Relationship between Stress and Strain

Relationship between Stress and Strain are derived on the basis of the elastic behaviour of material bodies.

A standard mild steel specimen( ductile specimen) is subjected to a gradually increasing pull by Universal Testing Machine. 

The stress-strain curve obtained is as shown below.

Stress strain diagram for ductile material

A -Elastic Limit
B - Upper Yield Stress
C - Lower Yield Stress
D -Ultimate Stress
E -Breaking Stress

Point A : Elastic limit point or Proportionality point: Proportional limit is point on the curve up to which the value of stress and strain remains proportional. The stress up to this point can be also be known as proportional limit stress.Hooke’s law is obeyed between the point O to A.

Point B : Upper Yield point:  Yield strength or yield point is the material property defined as the stress at which a material begins to deform plastically.Upper yield point is the point wherein the   stress increases and correspondingly strain also increases.

Point C : Lower Yield point : It is the point where the load remains constant and strain is increased correspondingly.

Point D : Ultimate Stress Point/ Maximum Stress point: Ultimate stress point is the maximum strength that material have to bear stress before breaking. It can also be defined as the ultimate stress corresponding to the peak point on the stress strain graph. 

Point E : Breaking point /Failure point/ Fracture point : Breaking point or breaking stress is point where strength of material breaks.  The stress associates with this point  known as breaking strength or rupture strength.

Stress strain diagram for Brittle material

Point A : Elastic limit point or Proportionality point: Proportional limit is point on the curve up to which the value of stress and strain remains proportional. The stress up to this point can be also be known as proportional limit stress.Hooke’s law is obeyed between the point O to A.

Point B : Breaking point /Failure point/ Fracture point : Breaking point or breaking stress is point where strength of material breaks.  The stress associates with this point  known as breaking strength or rupture strength.