What is the Stress-Strain Curve and What is it Used For?

Stress-Strain curve for a ductile material
What does a stress-strain curve show? Plotting the stress-strain curve of a material gives us useful insights into its strength and ductility. This Buzzle post explains what a stress-strain curve actually is, and what all we can learn from it.
The shape of the stress-strain curve depends on:
  • composition of the metal
  • heat treatment it is subjected to
  • whether it was subjected to deformation before
  • temperature
  • nature of the stress that it is subjected to
Stress-Strain Curve
We take a metal rod and apply tensile force to it, i.e., force is applied to the metal rod along a longitudinal direction. We keep increasing the force. We also note the corresponding elongation that has occurred in it.

The stress that a particular metal is subjected to is plotted along the Y-axis, and the corresponding strain that occurs in it is plotted along the X-axis. The curve so obtained is useful in studying the strength of that material.
What We can Learn from It
If you observe a stress-strain curve, you will notice that it is linear up to a point, and then it is curved. There are various points on a stress-strain curve that represent the strength of the material at different stages. We observe the response of the material when stress is zero. Then the stress gradually keeps on increasing to the point that the material breaks.

Following are the points that we can learn from a stress-strain curve plotted for a particular material.
Elastic Limit/Proportional Limit
This is the maximum stress that a material can withstand, such that when it is removed, the material regains its original dimensions and does not suffer any permanent deformation. On the stress-strain graph, the elastic limit is the point up to which the graph is a straight line.
Elastic and Plastic Region
When the stress applied to the metal rod exceeds the elastic limit, there remains a permanent deformation in it. Hence, beyond an elastic limit, the material ceases to be elastic, and it becomes plastic. The region from origin of the graph to the elastic limit is called the elastic region. The region further onward this elastic limit is the plastic region.
Elastic Modulus or Modulus of Elasticity
The slope of the stress-strain graph in the elastic portion is called the modulus of elasticity.

Modulus of elasticity, 'E', is given by the formula: E = stress/strain.

Hooke's Law states that, within an elastic limit, stress is directly proportional to strain.

Stress ∝ strain
σ =kε , where k is the constant of proportionality. Here, it is the modulus of elasticity. In this case, tensile (longitudinal) force is applied to the material. The modulus of tensile elasticity is also called Young's modulus.
Yield Strength
When stress is not directly proportional to strain, i.e., when elongation (strain) increases, such that it is not in proportion with load (stress), then it is the onset of plastic deformation. Yield strength is determined by drawing a line parallel to the elastic portion of the curve, but to the right by an offset of 0.002. The material displays plastic behavior beyond this point.
Yield Point
Yield point is the point on the stress-strain curve where even if the stress is not increased, the material yields, i.e., it shows a considerable elongation.
Ultimate Tensile Strength
The maximum 'y' coordinate in the stress-strain diagram is the ultimate strength of the material.
Rupture Strength
The maximum strength that a material can withstand without rupturing or breaking is called its rupture strength. It is the strength of the material at rupture.
Fracture Strain
Fracture strain is the strain of the material at the time of fracture.
Fracture Point
The point on the stress-strain curve that represents the actual fracture or breakage of the material is referred to as the fracture point.
The resilience of a material is its ability to take in energy without getting deformed permanently.
Modulus of Resilience
When the force or stress on a material is increased from zero to the proportional limit, the work done on a unit volume of the material is the modulus of resilience of that material. Graphically, it is represented by the area under the stress-strain curve from its origin to the elastic limit. Its unit is N.m/m3.
The toughness of a material is its ability to absorb energy without getting broke or ruptured permanently. The area under the stress-strain curve represents the toughness of the material.
Modulus of Toughness
The energy absorbed by a body when the force or strength on it is increased from zero to the point of rupture is called the modulus of toughness of the material. Graphically, it is the area under the graph from the origin to the point of rupture.
Working Stress
The actual stress of a material under a particular load or stress is called the working stress.
Allowable Stress
The maximum stress that a material can carry safely is called allowable stress. Allowable stress does not exceed the proportional limit. Proportional limit is difficult to determine. Hence, allowable stress is calculated by dividing the yield point by the factor of safety.
Factor of Safety
The ratio of yield strength to allowable strength is called the factor of safety.
As we can see from the above sections, the stress-strain curve helps in analyzing various properties of a given material.