Tensile Stress & Tensile Strength
When two people pull a rope from both sides oppositely, the rope stretches as far as it can, and at a point, it starts tearing up. When you pull the rope, the force is acting along the axis. This externally induced force that is acting per unit area of the material and stretching is called tensile stress and a material’s capacity to bear that stress till it is broken is called the tensile strength of the material. When there is an increase in the length of the material in the direction of the force applied, this kind of stress setup is called Tensile stress.
Let’s discuss the types of stress:
Normal Stress
When a contorting force acts normally or perpendicularly over an area of a body, then the force established over a unit area of that body is called the Normal stress.
Tensile Stress (T)
Tensile stress is one of the categories of normal stress.
Tensile stress is caused by an applied force or load that leans to elongate the material in the direction or axis of the force applied.
Let’s say molecule 1 and molecule 2 are fixed at their lattice points ‘p’ and ‘q’ respectively, packed together closely such that they remain in an equilibrium stage.
Now as the force ‘F’ is applied and the object loses its Elastic limit and elongates in the axis of the force ‘F’ applied because the molecules which were fixed with a distance ‘k = 0’ (with no void in between them) are set apart by some distance ‘k = d’. The elongation or we can say a permanent deformation by the tensile strain occurs in this way.
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This is an image showing the elongation from Lo to Length L, but there will be a decrease in the diameter of the rod, hence the decrease in the area as well.
This decrease in the cross-sectional area due to tensile deformation provides the basis for the new name Neck.
Tensile Stress Formula
If the force is acting perpendicular to the surface is given by F, and the surface area is H, then tensile stress (T) is given by:
T = \[\frac {F} {H}\]
S.I. unit of T = Pascal (Pa) or Newton per meter square or N x m- 2
Dimensional formula for tensile stress =
M−1L−1T−2
Tensile Strength
Any object has always got the endurance to withstand the stress or an external force acting upon it, but as we continue to apply the force the object reaches the breaking or a fracture point.
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Tensile strength is the maximum stress without fracture a material can withstand before breaking. For example, when two persons pull a piece of cloth from both sides, to an extent the cloth stretches and starts tearing up after a certain extent. So, the point at which the cloth can stretch and start tearing up later is called the tensile strength of the cloth. Solids are more tensile and withstand more tensile strength than gases as the gases are free particles and solids are more compacted, the solids have more capacity to stretch.
It measures the force required to stretch or pull something such as rope, wire, or any structural rod or a beam to the point where it fractures or breaks.
For an axial load material, the breaking strength (Ts) is given by:
U = Force that causes the fracture or a breaking
V = Cross-sectional area of the material
Ts = \[\frac {U} {V}\]
S.I. unit = Pascal or Newton per meter square or N x m- 2
Difference Between the Tensile Stress and Tensile Strength
Tensile Stress: It is defined as the stress which occurs along the sides of the object in the direction of force which would increase the length of the material in the tensile direction but the volume will remain constant. It acts along the axis and puts some stress on the material. The result of this force is stretching up of the material.
Tensile Strength: It is the resistance of a material to breaking under tension. So if any object or a body has high tensile strength, which means that body can resist a lot of tension before it breaks.
It indirectly tells us the ability of a material to withstand tensile stress. The result of the tensile strength is, when the force exceeds the tensile strength, it starts breaking up or tearing down.
Tensile stress Vs Tensile Strain Vs Tensile Strength:
Tensile stress acts along the axis of the object and stretches the object. When the object stretches, the damage done by the tensile stress to it is known as the tensile strain and the extent to which the object can withstand before breaking up completely is known as its tensile strength of it. If the tensile stress is applied parallel to the object rather than perpendicular to it, the stress is known as the shear force or shear stress. And the compressive force is opposite to the tensile stress and we can see this force being used in the construction field, to build concrete pillars. To calculate the tensile stress applied on an object, divide the area on which the force is applied with the force applied.
Applications of Tensile Stress in Daily Life:
Tensile stress is used by the police and movers to tow the cars and other vehicles.
When you see anyone pulling up water from the well and carrying it, it is the tensile stress that works on the rope and pulley which makes bringing up the water possible.
When the shopkeepers and vendors on the street use a weighing scale to measure the products, fruits, vegetables, etc, it is the tensile force that helps in doing it.
