SUBMITTED BY:

MUHAMMAD DANYAL YASEEN

SUBMITTED TO:
ENGR.QASIM ALI
ROLL NO :
BMEF19M006
SUBJECT:
MECHANICS OF MATERIAL-I

DEPARTMENT OF MECHANICAL ENGINEERING

CET,UOS
 STRESS STRAIN CURVE:
The stress-strain curve provides design engineers with a long list of important parameters needed for
application design. A stress-strain graph gives us many mechanical properties such as strength,
toughness, elasticity, yield point, strain energy, resilience, and elongation during load. It also helps in
fabrication. Whether you are looking to perform extrusion, rolling, bending or some other operation, the
values stemming from this graph will help you to determine the forces necessary to induce plastic
deformation.

The accuracy of mechanical properties obtained from tensile test data of natural fibers and their
composites can be greatly improved using a model fit to the stress-strain curve... The new approach
produces values of Young’s modulus and yield strength that vary significantly from results
obtained using the traditional technique but are in agreement with observations. This new
technique is recommended to obtain more accurate measures of modulus of elasticity and yield
strength for natural fibers and their composites.

For Ductile:

 Point A is the proportionality limit, up to A, stress is directly proportional to strain i.e.

Hook's law followed.
 Point B is the elastic limit.
 Point C is the yield point. At yield point, the resistance suddenly decreases. Therefore,
stress is also decreased, this is the particular property of mild steel.
 Point F is the ultimate tensile strength. At point F necking starts and due to necking 45-
degree micro cracks generates.
 Point G is the breaking point. At G component break into two pieces and failure is the cup-
cone failure. The cup-cone failure is a shear failure.
For Brittle:

 Brittle material never yields, a point similar to yield point is first cracking point, where
simple cracks develop; which may expand further leading to failure.
 A point is the first cracking point. After first cracks develop, the material undergoes an
increase in strain by widening the crack and fails almost at the same stress. Therefore for
all calculation in brittle material design stress is ultimate or breaking stress i.e. Sut.

Elastics Region:

What is the elastic region? It is the region where the material can be deformed and when released
will return back to its original configuration. Many metals in the elastic region have a resulting
strain that is proportional to the tensile load when the applied tensile load is small. Mathematically,
this can be written as

𝜎 = 𝐸𝜀 ,

and more generally is known as a form of Hooke's law. E is the proportionality constant and is
called the modulus of elasticity or Young's modulus. Physically, the larger the value of the modulus
of elasticity the stiffer the material is, i.e., the more resistant to bending the material is. . The region
of the stress-strain curve in which the material returns to the undeformed state when applied forces
are removed is called the elastic region.

Plastic Region:

The region in which the material deforms permanently is called the plastic region. For stresses
beyond the elastic limit, a material exhibits plastic behavior. This means the material deforms
irreversibly and does not return to its original shape and size, even when the load is removed.
When stress is gradually increased beyond the elastic limit, the materials undergo plastics
deformation.
Necking:

Necking, in engineering or materials science, is a mode of tensile deformation where relatively

large amounts of strain localize disproportionately in a small region of the material. The resulting
prominent decrease in local cross-sectional area provides the basis for the name "neck".

Proportional Limit:
The proportional limit is the point on a stress-strain curve where the linear, elastic deformation
region transitions into a non-linear, plastic deformation region. In other words, the proportional
limit determines the greatest stress that is directly proportional to strain.

Elastic Limit:

Elastic limit, maximum stress or force per unit area within a solid material that can arise before
the onset of permanent deformation. When stresses up to the elastic limit are removed, the material
resumes its original size and shape. Stresses beyond the elastic limit cause a material to yield or
flow. For such materials the elastic limit marks the end of elastic behaviour and the beginning
of plastic behaviour. For most brittle materials, stresses beyond the elastic limit result in fracture
with almost no plastic deformation.

Yield Point:

In materials science and engineering, the yield point is the point on a stress-strain curve that
indicates the limit of elastic behavior and the beginning of plastic behavior. Prior to the yield point,
a material will deform elastically and will return to its original shape when the applied stress is
removed. Once the yield point is passed, some fraction of the deformation will be permanent and
non-reversible and is known as plastic deformation.

Ultimate Tensile Strength:

Ultimate tensile strength is the amount of stress that pushes materials from the state of uniform
plastic deformation to local concentrated deformation. The necking phenomenon begins at this
point. Ultimate tensile strength is an intensive property. In other words, it does not depend on the
size of the sample. The tensile strength was obtained as the highest point on the stress-strain curve;
this often corresponds to the highest value of stress recorded on the stress versus strain table from
which the stress-strain curve was plotted.

