Mechanical properties of materials
The behavior of material is mainly determined by various mechanical properties of the material
when subjected to different loading conditions. Such properties mainly include Young’s
modulus, various types of strength of the material, hardness, ductility etc. and are found to be
very important both for design & manufacturing viewpoint. The design engineer should also
consider the manufacturing constraints during the design of a part.
Three basic types of stresses which are produced when a material is subjected to various loading
conditions are
a) Tensile Stress
b) Compressive Stress
c) Shear stress
Tensile properties
Tensile strength is defined as the ability of a material to support axial load without rupture and is
determined through the tensile test. When equal and opposite forces are applied simultaneously
at both the ends that pulls the material, it tries to elongate it and the diameter reduces. The test
specimen and general setup has been shown in the Figure M1.4.1.
(a)
(b)
Figure M1.4.1: (a) Test specimen (b) Setup for the test
Due to the stretching of the specimen in tensile test, the initial test specimen length L0 is
increased to L and area A0 is reduced to A. The tensile testis carried out at a constant cross head
speed and extensometers of required gauge length are used to capture the elongation depending
on the requirement. In this process the material first elongates, then necking occurs & the
fracture is produced. The necking phenomenon is observed mostly in tensile test and it also
mainly depends upon the material that isused for test. If the material is brittle there is no chance
of necking. From the measured data from the tensile test, the stress- strain curve is plotted.
Mainly there are two type of stress-strain curves which are described below:
1) Engineering stress-strain
2) True stress strain
Generally in design application the engineering stress-strain curve is used as there is no
expectation of change in shape due to strain. The true stress strain curve is important in
manufacturing.
Engineering stress-strain
Engineering stress-strain is mainly illustrated by taking original cross section and original length.
The stress-strain diagram for a metal is shown in Figure M1.4.2.
Figure M1.4.2: Engineering stress-strain diagram of an metal
The engineering stress at any point on the curve is the force divided by the original area
s=
F
A
Where e= Engineering stress (MPa)
F= applied force in the test, (N)
Ao= Original area of the test specimen (mm2)
Engineering strain at any point is the ratio between change in length to the original gage length.
e=
L−L
L
Where e= engineering strain, mm/mm,
L= length at any point during elongation, mm
Lo= Original gage length, mm
Further, in the stress-strain curve, two distinct regions namely elastic region and plastic region
represent different material behavior of the material. In the elastic region, the relation between
stress and strain is linear. The relationship between stress and strain in the elastic region is
defined by Hooke’s law:
s = Ee
Where E= Young’s modulus, MPa
The value of E varies form one material to other which mainly indicates the stiffness of the
material. In further addition of stress, the material begins to yield which is the end point of the
elastic region (shown in the Figure M1.4.2).
At this point there is change in slope of the curve occurs. This point is called as yield point which
could be measured by drawing a straight-line parallel to the slope of the load-extension curve of
the metals like titanium, steel, low carbon steel, and molybdenum at 0.2% offset. At this yield
point there is slight extension of the specimen occurs without increase in stress level. The
strength of the material at this point is called as yield strength.
Beyond yield point, as the load increases, elongation of the specimen proceeds at a faster rate
than before. This part of stress strain curve is called hardening region.When the load reaches a
maximum value, the engineering stress at this point is called the tensile strength or ultimate
tensile strength of the material.
In the stress- strain diagram, beyond the tensile strength, the load carrying capacity reduces and
the test specimen goes through a localized elongation called necking.There will not be constant
strain in this region and the elongation occurs in one small segment of the specimen. The stress
measured just before failure is known as the fracture stress.
The amount of strain that the material sustain before failure is an important property in
mechanical engineering, which is used specially in manufacturing. This property is called
ductility and is measured in terms of elongation or area reduction.
EL =
L −L
L
AR =
A −A
A
Where EL= elongation, in %
Lf= Specimen length in mm
Lo= Original specimen, mm
AR= Area reduction, in %
Ao= Original area, mm2
Af=Area of cross-section at the point of facture, in mm2
True Stress-strain
In the computation of engineering stress, the original cross sectional area has been used.
However, during the process of loading the area reduces. In the computation of true stress the
actual or instantaneous area is used. As the length increases, the cross sectional area decreases.
Hence the calculated stress value will be higher. The instantaneous load divided by instantaneous
cross-sectional area is called true stress.
σ=
F
A
Where  = true stress, MPa
F= force, N
A=Actual area resisting the load, mm2
True Stress & strain is related to engineering stress & strain in the following way.
Keeping the volume of material constant.
A ×L =A×L
=
F
F A
L
L−L +L
=
×
=s× =s×
= s × (1 + e)
A A
A
L
L
Similarly true strain offers a more accurate calculation of the instantaneous elongation per unit
length of the material.The true stress is generally increased rapidly than engineering stress once
the strain increases and the accordingly, the cross sectional of the specimen decreases.
