11

Strength and DuctilityStrength and Ductility

22

Determining Tensile Strength from the Determining Tensile Strength from the stress-strain curve is easy. Just locate the stress-strain curve is easy. Just locate the highest point on the curve.highest point on the curve.

TS = 82 ksi

33

Yield strength Yield strength yy is defined as the stress needed is defined as the stress needed

to permanently stretch a tensile specimen so that to permanently stretch a tensile specimen so that the permanent strains is 0.002 (0.2%)the permanent strains is 0.002 (0.2%)

44

Example: Determine the 0.2% yield Example: Determine the 0.2% yield strength of this materialstrength of this material

55

Start by drawing a line from .002 parallel to the Start by drawing a line from .002 parallel to the elastic portion of the stress-strain curveelastic portion of the stress-strain curve

66

This gives the yield strength – about 78 ksi in this This gives the yield strength – about 78 ksi in this casecase

77

When a part is stressed plastically, part of the When a part is stressed plastically, part of the strain is elastic and temporary, part is plastic and strain is elastic and temporary, part is plastic and permanent.permanent.

Permanent strain is .002

Total strain under load is about .0046

88

Example: Determine the true stress and Example: Determine the true stress and strain just before necking occursstrain just before necking occurs

Answer: = 82 ksi just before necking occurs

At this point = 0.014

T = (1+) = 82ksi (1.014) = 83 ksi

T = ln(1+) = ln(1.014) = .0139

99

An edge dislocation appears as an extra half-plane of atoms inserted into the crystal

1010

Edge dislocations appears as black lines in a high magnification

micrograph

51,540X

Dislocation

1111

A screw dislocation is like a tear in the material

Shear force

Shear forceIt is called a screw dislocation because the dislocation causes planes in the lattice to take a helical shape much like the screw thread

Maximum strain energy is concentrated along this line

1212

Movement of Dislocations

Both edge and screw dislocations can move when a shear stress is applied. The “extra plane” of atoms moves gradually through the crystal, much as a caterpillar moves.

1313

The Burgers vector b is a vector with the length and direction that the

dislocation line will move during slip

edge dislocation screw dislocation

1414

Slip system

Burger’s vector Slip plane

Dislocation line

•The Burger’s vector and the dislocation line together form a slip plane

•The Burger’s vector defines the slip direction

The slip direction and the slip plane together form a slip system

1515

Slip occurs preferentially in close-packed directions on close-packed planes

Example: FCC has 4 close packed planes. There are 3 close-packed directions in each plane. 4 planes x 3 directions/plane = 12 possible slip systems in FCC

1616

Slip occurs preferentially in close-packed directions on close-packed planes

BCC has 6 “kind of” close packed planes (the {110} family). There are 2 close-packed directions in each plane. 6 planes x 2 directions/plane = 12 possible slip systems in BCC

Because the planes are not close-packed, slip is not as easy in BCC as in FCC.

1717

Slip occurs preferentially in close-packed directions on close-packed planes

Example: HCP has only 1 set of close-packed planes. There are 3 close-packed directions in this plane. 1 plane x 3 directions/plane = 3 possible slip systems in HCP. Consequently slip is not easy in HCP materials.

1818

Specimens in tension deform most readily when the slip system is at a 45°angle to the

direction of pullExample: Hexagonal Close-packed crystals have one close-packed plane

(0001 plane)

1919

Grains boundaries are zones of atomic disorder between regions of

well-ordered atoms

Well-orderedatoms Zone of disorder Grain Grain

boundary

2020

Slip lines are oriented differently within each grain of this plastically deformed copper sample

Even within crystals, different slip systems can be seen

2121

Plastic deformation alters the grain structure of polycrystalline materials

Before deformation After deformation

2222

The term microstructure refers to the shape and size of grains

1. Polish the surface of the metal

2. Attack it with an acid to preferentially remove material between grains

3. Observe under a microscope, and photograph it.

Microstructure is best observed using a photomicrograph

2323

Linear Grain Size Determination

A

B

C

90X

Each line is 50 mm long in a 90X micrograph

1. Count # of boundaries each line crosses2. Divide by 50 to get grains/mm in the photo3. Multiply by 90 to get true # of grains/mm

2424

Area-based Grain Size Determination

Grain size 6

N = 2n-1

Where: N = number of grains per square inch at 100X n = grain size

Grain size 5 Grain size 4 Grain size 3

The American Society of Testing and Materials (ASTM) provides a standard set of hexagonal grids to be used with 100X photomicrographs

Grains per square inch is given by:

2525

Example: Are the grains in the photo grain size 6?

100X

Grain size 6

N = 2n-1

Where: N = number of grains per square inch at 100X n = grain size

Try to match the hexagon size to the grainsize in the micrograph

2626

Are the grains in the photo grain size 5?

100X

Grain size 5

N = 2n-1

Where: N = number of grains per square inch at 100X n = grain size

2727

Are the grains in the photo grain size 4?

100X

Grain size 4

N = 2n-1

Where: N = number of grains per square inch at 100X n = grain size

2828

Are the grains in the photo grain size 3?

100X

Grain size 3

N = 2n-1

Where: N = number of grains per square inch at 100X n = grain size

2929

Are the grains in the photo grain size 2?

100X

Grain size 2

N = 2n-1

Where: N = number of grains per square inch at 100X n = grain size

3030

A Frank-Read source can generate dislocations

(a) A dislocation is pinned at two ends by lattice defects.

(b) As the dislocation continues to move, it bends.

(c) Dislocation loops back on itself.

(d) A new dislocation is created.

3131

Coldworking increases dislocation density to the point that they start to interfere with each other

3232

Yield Strength, Tensile Strength, and Ductility as Functions of % Cold Work

Yield Strength Tensile Strength Ductility

% Cold Work

MP

a

MP

a

%E

L

ksi

ksi

3333

Recrystallization of cold-worked brass

a) 33% cold-worked brass beforeannealing

b) 3 s at 580°C – onset of recrystallization

c) 4 s at 580°C d) 8 s at 580°C – recrystallization is complete

3434

Recovery Grain growth

Annealing Temperature (deg C)

Effect of annealing on a cold-worked brass

Recrystallizationd

uct

ility

TS

Gra

in s

ize