# Explain stress and strain curve with diagram and the terms explained in it.

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by Raksha1

2015-09-11T17:26:56+05:30

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Please see the diagram enclosed.

We take generally a solid substance and apply some tensile stress (force/area) in longitudinal direction. The object may be in the shape of a wire or cylinder or cuboid..

We find  strain = ε = ΔL / L  and    stress = σ = F / A

At O, strain is zero as stress is 0.  When stress is applied, the material behaves elastically with Hookes' law being obeyed.  So stress = Young's modulus * strain.   σ / ε = Y

This proportional behaviour continues until point A, where strain reaches the proportional limit.  If strain is increased beyond this limit, the Hookes' law is not valid.

From A to B, the substance expands with increasing stress, but less as compared to the Hookes law region.  When stress is released, the substance regains its original shape and size.  So B is the elastic limit or yield limit.  After that the substance yields.

From B to D, the region is called plastic region. The material expands when stress is more than the elastic limit, but does not regain its original size when stress is removed or reduced.  The strain remains somewhere at C in between B and D.  So the material is said to be permanent set.

Further from B if the stress is increased, strain increases till D, but much more rapidly. Even a little stress makes the material expand a lot.  At D the stress that the material takes is maximum. So it is called the ultimate tensile strength of the material.

Once the ultimate tensile strength is applied to the substance, after that point, even reducing the stress will continue to expand the substance and add more strain.  It will continue as long as there is some stress on the material.  Further at point E the substance breaks into pieces and so it is called the breakpoint or fracture point of the substance.  The stress at this point is called the breaking stress.

If the region B to D is large with a large amount of strain between the ends, then the material is ductile and malleable, like metallic wires, plastic.

If the region between B to D is very small, then the material is brittle and breaks into pieces quickly without much expanding.  like glass, mirror, stones, bones etc.

The materials like rubber and aorta (present in the heart) have a large elastic region. They are called elastomers.  Aorta is the large tube - blood carrying vessel from heart to outside. Aorta does not obey Hooke's law.  The stress-strain curve is a second degree curve, with more strain for the same stress as predicted by Hooke's law.

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see the second diagram:

This is for materials like rubber - vulcanized.  The strain is much more than the original size of the substance.  Rubber can expand to 8 times its size.  It regains its shape back again.  The work done in expanding the substance is stored as elastic potential energy.

When the stress is reduced back to zero, the substance does not return all the energy back (like in a spring) in mechanical energy form.  Some energy is released as heat. Also the path the substance takes in stress-strain diagram is different (dashed line) while reducing the stress.  This behaviour is called elastic hysteresis.  That is why such materials are used in shock absorbers.

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see the third diagram.

Aorta in our heart has somewhat a different behaviour from above.  It expands at most by a factor of strain = 1. It is an elastomer.

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