ϵ=
dL
L
L−L +L
= ln
= ln
= ln(1 + e)
L
L
L
Where L= instantaneous length at any moment during elongation
ϵ = true strain
The true stress-strain relationship in plastic region can be represented by the following flow
curve:
σ = K ×∈
Here the constant K=strength coefficient
n= Strain hardening exponent
The value of K & n varies form one metal to other & mainly depends upon metal’s tendency to
work harden.
The behavior of nearly all type of solid material are described by three types of stress-strain
relationship diagram as shown in Figure M1.4.3.
A) Perfectly elastic
The behavior of the material is absolutely defined by its stiffness. Such material directly
fractures without yielding when it reaches ultimate strength material. These materials are called
brittle materials. Examples of brittle material are ceramics, cast iron, etc. These materials are not
suitable for forming operation, where permanent plastic deformation is required to get the final
product.
B) Elastic and perfectly plastic
For this type of material, when the stress level reaches the yield point plastic deformation begins
at the same stress level. Metals behave in this mode, when they are heated to high temperatures.
This type of behavior occurs mainly at higher temperature doesn’t strain harden rather it
recrystallize during deformation.
C) Elastic and strain hardening
This kind of material obeys Hooke’s law in the elastic region and begins to flow at its yield
point. During cold working, most of the ductile material behave in this manner.
Figure M1.4.3: The stress-strain relationship diagram for a) perfectly elastic b) elastic &
perfectly plastic c) elastic & strain hardening.
Compression Properties
Compressive test is performed to determine the compressive strength of the material. The
material is applied equal and opposite compressive load. Engineering stress is defined as
s=
F
A
Where Ao= Original area of cross section, mm2
Engineering strain is defined as
=
ℎ−ℎ
ℎ
Where h= height of the specimen at a particular moment into the test, mm
h0= starting height, mm
The strain will be negative. Usually the negative sign of the strain are ignored. The stress strain
diagram is shown in the Figure M1.4.4.
The stress strain curve shown in Figure M1.4.4 for compression test is different in the plastic
region of stress strain curve for tensile test for same material. The reason of this variation is
compression helps in increase in the cross section. The load rises more quickly than the tensile
test.
In compression operation, due to friction between the surfaces there is an increase in area of the
middle of the specimen than at the ends. This effect is called barreling effect in a compression
test.
Figure M1.4.4: Stress-strain diagram for compression test
Compression operations are used mostly in metal forming than stretching operations. Generally
forging, rolling etc. are the compression operation used in industry.
Shear properties
Shear stress involves application of load parallel to the surface of material in opposite direction
as shown in Figure M1.4.5.
The shear stress is defined as
τ=
F
A
(a)
(b)
Figure M1.4.5: Shear (a) stress (b) strain
Where τ = shear stress, MPa
F= applied force, N
A= area over which the force is applied, mm2
Shear strain can be defined as
γ=
δ
b
Where γ =shear strain, mm/mm
δ= the deflection of the element, mm
b= the orthogonal distance over which deflection occurs, mm
In case of shear stress–strain curve, the relationship for elastic region is defined by
=
×
Where G=the shear modulus, MPa
For plastic region the relationship between the shear stress–strain is similar to flow curve. Due to
strain hardening the applied load increases until the fracture occurs. The relationship between
shear strength (S) & Tensile strength (TS) can represented by data approximation as below:
S = 0.7 × (TS)
Different cutting operations like blanking, punching etc. used in industry are included in shearing
operation. Due to mechanism of shear deformation the material is removed in the machining
process.
Hardness
Hardness is a measure of how resistant solid matter is to various kinds of permanent shape
change when a force is applied.
Vickers hardness test: It is easier to use in comparison to other hardness tests since the required
calculations are independent of the size of the indenter, and the indenter can be used for all
materials irrespective of hardness. The unit of hardness given by the test is known as the Vickers
Pyramid Number (HV).
In Vickers hardness test the surface is subjected to a standard pressure for a standard length of
time by means of a pyramid-shaped diamond. The diagonal of the resulting indention is
measured under a microscope and the Vickers Hardness value is read from a conversion table.
The Vickers number (HV) is calculated as:
HV = 1.854(F/D2)
Where F=the applied load,kgf
D= the area of the indentation, mm2
Brinell hardness test:It is widely used for testing metals and non-metals of low to medium
hardness. A ball shaped indenter made of cemented carbide is used for harder material in this
test.
Knoop Hardness Test: It is used for generally small & thin specimen. A pyramid-shaped
diamond indenter is used whose length-to-width ratio of about 7:1.
Rockwell Hardness Test: It is used for variety of material like carbide, ceramic, tool steel etc.
where a cone-shaped indenter, with diameter 3.2 mm is forced into the specimen using a minor
load of 10 kg & then a major load of 150 kg is applied, helping the indenter to penetrate into the
specimen a certain distance beyond its initial position. This extra penetration distanced is
converted into a Rockwell hardness.
There is a good correlation between hardness & strength for most metals as hardness is usually
based on resistance to indentation, which is a form of compression.
Brinell hardness (HB) shows a close correlation with the ultimate tensile strength (TS) for steel
is given below:
TS = 3.45 × (HB)