The document discusses the mechanical properties of materials when subjected to different types of loading like axial, lateral, and torsional loads. It defines concepts like stress, strain, elastic and plastic deformation. It explains stress-strain diagrams and how they are used to determine properties like modulus of elasticity, yield strength, tensile strength, ductility, toughness, and resilience. Typical stress-strain behaviors of ductile and brittle materials are compared. Examples of determining properties from stress-strain curves are also provided.

1. Mechanical properties
of materials

2. Types of loading
 Axial load “load that act
along the axis of the rod
(tension or compression
members)
 Lateral load “ transverse
load which acting
perpendicular to its axis
(shearing force)
 Torsion “members subject
to equal and opposite
torques T

3. The concept of stresses
 Definition of stresses:
stress is the internal
resistance offered by a
unit area of the material
from which the member
is made to an externally
applied load.
 Stress is the force by
unit area
 σ =force/area= P/A

4.  Normal stress distribution
in axially loaded member is
uniform.
 Application of normal
stresses
1. Bridge truss which consist
of two force members that
may be in tension or
compression
2. A rod supporting a heavy
load that tend to pull the
rod with tension force
3. Short blocks supporting
heavy loads that tend to
crush them with
compressive forces

5. Units of stresses
 SI metric units
Load p expressed in Newton (N) and A in square
meters (m2) so σ will be expressed in N/ m2 “pascal”
(Pa)
1KPa =103 Pa=103 N/ m2
1Mpa =106Pa=106 N/ m2
1GPa =109Pa=109 N/ m2
U.S units
Load p expressed in pounds (Ib) or kilopounds (Kip)
and A in square inches (in2) so σ will be expressed in
pound/square inch (Psi) or kilopounds per square
inch (Ksi)

6. Stress & strain : axial loading
 Deformation which caused by the load applied
to a structure is very important aspect of
analysis and design.
 Suitability of a structure or machine may
depend on the deformations in the structure as
well as the stresses induced under loading.
Statics analyses alone are not sufficient.
 Determination of the stress distribution within
a member also requires consideration of
deformations in the member

7. Normal strain

8. Mechanical properties of metals
 Stress - 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)
 Elasticity: ability of materials to retune to its original shape
&size after removing the load.
 Plasticity: ability of materials to keep the deformation after
removing the load.
 Stiffness: ability of materials to resist a deformation within
the linear range


9. Stress- strain test

10. Stress- strain diagram , brittle
materials

11. Tensile properties : ductility
EL% 
Lf  Lo
Lo
x 100
 Elongation
 Area reduction
AR% 
Ao  Af
Ao
x 100
EL% 
Lf  Lo
Lo
x 100

12. Stiffness Hooke’s Law
Elastic Deformation
 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:
 σ=E Ɛ
Where E is the modulus of elasticity, the property which
expressed to stiffness of materials

13. Mechanical properties of
metals
How do metals respond to external loads?
Stress& strain
Elastic deformation.
Plastic deformation.

14. • Typical tensile specimen
9
• Other types of tests:
--compression: brittle
materials (e.g., concrete)
--torsion: cylindrical tubes,
shafts.
• Typical tensile
test machine
Adapted from Fig. 6.2,
Callister 6e.
Adapted from Fig. 6.3, Callister 6e.
(Fig. 6.3 is taken from H.W. Hayden,
W.G. Moffatt, and J. Wulff, The
Structure and Properties of
Materials, Vol. III, Mechanical
Behavior, p. 2, John Wiley and Sons,
New York, 1965.)
STRESS-STRAIN TESTING

15. Raw Data Obtained
Load,
P
(kN)
Elongation, DL (mm)
Uniform Deformation
Total Elongation
Elastic
Deformation
X
Maximum
Load, Pmax
Load,
Pf

16. Engineering Stress-Strain Curve
Elongation
0.2% offset
yield stress
Proportional Limit
E
E
(Ultimate)
Engineering Strain, e = DL/Lo)
Engineering
Stress,
S=P/Ao
Sy
Su

17. Stress-strain behavior

18. Elastic behavior
 In brittle materials
 Non linear elastic
behavior
 In ductile materials
 Linear elastic behavior

19. 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

20. Elastic properties of materials
 Poisson’s ratio:
When a metal is
strained in one
direction, there are
corresponding
strains in all other
directions.
  
ex
ez
 
ey
ez
For most metals,
0.25 <  < 0.35
in the elastic range

21. Stress-strain behavior
 Elastic deformation
 Reversible: when the stress is
removed, the material returns to
the dimension it had before the
loading. Usually strains are small
(except for the case of plastics).
 Plastic deformation
 Irreversible: when the stress
 is removed, the material
 does not return to its
 previous dimension.

