# Mechanical Properties of Materials

```Mechanical Properties of Materials
The strength of a material is not only the only criterion
that must be considered in designing structures.
Mechanical properties such as hardness, toughness,
ductility determine the selection of a material. These
properties are determined by making tests on the
materials and comparing the results with established
standards.
Stress strain diagrams
Test results generally depend upon the size of the specimen being tested.
Since it is unlikely that we will be designing a structure having parts that
are the same size as the test specimen, we need to express the test results in
a form that can be applied to members of any size. A simple way to achieve
this objective is to convert the test results to stresses and strains.
Calculation of stress: The axial stress б in a test specimen is calculated by
dividing the axial load P by the cross sectional area.
When the initial area of the specimen is used in calculation, the stress is
called nominal stress (also named as engineering stress or conventional stress)
When the actual area of the bar at the cross section where failure occurs is
taken for stress calculation then this stress is called true stress.
Calculation of strain: If the initial gage length is used, then nominal strain is
obtained.
Since the distance between the gages marks increases as the tensile load is
applied, we can calculate the true strain (also named natural strain) at any
value of the load by using the actual distance between the gage marks.
Characteristics features of a typical stress strain diagram:
Sample Description
Test Name
:
:
M.S Rod
Tensile test
Figure-1: Typical stress-strain diagram of MS Rod
Description:
The stress strain diagram of a MS Rod is shown in the Figure-1. Strains
are plotted on the horizontal axis and stresses on the vertical axis. The
diagrams begin with a straight line from the origin O to point A, which
means that the relationship between stress and strain in this initial
region is not only linear but also proportional. Beyond point A, the
proportionality between stress and strain no longer exists; hence the
stress at A is called the Proportional limit. The slope of the straight line
from O to A is called modulus of elasticity.
With an increase in stress beyond the proportional limit, the strain begins to
increase more rapidly for each increment in stress. Consequently, the stressstrain curve has a smaller and smaller slope, until, at point B, the curves
becomes horizontal. Beginning at this point, considerable elongation of the test
specimen occurs with no noticeable increase in the tensile force (from B to C).
This phenomenon is known as yielding of the material and point B is called
yield point. The corresponding stress is called yield stress.
In the region from B to C, the material becomes perfectly plastic, which
means that it deforms without an increase in the applied load.
After undergoing the large strains that occur during yielding in the
region BC, the steel begins to strain harden. During strain hardening,
the material undergoes changes in the crystalline structure, resulting
increased resistance of the material to further deformation. Elongation
of the test specimen in this region requires an increase in the tensile
load, and therefore stress-strain diagram has a positive slope from C to
D. the load eventually reaches its maximum value and the
corresponding stress at D is called ultimate stress.
Further stretching of bar is actually accompanied by a reduction in the
load and fracture finally occurs at a point such as E.
When a test specimen is stretched, lateral contraction occurs. The
resulting decrease in cross sectional area is too small to have a
noticeable effect on the calculated value of stresses up to about point
C, but beyond that point the reduction in area begins to alter the shape
of the curve. In the vicinity of ultimate stress, the reduction in area of
the bar becomes clearly visible and a pronounced necking of the bar
occurs. If the cross sectional area at the narrow part of the neck is used
to calculate the stress, the true stress-strain curve is obtained
To define a clear yield point
When a material does not have definite yield point, an arbitrary yield
stress may be determined by the offset method. A straight line is drawn
on the stress-strain diagram parallel to the initial linear part of the curve
but offset by some standard strain, such as 0.002. The intersection of the
offset line and the stress-strain curve defines the yield point.
Some important parameter
Percent elongation = (L1 – L0)/L0 * 100
Where, L1 = Distance between gage marks at fracture
L0 = Original gage length
Percent reduction in area = (A0 – A1)/A0 * 100
Where, A0 = Original cross sectional area
A1 = Final area
Mechanical properties
•Elasticity: Elasticity is that property which enables a body deformed by
stress to regain its original dimensions when the stress is removed.
•Plasticity: A perfectly plastic body is one which does not make any
recovery of its original dimensions upon the removal of a stress.
•Stiffness: Stiffness is the property that enables a material to withstand
high unit stress without great unit deformation. Stiffness is associate with
resistance to bending.
•Ductility: Ductility is the property that enables a material to undergo
plastic deformation under tensile stress.
•Malleability: Malleability is the property which enables a material to
undergo plastic deformation under compressive stress.
•Brittleness: Brittleness is the absence of plasticity. A brittle material is
neither ductile nor malleable.
•Toughness: Toughness is the property of a material that enables it to
endure shock or blows.
Typical stress-strain diagram for brittle materials
Figure-2: Stress-strain diagram of brittle material
Assignment – 01
The following data were obtained during a tension test of an aluminum alloy. The initial diameter of the
test specimen was 0.505 inch and the gage length was 2.0 inch.
0
2310
4640
6950
9290
11600
12600
14000
14400
14500
14600
14800
14600
13600
Elongation (inch)
0
0.00220
0.00440
0.00660
0.00880
0.0110
0.0150
0.0200
0.0250
0.0600
0.0800
0.100
0.120
Fracture
Plot the stress-strain diagram and determine the following mechanical properties:
a) proportional limit b) modulus of elasticity c) yield point
d) yield strength at 0.2% offset
e) ultimate strength f) rupture strength
Problems on Simple strain
Problem-01
An aluminum bar having a cross sectional area of 0.5sqinch carries the
axial loads applied at the position shown in the following figure.
Compute the total change in length of the bar if E = 10 x 106 psi. Assume
the bar is suitably braced to prevent lateral buckling.
Problem-02
A bronze bar is fastened between a steel bar and an aluminum bar as
shown in the figure. Axial loads are applied at the positions indicated. Find
the largest value of P that will not exceed an overall deformation of 3.0mm,
or the following stresses: 140 Mpa in the steel, 120 Mpa in the bronze, and
80 Mpa in the aluminum. Assume that the assembly is suitably braced to
prevent buckling.
Problem-03
The rigid bar AB attached to two vertical rods as shown in the figure, is
horizontal before the load P is applied. Determine the vertical movement
of P if its magnitude is 50 KN.
Problem-04
A uniform concrete slab of total weight W is to be attached shown in figure,
to two rods whose lower ends are on the same level. Determine the ratio of
the areas of the rods so that the slab will remain level.
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