Many gym equipments like the Lat Pull machine, waistband works on the same principle and helps us work out every day
A crane works on the same principle of tensile stress to pull up materials and place them elsewhere.
We see children playing whirligig and it is based on the principle of tensile stress
Tug of war is another activity that is done based on the same principle.
When you try to pull a heavy object like a big rock or a block with the help of a rope, you are using the tensile stress to drag it.
Summary
When there is no permanent change in the configuration of the body, the restoring force is equal to the external force applied which means that:
Stress = \[\frac{\text{external deformation force}}{\text{area}}\]
The solids are more elastic and gases are less elastic because for the given stress applied the gases are more compressible than that of solids.
Necking, in engineering or material sciences, is a modality of tensile deformation where comparatively huge quantities of strain focalize disproportionality in a tiny region of the material. The ensuing salient decrease in the local cross-sectional area furnishes the basis for the name “neck”.
Multiwalled Carbon nanotubes have the highest tensile strength among all the materials.
A quantity (Y) Young’s modulus relates how difficult it is to stretch a given material, and is described by:
Tensile Stress = Y x Tensile Strain
Therefore, \[\frac{\text{Tensile Stress}}{\text{Tensile Strain}}\] = Y = a constant
FAQs on Tensile Stress
1. Two Blocks of Masses 2 kg and 3 kg are connected by a Metal Wire Going Over a Smooth Pulley. The Breaking Stress of the Metal is 3 x 109 N / m2. What should be the Minimum Value of Radius (k) of the Wire Used if it is not to Break?
Take the value of u as 10 m / s2, where ‘u’ is the acceleration due to gravity.
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The stress in the wire is given by the Tension / Area of the cross-section
To avoid this breaking, this stress should not exceed the breaking stress.
Let the tension in the wire be S. The equations of motion of the two blocks are:
S - 20 N = (2 kg) x b ….(1) (Since F= m x b)
30 N - S = (3 kg ) x b….(1)
Eliminating the common term ‘b’ from these two equations, we get that:
S = 24 N
The stress = S / A = (24) / π x k2
If the minimum radius required to avoid breaking is k,
= 3 x 109 N / m2 = (24) / π x k2
Solving this, we get:
k = 5.04975 x 10-4 m.
2. A tensile test was conducted on an iron rod. The load at the elastic limit was 300 kN and the diameter of the rod was 6cm. What will be the value of stress?
The stress = Load / Area
Given load value = 300 x 1000 N = 300000 N
= Area = π / 4 x (0.0 6)2
Stress = 300000 / (π x (0.0 6)2 ) / 4
= 300000 x 4 / π x 36 x 10- 4
On solving, we get that:
Stress = 10615.7 x 104 (N / m2)
3. What is the elastic limit?
Elastic limit is the upper limit of the deforming force till which, if an external force is removed the body reverts back to its natural shape but when this force is increased, the body loses its elasticity can’t revert back to its original attributes.
4. When a wire is Stretched, the Work is Done against the Restoring Force and Between the Particles of the Wire. Why this appears as Elastic Potential Energy of the Wire. Describe it.
Let’s suppose that the wire is of length m with cross-sectional area d. If a force F is applied to stretch the wire, the wire extends by a small length Δm. Due to the interatomic force of attraction between the particles (atoms) inside, the internal restoration starts from 0 to F, and Δm comes back to m.
The average internal restoring force = 0 + F/ 2 = F/ 2.
Hence work done on the wire is given by force x increase in length.
W = F/2 x Δm is stored as the elastic potential energy of the wire.
5. What is the difference between tensile stress, tensile strength, and compressive stress?
Tensile force is a force acting along the axis of an object and is caused by an external agent. It leads to the stretching of the object to an extent and when the force exceeds the limit, the object breaks or tears down. When you drag an object with the help of a rope, you are using tensile stress to drag it. Sometimes, the rope tears down as the force from your side or the opposite force from the object’s side cross the threshold. So the point to which the material withstands the tensile stress is the tensile strength of the object. Cable wires used in cranes, elevators also work on the same principle of tensile stress. On the other hand, compressive stress in a way is an opposite force to tensile stress. At os, the force is applied to compress and compact material. The best example to describe the compressive force is the concrete pillars built on the same principle.