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Tensile Modulus, Elastic Limit, Tensile Strength and Hardness

There are many different types of metal, each with its own set of properties. Hardness, tensile modulus, elastic limit and tensile strength are some of the important properties which needs to be taken into consideration when a metal is selected. Every type of metal has particular properties making it suitable for specific applications. The tensile modulus, elastic limit and tensile strength are all related to the stress-strain curve.

Stress-Strain Curve:

The stress-strain curve is the result of a tensile test which determines the tensile modulus, elastic limit and tensile strength. A test piece is fixed between two clamps, one applies tension on the test piece which will increase the surface tension. Deformation and ultimate fracturing may be caused by the surface tension.

Tensile Modulus:

The tensile modulus (E) indicates how easy the length of the material changes under pressure. The results are shown in the first part of the stress-strain curve. The more horizontal the curve is, the more force is required for stretching the material, indicating that the material is more resistant to change under pressure. The required force, for some materials, will also depend on the direction of the force applied. The tensile modulus is measured in N/mm2.

The following formula can be used to determine the tensile modulus:

  • E = Tensile Modulus
  • F = Force exerted on an object
  • A0 = Surface of the original test piece
  • L = Change in length when force is exerted
  • L0 = Original length of the test piece

Elastic Limit:

The point where material begins to deform under pressure is known as the elastic limit. Deformation of material is undesirable due to the affect it has on the functionality, strength and safety of a construction. The elastic limit (Re) indicates the maximum amount of stress that can be applied without deforming the material. It is not possible to determine the point where deformation starts to occur for certain materials, in which case a 0.2% elastic limit is used to indicate the point at which the material is 0.2% longer than it was before any stress was applied. Re = 0.2%.

Tensile Strength:

Tensile strength (Rm) is the maximum stress which material can withstand. Never to be exceeded.


Hardness measures the resistance of material to change shape. The Brinell, Rockwell and Vickers scales are methods to determine the hardness by measuring the depth of penetration of an indenter on the material surface.

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