Mechanical Properties

Lecture 9

Elastic & plastic deformation

Stress-Strain curve

Ductility, Toughness, Hardness

What we learned

Economic Price & Availability Recyclability

General Physical Density

Mechanical Modulus (Stiffness) Yield and Tensile Strength Hardness Fracture Toughness Fatigue Strength Creep Damping

Thermal Thermal Conductivity Specific Heat Thermal Expansion Coefficient

L0

L

F F

LawsHookeE

ndeformatioElastic

'

Tensile testing The material’s response to the applied tensile or compressive load is a change in

length (and cross-sectional area).

We can monitor the change in length very precisely with an instrument called

an extensometer.

L0

L

F F

0LLL

strain

Pastress

lengthinitialL

extensionlengthinchangeL

mareainitialA

NloadforceF

0

2

0

/

/ tensile test of annealed Cu x20 tensile test of annealed Cu x5 (necking)

00 L

L

A

F

Stress-strain curve Stress-strain curves are an extremely important

graphical measure of material’s mechanical properties

Elastic Modulus (Stiffness)

Yield Strength

Tensile Strength

Strain at Failure

Hardness

Fracture Toughness

Ductility

Elastic Behaviour Initially, stress and strain are directly proportional to each other.

Hooke’s Law:

E - Modulus of Elasticity is the slope of the linear part of the stress-strain curve.

It quantifies the stiffness of a material. Deformation is elastic, and reversible.

L0

L

F F

LawsHookeE

L

L

A

F

'

0

0

σ (

MPa

)

ε (%)

Gradient = E

E

Proportional Limit Point P: Proportional (Elastic) Limit is the point where the stress-strain curve

becomes nonlinear (the strain not proportional to the stress).

The stress and strain values at this point are known as the proportional-limit stress (σp)

and strain (εp), respectively. Beyond this point Hooke's law can no longer be used.

Elastic vs. Plastic Deformation After the elastic deformation, material starts to deform plastically (permanently).

Plastic deformation: deformation is not reversible.

Deformation occurs by breaking and re-arranging of atomic bonds

(movement of dislocations)

Yield Point When the plastic deformation begins, material starts to yield (permanent deformation).

Point Y: Yield Point : yield stress (σy) and strain (εy)

Although the yield and the proportional limit points are close to each other, they do not correspond to the same location on the stress-strain curve.

Some materials (like low-carbon steel) have 2 yield points on the stress-strain curve: lower and upper. Lower yield point is always used.

Mechanical Behaviour As stress increases, the plastic deformation continues...

Point M: Maximal Point on the stress-strain curve: ULTIMATE TENSILE STRESS (UTS)

In practical applications, we are usually more interested in yield stress than UTS,

because we want to use the material which will resist plastic deformation during usage.

At UTS point, necking occurs.

The cross-sectional area is narrowing (A < A0).

Force increases more, but stress is calculated

using A0 so it seems to decrease.

Eventually the specimen breaks.

Point F: Failure Point: failure strength (σf)

and strain at failure (εf)

Engineering Stress vs. True Stress Since the actual cross-sectional area is reduced, use of the initial area gives a lower

value than the actual one (we are dividing with a bigger value).

Even though the true stress-strain curve gives a more accurate picture of the breaking

strength of a material, it is difficult to obtain measurements of the actual area in real-

time. Usually, the reported values are the engineering stress.

True fracture strength ( ) > tensile strength ( )

A < A0

σreal = F / A

σeng = F / A0

Example

Modulus of Elasticity?

GPaMPa

EP

P 75002.0

150

0

0

Change in length at 345 MPa (L0 = 250mm)

Yield Strength? For many materials σy is located using 0.002 strain offset method 1. Find 0.002 strain point on X-axis 2. Draw a line parallel to the stress-strain

curve in the elastic region 3. Find intercept with stress-strain curve σy = 250 MPa

Maximum load sustained by a cylindrical specimen (d = 12.8mm)

kN

mMPaF

AFA

FUTSUTS

88.574

108.12450

23

max

0max

0

max

mmLLL

mmmmLLL

L

MPa

AA

AAA

A

AA

26515250

1525006.0

06.0345

0

0

0

Ductility

Ductility measures the amount of plastic deformation that material goes through by

the time it breaks.

Ductility is a measure of how much strain a given stress produces.

Two measures of ductility:

Percent Elongation

Percent Reduction in Area

ductile metals can exhibit significant strain before fracturing.

brittle materials frequently display very little strain.

%100%

lenghtInitial

lenghtInitiallenghtFinalEl

%100%

areaInitial

areaFinalareaInitialRA

Toughness

Toughness describes material's ability to absorb energy before fracture.

On a stress-strain curve toughness is the area under the curve up to fracture.

Larger area → Tougher material

Example A cylindrical metal specimen with an original diameter of 12.3 mm and gauge length

of 50.80 mm is pulled in tension until fracture occurs. The diameter at the point of

fracture is 6.60 mm, and the fractured gauge length is 72.14 mm. Calculate the ductility

in terms of percent reduction in area and percent elongation.

%01.42%10080.50

80.5014.72%

%100%

El

lenghtInitial

lenghtInitiallenghtFinalEl

%21.71%1003.12

60.63.12%100

4

3.12

4

60.6

4

3.12

%

%100%

2

22

2

22

RA

areaInitial

areaFinalareaInitialRA

Hardness

Hardness is a measure of material's resistance to localised plastic deformation.

As a quality: Mohr’s scale (ability of a material to scratch another material)

From 1-softest (talk) to 10-hardest (diamond)

As a quantity: different types of hardness tests

• Rockwell

• Brinell

• Wickers

Hardness tests

A small indenter is forced into the surface of a material under controlled magnitude

and rate of loading, and hardness is estimated from the depth or size of the indent.

• Rockwell (hardened steel ball or diamond cone; depth)

• Brinell (hardened steel ball; diameter)

• Vickers (diamond pyramid; size)

Popular: easy, quick & non-destructive