On 10/8/2026 during our normal lecture hours, we will have first
exam which cover Ch1, 2 and ch3.
• Close-note exam but you can have four sheets of notes
MECH2500 Mechanics of material
Lecture 6 Stress stain diagram
Ch3.1~3.4
Professor Xiaobin Le, Ph.D., PE.
Mechanical Engineering Program
Wentworth Institute of Technology
Office: Kingman hall 206
Email: Lex@wit.edu
Phone:617-989-4223
Chapter 3 Mechanical Properties of Materials
A: Tensile test
B: Stress-strain diagram
C: Ductile and brittle materials
Contents
Objectives
•
•
•
•
Understand the purpose of tensile test
Be able to interpret tensile stress-strain curve
Understand the Hooke’s law
Understand typical mechanical properties
Study chapter 3.1~3.4
A: Tension test or compression tests
ASTM Test standards
ASTM = American Society for testing and Materials. Now, it has
been changed into “ASTM International”
• ASTM International, formerly known as American Society for
Testing and Materials, is a standards organization that develops
and publishes voluntary consensus technical international
standards for a wide range of materials, products, systems and
services. Some 12,575 apply globally.
• Why do we need standards for testing?
• ASTM E8/E8M-22: Standard Test Methods for Tension
Testing of Metallic Materials
Tension and compression tests
• The strength of a material depends on its ability to sustain a load without undue deformation
or failure.
• The strength, and other mechanical properties of materials are not derived from theoretical
calculation. They come from experiments.
• The tension or compression tests are typical experiments for obtaining mechanical properties
of materials
Standard test specimen
The specimen in the tensile or compression test is a standard specimen with specified shape
and size. It has a constant circular cross section
with enlarged ends, so that failure will not occur at
the grips. Before testing, two small punch marks
are placed along the specimen’s uniform length.
Measurements are taken of both the specimen’s
initial cross-sectional area A0 and the gauge-length
distance L0 between the punch marks
Standard specimen
• The standard tensile test specimen is
properly mounted in the testing machine so
that there is only tensile load with no
bending load on the specimen.
• The testing machine stretch the specimen
at a very slow, constant rate until it falls.
• During the testing, the average normal
stress can be recorded, which is equal to
σ = P / A0
• During the testing, the elongation δ
between the two punch marks on the
specimen can be measured by caliper or
extensometer, so the average normal strain
ε = (L − L ) / L = δ / L
is
0
0
0
Instron universal test machine
B: Tensile stress-strain curve
B: tensile stress-strain curve
P
σ=
A0
ε=
A typical stress- strain curve
L − L0
L0
A typical stress-strain curve for a low-carbon steel can be divided into three
regions
(1)Elastic region:
In this section, the component will be recovered after the loading is removed.
There is a linear relationship between the stress and strain. This relationship
is called Hooke’s Law.
the Hooke’s law
σ = Eε
E is the slope of the straight line and is called
Modulus of Elasticty (Young' s Modulus)
For most of engineering design, the deformation is generally very small for the proper
function and performance of component. Therefore, deformation is generally in the
elastic region, that is, Hooke’s law provides the linear relation between the stress and
strain.
Notes:
(2) For different material, the Young’s
(1) For the same stress, the bigger
Modulus is different, But for different brand
Young’s Modulus, the smaller the strain.
of steels, the Young’s modulus is also most
So in order to have smaller deformation,
the same. It is 29000 ksi (200 Gpa)
the material with larger Young’s
modulus should be used.
Example 1
A round bar with diameter 1” made from 1020 Hot-rolled carbon
steel with E=30000 ksi. According to experiment, the strain of
the loaded bar is 0.0010 in/in. Determine the stress of the bar
and the applying axial load on the bar.
Solution:
E = 30,000ksi,σ = Eε = 30,000 X 0.001 = 30ksi
2
F = σA = 30,000 × (π 1 / 4) = 23562(lb)
(2) Yielding:
•yielding means significant strain/ deformation increase without stress increase.
In yielding, there is significant plastic deformation which can not recovered after
loading is removed. For steel, there is clear yielding phenomena.
• For some high strength materials, or aluminum, this
material, there is not clear yielding. In industries,
the offset method by 0.2% strain is used to define
the yield point as shown in the figure. Draw a line
from the point with 0.2% strain to parallel the initial
straight-line. The intersection point of this line with
the strain-stress curve is the yield point.
Yield strength σy is the value of stress at the yield point.
Notes:
Yield strength is one of typical mechanical properties used in mechanical design. In
mechanical design, we don’t want components to have excessive deformation,
therefore, we don't allow that the actual stress (design stress) of the components is
larger than the yield strength.
Unloading and reloading paths
(3) Necking:
•Up to the ultimate stress as the specimen elongates, its crosssectional area will decrease for a ductile material. This is called
necking. The sample will break at the necking place.
•The brittle material will fracture without clear necking.
The ultimate strength σu is the highest value of apparent stress on the
stress-strain curve.
Notes:
The ultimate strength is one of mechanical properties used in mechanical design.
When the actual stress is over the tensile strength (ultimate strength), the component
will start necking and might break at any time. Since the safety of components is #1
design criteria which must be satisfied for every product or components, the actual
stress is not allowed to be larger than the ultimate strength for component design.
C: Ductile and brittle materials
Percent elongation
The percent elongation is the ratio of the plastic elongation of a
tensile specimen after the ultimate failure within a set of gage
marks to the original length between the gage marks
Percent elogation
Final length - Gage length
=
%
gage length
Ductile material: materials that can be
subjected to large strain (with a clear
necking ) before it fractures is called a
ductile material
Brittle material: Material that exhibit little or no
yielding before failure are referred to as brittle
materials.
Ductile and brittle material
– A ductile material is one that can be stretched, formed, or drawn to a
significant degree before fracture. A metal with a percent elongation
greater than 5.0% is considered to be ductile
– A brittle material is one that fails suddenly under load with little or
plastic deformation. A metal that exhibits a percent elongation less
than 5.0% is considered to be brittle.