How To Measure Young’s Modulus

Young’s Modulus or modulus of elasticity is a mechanical property of linear elastic solids such as rods, wires, and similar objects. Stress relates to the quantity of force acting per unit region (σ =F/A), and a strain refers to the amount of elongation per length l (ε =dl/l). The stiffness of a solid, or its resistance to elastic deformation, is measured by Young’s modulus (E or Y). It connects strain (proportional deformation) to stress (force per unit area) along an axis or line. 

A solid with a weak Young’s modulus is elastic.

A solid with a strong Young’s modulus is inelastic or rigid.

Young’s modulus or Modulus of elasticity

Young’s modulus describes a material’s relative stiffness, which is assessed by the elastic slope of a stress-strain graph. The ratio of the stress value to the strain value is used to compute it. The modulus of elasticity, often known as Young’s modulus, is the proportionality constant (E).

The term “elastic modulus” refers to a material’s relative stiffness or rigidity; a hard material will have a high elasticity module, whereas a soft material will have a low elasticity module. The elastic modulus is measured in giganewtons per square meter (GN/m2).

Units and Equation

Young’s modulus formula is;

E = σ / ε = (F/A) / (ΔL/L) = FL / AΔL 

Where:

• Young’s modulus (E) is a mathematical term that is commonly stated in Pascal (Pa)
• σ  is the stress in a single direction,
• ε  is the strain,
• F is the compression or extension force.
• The letter A denotes the cross-sectional surface area or the cross-section perpendicular to the applied force.
• The length change is denoted by the letter ΔL. (negative under compression; positive when stretched)
• The original length is L.
• Young’s modulus is measured in megapascals (MPa), Newtons per square millimetre (N/mm²), gigapascals (GPa), or kilonewtons per square millimetre (kN/mm²). The pound per square inch (PSI) or mega PSI is the most common English unit (Mpsi).

The width of a metal rod under tension is slightly reduced when it is elongated. This lateral shrinkage results in a transverse strain equal to the width change divided by the initial width. Poisson’s ratio is the proportion of transverse strain to longitudinal strain. Steels have a Poisson’s ratio of 0.28, while aluminium alloys have a Poisson’s ratio of 0.33. Materials with Poisson’s ratios less than 0.50 have a higher volume during longitudinal tension and a lower volume under longitudinal compression.

Young’s modulus formula tells the elastic properties of the solid experiencing tension or compression only in one direction, such as a metal rod that returns to its original length after becoming stretched or compressed lengthwise. Young’s modulus formula is named after Thomas Young, an eighteenth English physician and physicist.

The Young’s Modulus of Steel

At room temperature, Young’s modulus of steel (also known as elastic modulus of steel) ranges between 190 and 210 GPa, or roughly 27500 and 31200 ksi. Steel’s young modulus measures its stiffness and resistance to tensile loads. Young’s modulus of steel values varies due to the manufacturing process, which considers the number of contaminants in the steel and the category of steel specified. The Gigapascal (GPA), Pascals x 106, is the most common unit of Young’s Modulus. By EN 1993-1-1 Section 3.2.6, the European standard indicates that the young’s modulus of steel is 210,000 MPa.

How can we calculate the steel Modulus of Elasticity?

The young’s modulus of steel is calculated using data from a tensile test performed on such a material specimen. The tensile test places a tensile tension on the material, and also the distortion (strain) is measured when the load is increased. The steel young’s modulus is the gradient of the elastic range component of the stress-strain curve, which is graphically displayed. Young’s modulus of steel can be calculated using Hooke’s law ( E = σ / ε ). This formula has been rearranged into the equation above: (σ = E ε ).

Conclusion

By examining the modulus of elasticity of steel, we can conclude that it is more durable than wood or polystyrene since it has a lower tendency to deform under applied load. Young’s modulus can also calculate how a body will deform when subjected to a given load. 

Another thing to remember is that the lesser the Young’s Modulus of a material, the greater the distortion experienced by the body. In the case of clay and wood, this distortion might vary within a single sample. A part of the clay sample deforms more than another, whereas a steel bar deforms evenly around.