Fracture Strength:

Fracture strength, also known as breaking strength, is the stress at which a specimen fails
via fracture. This is usually determined for a given specimen by a tensile test, which charts
the stress-strain curve.
 Mechanical Properties of Materials

Material Stress and Strain:

First, we need to explain some of the physical concepts behind the mechanical properties. The main one
is stress. Stress tells you how big of a force applies to an area. In mechanical engineering, it is mostly
expressed in MPa’s or N/mm2. Those two are interchangeable. The formula for stress is:

σ=F/A, where F is force (N) and A is area (mm2).

The second important concept is strain. Strain has no unit as it is a ratio of lengths. It is calculated as
follows:

𝑙 − 𝑙0
𝜀= ,
𝑙0

Where 𝑙0 starting or initial length (mm) and 𝑙 is stretched length (mm).

Young’s Modulus:

From those two concepts we get to our first mechanical properties – stiffness and elasticity as it’s
opposite. It is an important factor for engineers when solving physics problems (material suitability for
a certain application).

Stiff material does not compress nor elongate easily

Stiffness is expressed as Young’s modulus, also known as modulus of elasticity. As one of the primary
mechanical properties of materials, it defines the relationship between stress and strain – the bigger its
value, the stiffer the material.

This means that the same load would deform two equally-sized parts differently, if they have varying
Young’s moduli. At the same time, lesser value means that the material is more elastic. The formula for
Young’s modulus:
𝜎
𝐸 = 𝜀 (MPa)
Yield Strength:

Yield stress or yield strength is the value most often used in engineering calculations. It gives a material
a stress value in MPa it can take before plastic deformation. This place is called the yield point. Before
it, a material regains its former shape when lifting the load. After exceeding the yield point, the
deformation is permanent.

There is a good reason for using yield stress as the most important factor in mechanical engineering. As
can be seen from the stress-strain curve, when stress goes beyond the yield point, the damage is not yet
catastrophic. That leaves a “cushion” before a construction fails completely to the point of breaking.

Tensile Strength:

Ultimate tensile strength, or just tensile strength, is the next step from yield strength. Also measured in
MPa’s, this value indicates the maximum stress a material can withstand before fracturing.

When choosing a suitable material to tolerate known forces, two materials with a similar yield strength
may have different tensile strengths. Having higher tensile strength may help to avoid accidents, if
unforeseen forces are applied.

Plasticity:

Plasticity is a mechanical property of materials that shows the ability to deform under stress without
breaking, while retaining the deformed shape after the load is lifted. Metals with higher plasticity are
better for forming. This is evident in metal bending.

Two related mechanical properties of materials are ductility and malleability. Ductility has a pretty
much similar description to plasticity – it is a material’s ability to undergo plastic deformation before
breaking. It is expressed as a percent elongation or percent area reduction. Basically, ductility is a
property you need when drawing thin metal wires, for example. A good example of such a ductile
material is copper. This makes the fabrication of wires possible.
Malleability is, by definition, also similar. But it actually characterizes a material’s suitability for
compressive deformation. In essence, a metal with good malleability is fitting for producing metal plates
or sheets by rolling or hammering.

Toughness:

Toughness is a combination of strength and plasticity. A tough material can take hard blows without
rupturing. Toughness is often defined as a material’s ability to absorb energy without cracking.

An example of required toughness is quarry loaders. Throwing huge rocks into the bins results in
deformations, not cracks, if the material is tough.

Hardness:

Another important attribute for an engineering material. High hardness values show that a material
resists localized pressures. In simple terms, a hard material is not easy to scrape or punctuate with lasting
marks (plastic deformation). It is especially important when heavy wear processes take place. In such
circumstances, hard materials like Hardox are suitable. Hardness and toughness are two qualities that
account for durability.

Hardness is measured by scratching, bouncing or indentation. The most common way to describe
hardness is through indentation hardness. There are different ways to carry out these tests, depending
on the material. Each results in a different hardness unit – Brinell, Vickers or Rockwell. If you want to
compare 2 materials that have hardness values in different systems, you have to convert them to the
same type (e.g. Vickers) first.

Brittleness:

Brittleness is usually quite an unwanted material property in mechanical engineering. It means that a
material breaks without noticeable plastic deformation. An indication of a material’s brittleness is the
snapping sound it makes when breaking. Brittle materials leave broken edges that belong
recognizably together.

Although when thinking about brittleness, it may be associated with low strength but it is not so in
reality. Those two are not mutually exclusive. A strong material can still be brittle. An example of this
is ceramics. Cast iron is an example of a brittle metal.

Fatigue Strength:

Fatigue strength, or fatigue limit, expresses a material’s ability to withstand cyclic stresses. In case
of ferrous alloys, there is a clear limit the metal can resist. In case the stress is lower than the limit
(according to the number of cycles), there is no fear of breaking. With other metals, like aluminium and
copper, there is no clear limit for cyclical stress resistance. They still tend to break after a certain amount
of reversed bending stress. For such materials, there is another similar measurable value – endurance
strength.

With fatigue strength, a material has an infinite life, if the stress value is below the fatigue limit. In case
of endurance strength, you get a value below which the material can work for a certain number of cycles.
It is usually set at 107.