22. Elastic Recovery
Strain
Stress
Loading
Unloading
Loading
Unloading
Reloading
elastic strain
Strain

23. Elastic and Plastic Strain
(σ,Ɛ)
Stress
Strain
Plastic
Elastic
Ɛe
Ɛp
P
Total Strain
The 0.2% offset yield stress
is the stress that gives a plastic
(permanent) strain of 0.002.
Ɛ=Ɛe+Ɛp
Total strain =
elastic strain + plastic strain
Ɛe= σ/E
Ɛp=Ɛ- Ɛe

24. Tensile properties: Yielding
 Yield strength σy - is chosen
as that causing a permanent
strain of 0.002
 Yield point P - the strain
deviates from being
proportional to the stress (the
proportional limit)
 The yield stress is a measure
of resistance to plastic
deformation

25. Tensile properties: Yielding
 For a low-carbon steel,
the stress vs. strain
curve includes both an
upper and lower yield
point.
The yield strength is
defined in this case as
the average stress at
the lower yield point.

26. Tensile Strength
 For structural applications,
the yield stress is usually a
more important property
than the tensile strength,
since once the it is passed,
the structure has deformed
beyond acceptable limits

27. Ductility
EL% 
Lf  Lo
Lo
x 100
 Ductility is a measure
of the deformation at
fracture
 Define as elongation
percent or reduction in
area

EL% 
Lf  Lo
Lo
x 100
AR% 
Ao  Af
Ao
x 100

28. Ductile Vs Brittle Materials
 Only Ductile materials will exhibit
necking.
 Ductile if EL%>8% (approximately)
 Brittle if EL% < 5% (approximately)
Engineering
Stress
Engineering Strain

29. Energy
 Energy absorbed during loading
 Elastic energy
 Total energy until fracture

30. 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

31. Toughness, Ut
Engineering Strain, Ɛ = DL/Lo)
Engineering
Stress,
σ=P/Ao
σ u
σ y
Ut = ʃσ dƐ
Ut = σy+ σu (El%)
2 100

32. Resilience, Ur
Engineering Strain, Ɛ = DL/Lo)
Engineering
Stress,
σ=P/Ao
σ u
σ y
E
Ɛ y
Ur = area under elastic
zone

33. 25
• Compare to responses of other polymers:
--brittle response (aligned, cross linked & networked case)
--plastic response (semi-crystalline case)
Stress-strain curves
adapted from Fig.
15.1, Callister 6e.
Inset figures along
elastomer curve
(green) adapted from
Fig. 15.14, Callister
6e. (Fig. 15.14 is from
Z.D. Jastrzebski, The
Nature and Properties
of Engineering
Materials, 3rd ed.,
John Wiley and Sons,
1987.)
Stress strain curves for polymers
(Elastomers)

34. • Energy to break a unit volume of material
• Approximate by the area under the stress-strain
curve.
21
smaller toughness-
unreinforced
polymers
Engineering tensile strain, 
Engineering
tensile
stress, 
smaller toughness (ceramics)
larger toughness
(metals, PMCs)
TOUGHNESS

35. What are the limits (safe )of
deformation
 Design stress
Is the calculated stress
level and a design
factor used to
protect against
unanticipated failure.

36. Example problem
Determine the mechanical properties for metal which have the
stress-strain curve as shown If the specimen of this materials is
stressed to 300 MPa , determine the permanent strain that remains in the
specimen when the load is released.

37.  The elastic modulus is the slope in the linear elastic
region
For the yield strength, the 0.002 strain offset line is
drawn dashed. It intersects the stress-strain curve at
approximately 285 MPa

38.  (d) The tensile strength is approximately 370
MPa, corresponding to the maximum stress on
the complete stress-strain plot.
 If the gauge length (L0) = 12 cm , the length at
fracture (Lf) = 16 cm, original diameter (d0)= 12
mm, the diameter at fracture (df) = 8mm.
Then the ductility =

39. Example 2.
From the tensile stress- strain behavior for brass
specimen shown in figure. Determine the following
1 the modulus of elasticity
2 the yield strength at strain offest 0f 0.002
3 the maximum load that can be sustained by a
cylindrical specimen having an original diameter of
12.8 mm.
4 the change in length of a specimen originally 250 mm
long that is subjected to a tensile strength of 345 MPa

41. To compute the change in the length , it is first necessary to determine the
strain that is produced by the stress of 345 MPa from the curve which is equal
to 0.06 so the change in length = 0.06 x250mm =15 mm