Mechanical Properties of Metals

0.0100.0080.0060.0040.0020.0000

100

200

300

400

500

CONTINUED

Stre

ss (M

Pa)

Strain

Mechanical Properties• Stiffness - Elastic Modulus or Young’s Modulus (MPa)• Strength - Yield, Ultimate, Fracture, Proof, Offset Yield.

Measured as stress (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.)

Stress and Strain• In a simplistic sense, stress may be thought of

as Load/Area.• Similarly, strain is the deformation of the

component/original length.• A stress may be direct, shear, or torsional -

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

deformation can be.

Direct Stress ExamplesLoad, P

P

Area Ao

Lo

L/2

L/2

Direct Stress - Tension

Load, P

P

Area Ao

Lo

L/2

L/2

Direct Stress - Compression

S PAo

e LLo

Engineering Stress

Engineering Strain

Tension Test

Typical Universal Testing Machine

ExtensometerMeasures L

Measures P

Modern Materials Testing System

HydraulicWedge Grips

SpecimenExtensometer

ASTM Tension Test Specimen

0.505" Dia

2” Gauge Length

Ao=0.20 in2

Lo

Raw Data ObtainedLo

ad, P

(kN

)

Elongation, L (mm)

Uniform DeformationTotal Elongation

ElasticDeformation

X

Maximum Load, Pmax

Load, Pf

Engineering Stress-Strain CurveElongation

0.2% offset yield stress

Proportional Limit

E

E

(Ultimate)

Engineering Strain, e = L/Lo)

Engi

neer

ing

Stre

ss, S

=P/A

o Sy

Su

Duke’s Quick Tip!

• 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 gives Stress in ksi (kips/in2)

• 1000 psi = 1 ksi = 6.89 MPa

Nmm2 MPa

Hooke’s 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, Hooke’s Law may be applied:

• Where E is the modulus of elasticity (MPa)S Ee

Modulus of Elasticity - Stiffness

0.0100.0080.0060.0040.0020.0000

100

200

300

400

500

CONTINUED

Stre

ss (M

Pa)

Strain

E Se

(300 0)MPa(0.015 0.0)

2x105 MPa

Atomic Origin of Stiffness

Strongly Bonded

Weakly Bonded

Net

Inte

rato

mic

For

ce

Interatomic Distance

E dFdr

ro

Shear Stress and Strain

Shear Stress, Shear Strain,

shear stress, = Shear Load / Areashear strain, = angle of deformation (radians)shear modulus, G = /(elastic region)

GShea

r Stre

ss

Shear Strain

Elastic Properties of Materials• Poisson’s ratio: When a metal is strained in

one 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 the axial strain.

• The ratio of lateral to axial strains is known as Poisson’s ratio, .

Poisson’s Ratio,

ex

ez

ey

ezFor most metals, 0.25 < < 0.35in the elastic range

Furthermore:

E 2G(1 )

Plastic DeformationSt

ress

Strain0.002 0.002 0.002

Sy

Sy

Sy

Elastic Plastic

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

Elastic PlasticElastic Plastic

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.

Elastic and Plastic StrainSt

ress

StrainPlastic

Elasticeeep

P

Total Strain

(e,S) e ee ep

ee SE

ep e ee

The 0.2% offset yield stressis the stress that gives a plastic(permanent) strain of 0.002.

Elastic Recovery

Strain

Stre

ss

Loading

Unloading

Loading

Unloading

Reloading

elastic strainStrain

Ductility - EL% & AR%

• Elongation

• Area Reduction

EL% L f Lo

Lo x 100

AR% Ao A f

Ao x 100

Lo

Ao

Lf

Af

Ductile Vs Brittle Materials• Only Ductile materials will exhibit necking.• Ductile if EL%>8% (approximately)• Brittle if EL% < 5% (approximately)

X

XXA

B C

XD Brittle DuctileA & B C & D

Engi

neer

ing

Stre

ss

Engineering Strain

Toughness & Resilience

• Toughness: A measure of the ability of a material to absorb energy without fracture. (J/m3 or N.mm/mm3= MPa)

• Resilience: A measure of the ability of a material to absorb energy without plastic or permanent deformation. (J/m3 or N.mm/mm3= MPa)

• Note: Both are determined as energy/unit volume

Toughness, Ut

Engineering Strain, e = L/Lo)

Engi

neer

ing

Stre

ss, S

=P/A

o

X

Ut S deo

e f

(Sy Su )

2EL%100

SuSy

X

Resilience, Ur

Engineering Strain, e = L/Lo)

Engi

neer

ing

Stre

ss, S

=P/A

o

Ur S deo

e y

Sy ey

2

Sy

2

2E

SuSy

E

ey

Typical Mechanical Properties

Material Yield Stress(MPa)

UltimateStress (MPa)

DuctilityEL%

Elastic Modulus(MPa)

Poisson’sRatio

1040 Steel 350 520 30 207000 0.301080 Steel 380 615 25 207000 0.302024 Al Alloy 100 200 18 72000 0.33316 Stainless Steel 210 550 60 195000 0.3070/30 Brass 75 300 70 110000 0.356-4 Ti Alloy 942 1000 14 107000 0.36AZ80 Mg Alloy 285 340 11 45000 0.29

Metals in annealed (soft) condition