7.7)

Multimedia

• Virtual Materials Science & Engineering (VMSE):

http://www.wiley.com/college/callister/CL_EWSTU01031_S/vmse/

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1. Elastic Deformation• Elastic deformation is nonpermanent: when the applied load is released, the

piece returns to its original shape (not breaking atomic bonds).

• Hooke’s Law

E [Pa]: Modulus of elasticity, or Young’s modulus

2

Linear elastic deformation Nonlinear elastic deformation


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2. Plastic Deformation• Plastic deformation is irreversible.

• Elastic deformation of metals: up to strain of about 0.005

• Beyond this point, the stress is no longer proportional to strain, and plastic

deformation occurs.

• Breaking of bonds with original atom neighbors and reformation of bonds with

new neighbors.

3

Mechanisms

• Crystalline solids: slip

(Section 7.2)

• Noncrystalline solids:

viscous flow mechanism

(Section 12.10)


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MSE 3300 / 5300 UTA Spring 2015 Lecture 11 - 4

Elastic means reversible!

Elastic Deformation

2. Small load

F

δ

bondsstretch

1. Initial 3. Unload

return to

initial

F

δ

Linear-

elasticNon-Linear-elastic


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Plastic means permanent!

Plastic Deformation (Metals)

F

δ

linearelastic

linearelastic

δ plastic

1. Initial 2. Small load 3. Unload

planes

stillsheared

F

δ elastic + plastic

bonds

stretch& planesshear

δ plastic


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(at lower temperatures, i.e. T < T melt /3)

Plastic (Permanent) Deformation

• Simple tension test:

engineering stress,σ

engineering strain, e

Elastic+Plasticat larger stress

e p

plastic strain

Elasticinitially

Adapted from Fig. 6.10 (a),

Callister & Rethwisch 9e.

permanent (plastic)after load is removed


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1. Dislocations and Plastic Deformation

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• Two fundamental dislocation types: (1)

edge dislocation and (2) screw

dislocation

• Plastic deformation corresponds to themotion of large numbers of dislocation.


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Dislocation Motion: Edge Dislocation

Dislocation motion and plastic deformation

• Metals - plastic deformation occurs by slip: an edge dislocation (extra

half-plane of atoms) slides over adjacent plane half-planes of atoms.

• Slip: the process by which plastic deformation is produced bydislocation motion

• If dislocations can't move, plastic deformation doesn't occur!


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Dislocation Motion: Edge Dislocation

• Formation of a step on the surface of a crystal by the motion of an edge

dislocation


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Dislocation Motion: Screw Dislocation

• Formation of a step on the surface of a crystal by the motion of a screw

dislocation


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2. Slip Systems

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• Slip system: (1) slip plane and (2) slip direction

• Dislocations do not move with the same degree of ease on all crystallographic

planes of atoms and in all crystallographic directions.

• There is a preferred plane (slip plane) in that plane there are specificdirections (slip direction) along which slip occurs.

• Slip system: the atomic distortion that accompanies the motion of a

dislocation is a minimum.

(1) Slip plane: greatest planar density (densest atomic packing)

(2) Slip direction: highest linear density (most closely packed with atoms)

• A {111} slip system

shown within an FCC unit

cell• 12 slip systems (FCC): 4

unique {111} planes and 3

independent

directions within each plane


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Slip System

– Slip plane - plane on which easiest slippage occurs

• Highest planar densities (and large interplanar spacings)

– Slip directions - directions of movement• Highest linear densities

Slip Systems

Fig. 7.6, Callister &

Rethwisch 9e.

– FCC Slip occurs on {111} planes (close-packed) in directions (close-packed)

=> total of 12 slip systems in FCC

– For BCC & HCP there are other slip systems.


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Single Crystal Slip


Rethwisch 9e.


Rethwisch 9e.(From C. F. Elam, The

Distortion of Metal Crystals,

Oxford University Press,

London, 1935.)


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Table 7.1: Slip Systems

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• FCC and BCC: ductile (extensive plastic deformation is possible along the

various systems.

• HCC: brittle

• Direction of Burgers vector: Slip direction


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• Resolved shear stress:

• One slip system is generally oriented in a way

that it has the largest resolved shear stress

τ R(max).

3. Slip in Single Crystals

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• Resolved shear stress:

• Slip commences on the most favorably oriented

slip system when τ R, or τ R(max), reaches the

critical resolved shear stress τ crss

: it represents

the minimum shear stress required to initiate slip

(or yielding).

• The single crystal plastically deforms or yields

when τ R(max) = τ crss and the stress required toinitiate yielding (i.e., the yield strength y) is

3. Slip in Single Crystals

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Stress and Dislocation Motion

• Resolved shear stress, τ R – results from applied tensile stresses

slip plane

normal, ns

Resolved shear

stress: τ R =F s/ As

AS

τ R

τ R

F S

Relation betweenσ and τ R

τ R =F S/ AS

F cos λ A/cosϕ

λF

F S

ϕnS

AS A

Applied tensile

stress: = F / Aσ

F A

F


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• Condition for dislocation motion:

• Ease of dislocation motion depends

on crystallographic orientation 10-4 GPa to 10-2 GPa

typically

Critical Resolved Shear Stress

maximum at = = 45º

τ R = 0

λ= 90°

σ

τ R = σ /2

λ = 45°

ϕ= 45°

σ

τ R = 0

ϕ= 90°

σ


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Ex: Deformation of single crystal

So the applied stress of 45 MPa will not cause the

crystal to yield.

= 35°

= 60°τ crss = 20.7 MPa

a) Will the single crystal yield?

b) If not, what stress is needed?

σ = 45 MPa

Adapted from

Fig. 7.7,

Callister &

Rethwisch 9e.


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Summary

1. Dislocation and plastic deformation

2. Slip systems: (1) slip plane and (2) slip direction

3. Slip in single crystals: resolved shear stresses

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Homework 5

• 6.4, 6.7, 6.10, 6.13, 6.14

• 6.15, 6.26, 6.30, 6.53, 6.D1

* Problems from Callister, 9th Edition

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MSE 3300-Lecture Note 11-Chapter 07 Dislocation and Strengthening Mechanisms

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