 # Tensile Stress

Tensile Stress & Tensile Strength

When there is an increase in the length of the material in the direction of the force applied, this kind of stress set up is called Tensile stress.

Let’s discuss the type 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 a 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.

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 = 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 ^ -1 L ^ -1 T ^- 2 ]

Tensile Strength

Any object has always got an 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.

Tensile strength is the maximum stress without fracture a material can withstand before breaking.

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 =  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 tensile direction but the volume will remain constant.

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.

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 = external deformation force / 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, Tensile  Stress /  Tensile Strain = Y = a constant

Q1: 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 10 ^ 9 N / m ^ 2. 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 / s ^ 2, where ‘u’ is the acceleration due to gravity.

Ans: The stress in the wire is given by Tension / Area of 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 k ^ 2

If the minimum radius required to avoid breaking is k,

=  3 x 10 ^ 9 N / m ^ 2  =  (24) /  π x k ^ 2

Solving this, we get:

k = 5.04975 x 10 ^ - 4 m.

Q2: 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?

Ans: 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  10 ^ 4 (N / m ^ 2)

Q3: What is the Elastic Limit?

Ans: 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.

Q4: 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.

Ans: 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 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 elastic potential energy of the wire.