‘’DISLOCATIONS AND

STRENGTHENING MECHANISMS’’

IE-114 Materials Science and General Chemistry

Lecture-7

Typical Stress-Strain Curve of Non-Ferrous Alloys (Al, Cu, etc..)

Stress-Strain Curves

Plastic deformation is accomplished by means of a process called SLIP. (motion of dislocation)

Yield point (y) : Point at which dislocations start moving (plastic deformation)

Dislocations

Linear crystalline defects around which there is atomic misalignment

Edge Dislocation Mixed Dislocation Screw Dislocation

Characteristics of Edge Dislocations

There are lattice strains around the dislocation line

Compressive strains above the line (where the atoms are squeezed together)

Tensile strains below the line (where the atoms are pulled apart)

Introduced during solidification, plastic deformation and by thermal stresses

Dislocation Motion

Upon application of shear stresses extra half plane moves from left to right by successive and repeated breaking of bonds.

Shear stress () is needed for dislocation motion

Dislocations move in a preferred plane (the most dense atomic packing)

and directions (the highest linear density)

F

F F

F

Slip Systems

Slip plane is that having the most dense atomic packing, that is, has the

greatest planar density

Slip direction corresponds to the direction, in this plane, that is most closely

packed with atoms, that is, has the highest linear density.

Slip System: the combination of slip plane and slip direction

Slip is favored on close-packed planes since a lower shear stress for atomic

displacement is required. Moreover, slip occurs in close packed directions since

less energy is required to move atoms in these directions

The process by which plastic deformation is produced by dislocation motion

is termed SLIP.

Example: For FCC metals, slip occurs in {111} planes and <110> directions

Slip Systems in Some Crystals

Slip Systems Crystal Structure Number of Slip Systems

Ductility at room temperature:

FCC > BCC > HCP

Metals having highest number of slip systems are quite ductile because

extensive plastic deformation is normally possible along the various systems.

Ductility vs. Number of Slip Systems

Not all of these are

operative at room

temperature

Slip (process of dislocation motion) begins when shear stress ()

on the slip plane in the slip direction reaches a critical value (c).

Stress required to cause slip in single crystals depends on;

1) Crystal Structure (BCC, FCC, HCP,..)

2) Atomic bonding characteristics

3) Temperature of deformation

4) Orientation of the active slip planes with respect to the shear stress

Shear stress is required for plastic deformation

Slip in Single Crystal (Schmid’s Law)

: the angle between the normal to the slip

plane and the applied stress direction

: the angle between applied stress and slip

direction

R: Resolved shear stress

R = Cos Cos

During tension, although, applied stress may be pure tensile, shear components

exist in materials. These are termed resolved shear stress (R)

Schmid’s Law

One slip system which is oriented most favorably, has the largest resolved shear stress

Critical Resolved Shear Stress, crss

Slip (dislocation movement) in a single crystal starts on the most favorably oriented slip

system when the resolved shear stress reaches some critical value

R=

max

= crss

= y (Cos Cos)

max

Max. Resolved Shear Stress, max

Yielding Criteria in Single Crystals

Resolved Shear Stress on different slip systems

Slip Bands and Slip Planes in Single Crystals

Step markings on the surface; SLIP BANDS

Formation of Slip Bands in FCC metals

SLIP LINES

In FCC metals, slip occurs on many slip planes

within the slipbands

The direction of slip varies from one grain to another as a result of random

crystallographic orientations grains.

Slip lines

Plastic Deformation of Polycrystalline Materials

Plastic deformation of a polycrystalline

specimen corresponds to the comparable

distortion of individual grains by means of slip.

Polycrystalline metals are stronger than their

single-crystal equivalents, which means that

greater stresses are required to initiate slip or

for yielding.

Twinning

Plastic deformation mechanism (commonly seen in HCP metals)

A part of the atomic lattice is deformed so that it forms a mirror image of the

undeformed lattice next to it.

Twinning occurs on twin planes and in a specific direction; twin direction

Differences Between Slip and Twinning

1) In slip, the atoms on one side of the slip plane all move equal distances,

whereas in twinning the atoms move distances proportional to their distance

from the twinning plane.

2) Slip leaves a series of steps (lines), whereas twinning leaves small but well-

defined regions of the crystal deformed.

Deformation twins in unalloyed titanium

Slip Twinning

Twinning involves a small fraction of the total volume of the metal crystal, so

that amount of deformation is small

Lattice orientation changes that are caused by twinning may place new

slip systems into favorable orientation with respect to the shear stress

and thus enable additional slip to occur

Twinning is most important for the HCP structure because of its small

number of slip systems

Deformation Twinning occurs in;

HCP metals (Zn, Mg, Ti) at room temperature

BCC metals (Fe, Mo, W, Ta) at very low temperatures

Some BCC metals at room temp. at very high strain rates

The FCC metals show the least tendency to form deformation twins

Plastic deformation corresponds to the motion of large numbers of dislocations. Therefore strengthening of metals relies on this simple principle:

Restricting or hindering dislocation motion renders a material harder and stronger.

