4.Mechanical Properties of Metals

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Chapter 3: Mechanical Properties of Metals

0.0100.0080.0060.0040.0020.0000

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200

300

400

500

CONTINUED

Stress(MPa)

Strain


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Mechanical Properties Stiffnessis the ratio of the force required to create a specified

deflection or movement of a part. Elastic Modulus or Youngs Modulus (MPa)

Strength - is defined as the stress at which a predetermined

amount of permanent deformation occurs.

Yield, Ultimate, Fracture, Proof, Offset Yield. Measured asstress (MPa),

Ductility - Measure of ability to deform plastically without

fracture - Elongation, Area Reduction, Fracture Strain - (no units

or mm/mm) Toughness, Resilience - Measure of ability to absorb energy

(J/m3).

Hardness - Resistance to indentation/abrasion (Various scales,

e.g.; Rockwell, Brinell, Vickers.)


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Stress and Strain

In a simplistic sense, stress may be thought

of as Load/Area.

Similarly, strain is the deformation of thecomponent/original length.

A stress may be direct, shear, ortorsional -

leading to corresponding deformations. Stress cannot be measured directly, but

deformation can be.


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Direct Stress Examples

Load, P

P

Area

Ao

Lo

L/2

L/2

Direct Stress - Tension

Load, P

P

AreaAo

Lo

L/2

L/2

Direct Stress - Compression

SP

Ao

e L

Lo

Engineering Stress

Engineering Strain


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Tension Test

Typical Universal

Testing Machine

ExtensometerMeasures L

Measures P


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Modern Materials Testing System

Hydraulic

Wedge

Grips

SpecimenExtensometer


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ASTM Tension Test Specimen

0.505" Dia

2 Gauge Length

Ao=0.20 in2

Lo


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Stressstrain graph for typical metal


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Definition of terms Proportional limit: The greatest stress which a material

is capable of sustaining without deviation fromproportionality of stress and strain (Hooke's Law) or the

point on the stress-strain curve at which stress ceases to

be proportional to strain.

Yield point: the stress at which a predetermined amountof permanent deformation occurs.

Tensile strength: The resistance of a material to a force

tending to tear it apart, measured as the maximum

tension the material can withstand without tearing. Sample break: The point which material breaks.


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Raw Data Obtained

Load,

P(kN)

Elongation, L (mm)

Uniform Deformation

Total Elongation

Elastic

Deformation

X

Maximum

Load, Pmax

Load,

Pf


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Engineering Stress-Strain Curve

Elongation

0.2% offset

yield stress

Proportional Limit

E

E

(Ultimate)

Engineering Strain, e = L/Lo)

Eng

ineeringStre

ss,

S=P/Ao Sy

Su


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Express Load in Newtons (N) and Area in

mm2 to get Stress in MPa.

Mechanical properties of metals are almost

always given in MPa or ksi.

Imperial units: Load in kips (1000 lbf) &

Area as in2 givesStress in ksi (kips/in2)

1000 psi = 1 ksi = 6.89 MPa

N

mm2 MPa


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Hookes Law

Elastic Deformation Elastic deformation is not permanent; it means that when

the load is removed, the part returns to its original shape

and dimensions.

For most metals, the elastic region is linear. For some

materials, including metals such as cast iron, polymers, and

concrete, the elastic region is non-linear.

If the behavior is linear elastic, or nearly linear-elastic,

Hookes Law may be applied:

Where E is the modulus of elasticity (MPa)

S Ee


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Modulus of Elasticity - Stiffness

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500

CONTINUED

Stress

(MPa)

Strain

ESe

(300 0)MPa(0.015 0.0)

2x105MPa


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Atomic Origin of Stiffness

Strongly B onded

Weakly Bonded

NetInteratomicForce

Interatomic Distance

E

dF

dr

ro


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Shear Stress and Strain

Shear Stress,ShearStrain,

shear stress, = Shear Load / Area

shear strain, = angle of deformation (radians)

shear modulus, G = /(elastic region)

ShearStress

Shear Strain


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The force per unit area is referred to as the

shear stress, denoted by the symbol

(Greek letter tau), where

When shear stress is applied, there will be

an angular change in dimension, just asthere is a change in length when materials

are under tension or compression. Shear

strain, denoted by the symbol (Greekletter gamma), is defined by


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Elastic Properties of Materials

Poissons ratio: When a metal is strained inone direction, there are corresponding

strains in all other directions.

For a uniaxial tension strain, the lateral strains are

constrictive.

Conversely, for a uniaxial compressive strain, the

lateral strains are expansive.

i.e.; the lateral strains are opposite in sign to theaxial strain.

The ratio of lateral to axial strains is known as

Poissons ratio, n.


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Poissons Ratio,n

n ex

ez

ey

ezFor most metals,

0.25 < n< 0.35

in the elastic range

Furthermore:

E 2G(1n)


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Plastic Deformation

Stres

s

Strain0.002 0.002 0.002

Sy

Sy

Sy

Elastic Plastic

Most Metals - Al, Cu Clad Al-Alloys Low carbon Steel

Elastic Plastic

Elastic Plastic


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Microstructural Origins of Plasticity

Slip, Climb and Slide of atoms in the crystal structure. Slip and Climb occur at Dislocations and Slide occurs

at Grain Boundaries.


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Elastic and Plastic Strain

Stre

ss

StrainPlastic

Elastic

eeep

P

Total Strain

(e,S)

e ee ep

ee S

Eep e ee

The 0.2% offset yield stress

is the stress that gives a plastic

(permanent) strain of 0.002.


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Elastic Recovery

Strain

Stre

ss

Loading

Unloading Loading

Unloading

Reloading

elastic strainStrain


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Ductility - EL% & AR%

Elongation

Area Reduction

EL%

Lf Lo

Lo x 100

AR% Ao AfAo

x 100

Lo

Ao

Lf

Af


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Ductile Vs Brittle Materials

Only Ductile materials will exhibit necking. Ductile if EL%>8% (approximately)

Brittle if EL% < 5% (approximately)

Enginee

ringStress

Engineering Strain


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Toughness & Resilience

Toughness: A measure of the ability of amaterial to absorb energy without fracture.

(J/m3 or N.mm/mm3= MPa)

Resilience:A measure of the ability of amaterial to absorb energy without plastic or

permanent deformation.

(J/m3

or N.mm/mm3

= MPa) Note: Both are determined as

energy/unit volume


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Toughness, Ut


EngineeringStre

ss,

S=P/Ao

Ut Sdeo

ef

(Sy Su )

2

EL%

100

SuSy


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X

Resilience, Ur


EngineeringStre

ss,

S=P/Ao

Ur Sdeo

ey

Sy ey

2

Sy2

2E

SuSy

E

ey


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Typical Mechanical Properties

Material Yield Stress

(MPa)

Ultimate

Stress (MPa)

Ductility

EL%

Elastic Modulus

(MPa)

Poissons

Ratio

1040 Steel 350 520 30 207000 0.30

1080 Steel 380 615 25 207000 0.30

2024 Al Alloy 100 200 18 72000 0.33

316 Stainless Steel 210 550 60 195000 0.30

70/30 Brass 75 300 70 110000 0.35

6-4 Ti Alloy 942 1000 14 107000 0.36

AZ80 Mg Alloy 285 340 11 45000 0.29

Metals in annealed (soft) condition

4.Mechanical Properties of Metals

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