PROPERTIES
RELATED TO
STRENGTH
 Strength is the ability of a material to resist
applied forces without yielding or fracturing.
 Strength of a material may change considerably
with respect to the way it is deformed.
 Mode of stress, type of stress & rate of stress
application may affect the strength of a
material.
 Strength data are usually obtained from lab.
Tests which are performed under strictly
standardized specimens under controlled
conditions. These tests also serve for obtaining
σ-ε relationships.
 σ-ε curves can be grouped into three as:
• Ductile Materials → exhibit both elastic &
plastic behavior
• Brittle Materials → exhibit essentially elastic
behavior
• Viscoelastic Materials → exhibit large elastic
deformation
SPECIAL FEATURES OF STRESS-STRAIN
DIAGRAMS
D
σU
σF
σY
σE
σPL
E
C
A B
Point A (Proportional Limit): The greatest stress
(σPL) that can be developed in the material
without causing a deviation from the law of
proportionality of stress to strain. In other
words it is the stress upto which the material
responds following Hooke’s Law.
Point B (Elastic Limit): Maximum stress (σE) that
can be developed in a material without
causing permanent deformation. In other
words it is the stress upto which the
deformations are recoverable upon unloading.
Point C (Yield Point): The stress at which the
material deforms appreciably without an
increase in stress. Sometimes it can be
represented by an upper and lower yield
points. σY,U represents the elastic strength of
the material and σY,L is the stress beyond
which the material behaves plastically.
Point D (Ultimate Strength): It is the maximum
stress that can be developed in a material as
determined from the original X-section of the
specimen.
Point E (Fracture Strength): The stress at which the
material breaks, fails.
 In an engineering σ-ε plot the original area
(A0) & length (l0) are used when determining
stress from the load and strain from
deformations.
 In the true σ-ε plot instantaneous area &
length are used.
 The true values of stress & strain for
instantaneous area & length of the specimen
under tension will differ markedly, particularly
close to the breaking point where reduction in
cross-section & elongation of the specimen are
observed.
P
E 
A0
P
T 
Ai
 true
&

E 
l0
Engineering
&

T 
li
True
 li 
dl
   ln  
l
 l0 
l0
li
 eng
li
dl 1
 
l
l0
l0 0
 true  ln 1   eng 
li
l0
li  l 0 li

 1
l0
l0
For εeng ≤ 0.1 → ln(1+0.1) ≈ 0.1
 For small strains εtrue ≈ εeng

 true
P

Ai
&
 eng
P

A0
If you assume no volume change:
V  A0  l0  Ai  li
 true
li
P

  eng   eng 1   eng 
l0
l0
A0
li
l0
Ai  A0 
li
 true   eng 1   eng 
DUCTILITY & BRITTLENESS
 Ductility can be defined as strain at fracture.
 Ductility is commonly expressed as:
a) Elongation
b) % reduction in cross-sectional area
 A ductile material is the one which deforms
appreciably before it breaks, whereas a brittle
material is the one which does not.
 Ductility in metals is described by:
%RA 
A0  A f
A0
 100
 If %RA > 50 % →
Ductile metal
TOUGHNESS & RESILIENCE
 Toughness is the energy absorption capacity
during plastic deformation.
 In a static strength test, the area under the
σ-ε curve gives the amount of work done to
fracture the specimen.
 This amount is specifically called as Modulus
of Toughness.
 It is the amount of energy that can be
absorbed by the unit volume of material
without fracturing it.
σ
T (Joule/m3)
σu
σf
σPL
2
T   u f
3
εPL
εu
εf ε
The area under the σ-ε diagram can be determined
by integration.
If the σ-ε relationship is described by a parabole.
 Resilience is the energy absorption capacity
during elastic deformation.
1
R   PL
2
σ
σPL
R
εPL
If you assume σPL = σy

Since
ε
1  PL 
R
2 E
R
y
2
2E
2
 PL
E
YIELD STRENGTH
 It is defined as the maximum stress that can
be developed without causing more than a
specified permissible strain.
 It is commonly used in the design of any
structure.
 If a material does not have a definite yield
point to measure the allowable strains, “Proof
Strength” is used.
 Proof strength is determined by approximate
methods such as the 0.2% OFF-SET METHOD.
 At 0.2% strain, the initial tangent of the σ-ε
diagram is drawn & the intersection is located.
DETERMINATION OF E FROM σ-ε
DIAGRAMS
 For materials like concrete, cast iron & most non-
ferrous metals, which do not have a linear
portion in their σ-ε diagrams, E is determined by
approximate methods.
1. Initial Tangent Method: Tangent is drawn to the
curve at the origin
2. Tangent Method: Tangent is drawn to the curve
at a point corresponding to a given stress
3. Secant Method: A line is drawn between the
origin & a point corresponding to a given stress
σ
1
3
2
ε
HARDNESS
 Hardness can be defined as the resistance of a
material to indentation.
 It is a quick & practical way of estimating the
quality of a material.
 Early hardness tests were based on natural
minerals with a scale constructed solely on the
ability of one material to scratch another that
was softer.
 A qualitative & somewhat arbitrary hardness
indexing scheme was devised, temed as Mohs
Scale, which ranged from 1 on the soft end for
talc to 10 for diamond.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Talc
Gypsum
Calcite
Fluorite
Apatite
Orthoclase
Quartz
Topaz
Corundum
Diamond
An unknown material will
scratch a softer one & will
be scratched by harder
one.
EX:
HARDER
•Fingernail-(2.5)
•Gold,
Silver-(2.5-3)
•Iron-(4-5)
•Glass-(6-7)
•Steel-(6-7)
 The hardness of a metal is determined by
pressing an indenter onto the surface of the
material and measuring the size of an
indentation.
 The bigger the indentation the softer is the
material.
 Common hardness test methods are:
 Brinell Hardness
 Vicker’s Hardness
 Rockwell Hardness
1. Brinell Hardness
P
• Load P is pressed for 30
sec. and the indentation
diameter is measured as
d.
d
Brinell Hardness =

2P
D D  D  d
2
2

(kgf/mm2)
2. Rockwell Hardness
Initial
load
• Instead of the indentation
P1
H1
Final
load
P2
H2
diameter, indentation depth
is measured.
• However, the surface
roughness may affect the
results.
• So, an initial penetration is
measured upto some load,
and the penetration depth is
measured with respect to
this depth.
ΔH = H2 – H1
3. Vickers Hardness
P
• Instead of a sphere a
conical shaped indenter is
used.
Top
View
Indentation
d1  d 2
d
2
P
Vicker’s Hardness = 1.854 2
d
d1
d2
(kgf/mm2)