Chapter 3
Mechanical Properties of Materials
• Mechanical properties of materials is
about linking the relationship between
stress and strain
• Mechanical Characterization is usually
done through uniaxial stress/strain
experimental characterization
• This behaviour is inherent to the material
Test Specimens
• Need to follow ASTM(or
other) standards
• Concept of engineering
stress/true stress
• σengstress = P/A0
• A0  Original
undeformed area of cross
section
• σtruestress = P/A
• A = deformed area of
cross section
Testing set-up
Stress/strain curve
Testing
Necking
Stress/strain diagram for mild steel
Ductile/brittle behaviour
• A ductile material is subjected to large strains before it
ruptures
• Two measures for ductility
– Percent elongation =((Lf – L0)/ L0)) x (100%)
– For mild steel this value is 38%
– Percent reduction in area = ((A0 – Af)/ A0)) x(100%)
– For mild steel this value is 60%
Concept of offset method for yield
strength
• When yield point is not well defined (☺ ?) 
use 0.2% strain criterion
What about rubber?
• No Yield point
• Non-linear elastic behaviour
Brittle materials
• Exhibit no yielding before failure
Grey Cast Iron
Concrete
• Reinforced with steel to give the tensile resistance
Effect of temperature
Material behaviour
•
Elastic
–
•
•
•
•
linear or nonlinear no permanent deformation
Elastic-plastic permanent deformation --but no rate effects
Visco-elastic  rate sensitive & fading
memory ☺
Visco-plastic  rate sensitive and permanent
deformation
Piezo -electric  Material has electric and
mechanical properties (smart materials, biomaterials )
Some facts about automotive
use in U.S.A
• Employs millions of people
• A vehicle is sold every two seconds – excellent for personal mobility
• Paved area equal to the states of Ohio, Indiana and Pennsylvania,
requiring maintenance costing more than $200 million per day
• Maimed or injured 250 million people and killed more Americans than
have died in all wars in America’s history
• 8 million barrels of oil is used every day
• Creates 7 billion pounds of unrecycled scrap and waste every year
• Emits one-fourth of U.S generation of greenhouse gases so as to
threaten global climatic stability and agriculture
Reference: Natural Capitalism- The next Industrial Revolution; P.
Hawken, A.B. Lovins, L.H Lovins
How about efficiency?
• 80% of the fuel consumption is lost mainly in the
engine’s heat and exhaust
• Of the resulting force 95% is spent on moving
the car and only 5% is spent on moving the
driver
• 1% of fuel consumed is actually used in moving
the passengers
• Need light weight materials !!
• This means understanding of complicated
mechanics of these light weight material
behavior
Linear & Non-linear material
behaviour
• Linear materials are characterized by the
current (at any given instant) behaviour
• Non-linear material behaviour needs to be
characterized by the entire history of
loading
What is a good metric for failure?
• Stress based (Von Mises)
• Strain based
Hooke’s Law
• Linear elastic behaviour leads to:
σ = E ε (Hooke’s law)
• E = Young’s modulus (Thomas Young1807)
• E = (σpl / εpl)
• Typically E = 210 GPa (steel); 70
GPa(aluminium)
Strain Hardening
Strain Energy Density (u)
•
u = (1/2) σε
• u = (1/2) (σ2 / E)
• Modulus of Resilience (ur)
• ur = (1/2) σpl εpl = (1/2) (σ2pl / E)
• Modulus of Toughness 
entire area under the stressstrain curve
Poisson’s Ratio
• εlong = ( δ/L) ; εlat = ( δ’/r)
• Poisson’s ratio γ = - (εlong / εlat)  H.D Poisson (early
1800)
• Typical value ≈ 0.3 [ 0 ≤ γ ≤ 0.5 ]  possible values
Tension
Compression
Shear stress-strain behaviour
• Can be determined by subjecting circular
tubes to torsional loading
• τ = G/ 
• G  Shear modulus of elasticity
• G = ((E /(2(1+ γ)) : γ  POISSON’S RATIO
• Steel : E = 200 GPa ; G = 76 GPa;
Fatigue ☺(not tested in the exams)
• How will you design
the amusement park
rides?
• Damage Tolerance –
This is particularly
significant with
composite materials
Concept of S/N diagram
Summary
• The stress-strain relationships are
extremely important
• Building up this relationship is called
constitutive modeling and is an active
research area around the world
• Constitutive modeling will lead us to
understand and design a wide range of
products