The strengthening mechanisms for a single phase metals :

1) Solid solution alloying

2) Strain hardening

3) Precipitation hardening

4) Grain size reduction

Strengthening Mechanisms of Metals

1) Solid Solution Strengthening Alloying the metals with impurity atoms, which is solid solution (interstitial or

substitutional).

High purity metals are always softer and weaker than alloys composed of the

same base metal. This is because the impurity atoms that go into solid solution

impose lattice strains on the surrounding host atoms. Lattice strain between

dislocations and impurity atoms result and dislocation movement is restricted.

• Smaller substitutional impurity • Larger substitutional impurity

Impurity generates local shear at A and B that opposes

disl motion to the right.

Impurity generates local shear at C and D that opposes

disl motion to the right.

INTERSTITIAL SOLID SOLUTION

SUBSTITUTIONAL SOLID SOLUTION

2) Strain (Work) Hardening

Strain hardening is the phenomenon whereby a ductile metal becomes harder

and stronger as it is plastically deformed at room temperature.

Ao Ad

force

die

blank

force

- Drawing

tensile

forceAo

Addie

die

- Forging - Rolling

- Extrusion

Deformation Processes:

Result of Cold Work:

Dislocation density (rd) increases:

Undeformed sample: rd ~ 103 mm/mm3

Heavily deformed sample: rd ~ 1010 mm/mm3

The motion of dislocation is hindered by the presence of other

dislocations, which cause increase in strength value.

Strain hardening increases

Yield strength (y) increases.

Tensile strength (TS) increases.

Ductility (%EL or %AR) decreases.

Hard precipitates are difficult to shear.

Ex: Ceramics in metals (SiC in Iron or Aluminum).

y ~

1

S

3) Precipitation Hardening

Dislocations interact with precipitates

1.5mm CuAl2 precipitates

in Cu-Al alloy

Grain boundaries are barriers to slip (dislocation motion)

Smaller grain size:more barriers to slip.

Fine grained metals are stronger, harder and tougher

yield o kyd1/2

4) Grain Size Reduction

o and ky are constant for a particular material

d : average grain diameter

by rate of solidification from the liquid phase

by plastic deformation followed by appropriate heat treatment.

Hall-Petch Equation

Grain size can be adjusted;

Hall-Petch Equation does not apply to;

(1) extremely coarse and extremely fine grain sizes,

(2) metals used at elevated temperatures

Effect of grain diameter (d) on yield strength:

Grain size reduction by plastic deformation

followed by heat treatment

COLD WORKING (at room temp.) Heating to high temp.

This reheating treatment that softens a cold-worked metal is called annealing

During annealing metal structure will go through a series of changes called

(1) recovery, (2) recrystallization, (3) Grain Growth

1) Recovery

Some fraction of the energy expended in deformation is stored in the metals

as strain energy. During recovery, some of this energy is relieved by dislocation

motion which is the result of enhanced atomic diffusion at elevated temperature.

There will be reduction in the number of dislocations and new dislocation

configurations with low strain energies are produced.

Recovery of metals produces a subgrain structure with low angle grain

boundaries. This recovery process is called polygonization

2) Recrystallization

Recrystallization is the formation of new strain-free and equiaxed grains with

low dislocation densities and they have characteristic of the precold-worked

condition.

The driving force for the formation of new grains is the difference in the internal

energy of strained and unstrained one. Recrystallization of cold-worked material

is used to refine the grain structure.

33% cold

worked

brass

New crystals

nucleate after

3 sec. at 580oC.

Start of recrystallization Complete recrystallization

BRASS ALLOY

The temperature at which recrystallization just reaches completion in 1 h is

called recrystallization temperature. (The recrystallization temperature for the

brass alloy is about 450oC)

* 1/3-1/2 of the absolute melting temperature (K) of the metal or alloy.

X = 1 - exp(-Bt n )

Johnson, Mehl, Avrami, Kolmogorov approach;

X: fraction recrystallized

Increasing the percentage of CW enhances the rate of recrystallization and decreases the T of recrystallization. The rate of crystallization approaches a constant or limiting value at high deformations. This value is reported in the literature as the T of recrystallization.

Temperature of recrystallization depends on;

the amount of prior cold work

initial grain size

composition or purity of the alloy.

Recrystallization Temperature of

Some Pure Metals and Alloys

3) Grain Growth

At longer times, larger grains consume smaller ones. Why?

- Grain boundary area (and therefore energy) is reduced.

Following up recrystallization, strain free grains continue to grow at elevated

temperature.

Grain growth occurs by the migration of grain boundaries. Some of them grow, while the others shrink. Boundary motion is just a short range diffusion of atoms from one side to other.

Grain growth

dn do

n Kt

elapsed time

coefficient dependent on material and T.

grain diam.

at time t.

Exponent(n) typ. ~ 2

Empirical Relation for Grain Growth:

Schematic representation of grain growth

Dislocations are observed primarily in metals and alloys.

The process of dislocation motion is called slip. Slip occurs on planes

having highest planar density (slip plane) and in the direction which has

highest linear density (slip direction)

Particular ways to increase strength are to:

--solid solution strengthening

--precipitate strengthening

--cold work

--decrease grain size

Heating (annealing) can reduce dislocation density and increase grain

size.

Summary

Strength is increased by making dislocation motion difficult.